Student Quotes (317 quotes)
... an analysis that puts the final link in the chain, for here we see correlations between cytological evidence and genetic results that are so strong and obvious that their validity cannot be denied. This paper has been called a landmark in experimental genetics. It is more than that—it is a cornerstone.
Describing the paper 'A Correlation of Cytological and Genetic Crossings-over in Zea mays' published by Barbara McClintock and her student Harriet Creighton in the Proceedings of the National Academy of Sciences (1931), demonstrating that the exchange of genetic information that occurs during the production of sex cells is accompanied by an exchange of chromosomal material.
Describing the paper 'A Correlation of Cytological and Genetic Crossings-over in Zea mays' published by Barbara McClintock and her student Harriet Creighton in the Proceedings of the National Academy of Sciences (1931), demonstrating that the exchange of genetic information that occurs during the production of sex cells is accompanied by an exchange of chromosomal material.
Classic Papers in Genetics (1959), 156.
... he could have gone around among his students with his penis hanging out, and everyone would have been charmed by his eccentricity.
on J. Robert Oppenheimer, in The Fifties by David Halberstam (1993).
… just as the astronomer, the physicist, the geologist, or other student of objective science looks about in the world of sense, so, not metaphorically speaking but literally, the mind of the mathematician goes forth in the universe of logic in quest of the things that are there; exploring the heights and depths for facts—ideas, classes, relationships, implications, and the rest; observing the minute and elusive with the powerful microscope of his Infinitesimal Analysis; observing the elusive and vast with the limitless telescope of his Calculus of the Infinite; making guesses regarding the order and internal harmony of the data observed and collocated; testing the hypotheses, not merely by the complete induction peculiar to mathematics, but, like his colleagues of the outer world, resorting also to experimental tests and incomplete induction; frequently finding it necessary, in view of unforeseen disclosures, to abandon one hopeful hypothesis or to transform it by retrenchment or by enlargement:—thus, in his own domain, matching, point for point, the processes, methods and experience familiar to the devotee of natural science.
In Lectures on Science, Philosophy and Art (1908), 26
“Normal” science, in Kuhn’s sense, exists. It is the activity of the non-revolutionary, or more precisely, the not-too-critical professional: of the science student who accepts the ruling dogma of the day… in my view the 'normal' scientist, as Kuhn describes him, is a person one ought to be sorry for… He has been taught in a dogmatic spirit: he is a victim of indoctrination… I can only say that I see a very great danger in it and in the possibility of its becoming normal… a danger to science and, indeed, to our civilization. And this shows why I regard Kuhn’s emphasis on the existence of this kind of science as so important.
In Imre Lakatos and A. Musgrave (eds.), 'Normal Science and its Dangers', Criticism and the Growth of Knowledge (1970), 52-53.
[At my secondary school] if you were very bright, you did classics; if you were pretty thick, you did woodwork; and if you were neither of those poles, you did science. The number of kids in my school who did science because they were excited by the notion of science was pretty small. You were allocated to those things, you weren’t asked. This was in the late 1930s/early 1940s … Science was seen as something more remote and less to do with everyday life.
From interview with Brian Cox and Robert Ince, in 'A Life Measured in Heartbeats', New Statesman (21 Dec 2012), 141, No. 5138, 32.
[Certain students] suppose that because science has penetrated the structure of the atom it can solve all the problems of the universe. ... They are known in every ... college as the most insufferable, cocksure know-it-alls. If you want to talk to them about poetry, they are likely to reply that the "emotive response" to poetry is only a conditioned reflex .... If they go on to be professional scientists, their sharp corners are rubbed down, but they undergo no fundamental change. They most decidedly are not set apart from the others by their intellectual integrity and faith, and their patient humility in front of the facts of nature.... They are uneducated, in the fullest sense of the word, and they certainly are no advertisement for the claims of science teachers.
In Science is a Sacred Cow (1950), 18-19.
[De Morgan relates that some person had made up 800 anagrams on his name, of which he had seen about 650. Commenting on these he says:]
Two of these I have joined in the title-page:
[Ut agendo surgamus arguendo gustamus.]
A few of the others are personal remarks.
Great gun! do us a sum!
is a sneer at my pursuit; but,
Go! great sum! [integral of a to the power u to the power n with respect to u] is more dignified. …
Adsum, nugator, suge!
is addressed to a student who continues talking after the lecture has commenced: …
Graduatus sum! nego
applies to one who declined to subscribe for an M.A. degree.
Two of these I have joined in the title-page:
[Ut agendo surgamus arguendo gustamus.]
A few of the others are personal remarks.
Great gun! do us a sum!
is a sneer at my pursuit; but,
Go! great sum! [integral of a to the power u to the power n with respect to u] is more dignified. …
Adsum, nugator, suge!
is addressed to a student who continues talking after the lecture has commenced: …
Graduatus sum! nego
applies to one who declined to subscribe for an M.A. degree.
In Budget of Paradoxes (1872), 82. [The Latin phrases translate as, respectively, “Such action will start arguing with taste”, “Here babbler suck!” and “I graduate! I reject.” —Webmaster]
[Describing a freshman seminar titled “How the Tabby Cat Got Her Stripes or The Silence of the Genes”:] The big idea we start with is: “How is the genome interpreted, and how are stable decisions that affect gene expression inherited from one cell to the next? This is one of the most competitive areas of molecular biology at the moment, and the students are reading papers that in some instances were published this past year. As a consequence, one of the most common answers I have to give to their questions is, “We just don't know.”
As quoted by Kitta MacPherson in 'Exploring Epigenetics: President Shirley Tilghman in the Classroom,'
Princeton University Undergraduate Admission web page accessed 14 Oct 2013.
[E.H.] Moore was presenting a paper on a highly technical topic to a large gathering of faculty and graduate students from all parts of the country. When half way through he discovered what seemed to be an error (though probably no one else in the room observed it). He stopped and re-examined the doubtful step for several minutes and then, convinced of the error, he abruptly dismissed the meeting—to the astonishment of most of the audience. It was an evidence of intellectual courage as well as honesty and doubtless won for him the supreme admiration of every person in the group—an admiration which was in no wise diminished, but rather increased, when at a later meeting he announced that after all he had been able to prove the step to be correct.
In Obituary, 'Eliakim Hastings Moore', The American Mathematical Monthly (Apr 1933), 40, 191.
[Euclid's Elements] has been for nearly twenty-two centuries the encouragement and guide of that scientific thought which is one thing with the progress of man from a worse to a better state. The encouragement; for it contained a body of knowledge that was really known and could be relied on, and that moreover was growing in extent and application. For even at the time this book was written—shortly after the foundation of the Alexandrian Museum—Mathematics was no longer the merely ideal science of the Platonic school, but had started on her career of conquest over the whole world of Phenomena. The guide; for the aim of every scientific student of every subject was to bring his knowledge of that subject into a form as perfect as that which geometry had attained. Far up on the great mountain of Truth, which all the sciences hope to scale, the foremost of that sacred sisterhood was seen, beckoning for the rest to follow her. And hence she was called, in the dialect of the Pythagoreans, ‘the purifier of the reasonable soul.’
From a lecture delivered at the Royal Institution (Mar 1873), collected postumously in W.K. Clifford, edited by Leslie Stephen and Frederick Pollock, Lectures and Essays, (1879), Vol. 1, 296.
[F. Werner, while a student in Princeton,] came to me and expressed his bewilderment with the fact that we make a rather narrow selection when choosing the data on which we test our theories. “How do we know that, if we made a theory which focuses its attention on phenomena we disregard and disregards some of the phenomena now commanding our attention, that we could not build another theory which has little in common with the present one but which, nevertheless, explains just as many phenomena as the present theory?” It has to be admitted that we have no definite evidence that there is no such theory.
In 'The Unreasonable Effectiveness of Mathematics in the Natural Sciences,' Communications in Pure and Applied Mathematics (Feb 1960), 13, No. 1 (February 1960). Collected in Eugene Paul Wigner, A.S. Wightman (ed.), Jagdish Mehra (ed.), The Collected Works of Eugene Paul Wigner (1955), Vol. 6, 535.
[Florence Nightingale] was a great administrator, and to reach excellence here is impossible without being an ardent student of statistics. Florence Nightingale has been rightly termed the “Passionate Statistician.” Her statistics were more than a study, they were indeed her religion. For her, Quetelet was the hero as scientist, and the presentation copy of his Physique Sociale is annotated by her on every page. Florence Nightingale believed—and in all the actions of her life acted upon that belief—that the administrator could only be successful if he were guided by statistical knowledge. The legislator—to say nothing of the politician—too often failed for want of this knowledge. Nay, she went further: she held that the universe—including human communities—was evolving in accordance with a divine plan; that it was man's business to endeavour to understand this plan and guide his actions in sympathy with it. But to understand God's thoughts, she held we must study statistics, for these are the measure of his purpose. Thus the study of statistics was for her a religious duty.
In Karl Pearson, The Life, Letters and Labours of Francis Galton (1924), Vol. 2, 414-5.
[Simplicio] is much puzzled and perplexed. I think I hear him say, 'To whom then should we repair for the decision of our controversies if Aristotle were removed from the choir? What other author should we follow in the schools, academies, and studies? What philosopher has written all the divisions of Natural Philosophy, and so methodically, without omitting as much as a single conclusion? Shall we then overthrow the building under which so many voyagers find shelter? Shall we destroy that sanctuary, that Prytaneum, where so many students find commodious harbour; where without exposing himself to the injuries of the air, with only the turning over of a few leaves, one may learn all the secrets of Nature.'
Dialogue on the Great World Systems (1632). Revised and Annotated by Giorgio De Santillana (1953), 66.
[Student:} I only use my math book on special equations.
From movie Rock 'n' Roll High School (1979). Writers, Richard Whitley, Russ Dvonch and Joseph McBride. In Larry Langman and Paul Gold, Comedy Quotes from the Movies (2001), 359.
[The error in the teaching of mathematics is that] mathematics is expected either to be immediately attractive to students on its own merits or to be accepted by students solely on the basis of the teacher’s assurance that it will be helpful in later life. [And yet,] mathematlcs is the key to understanding and mastering our physical, social and biological worlds.
In editorial in Focus, a Journal of the Mathematical Association of America (1986), quoted in obituary by Eric Pace, New York Times (11 Jun 1992).
[To one of his students he saw in a school dramatic production:] I’ve always been proud that Course X leaves little time for outside activities. You have proved me wrong so far and I’m glad you have. But don’t push your luck too far!
As quoted in A Dollar to a Doughnut: The Doc Lewis Story (1953), 49, which was a privately printed collection of anecdotes published by former students upon his retirement. Note that “X” was the actual designation of his chemical engineering course at MIT. The boy was a Course X student who had played the leading “lady” in the previous MIT Tech Show. The anecdote continues: “A word to the wise was sufficient—the leading lady that year was not from Course X.”
[William Gull] sought to teach his students not to think they could cure disease. “The best of all remedies,” he would say, “is a warm bed.” “ I can tell you something of how you get ill, but I cannot tell you how you get well.” “ Healing is accomplished ‘By an operation more divine Than tongue or pen can give expression to.’” “Remedies act best when there is a tendency to get well.”
Stated in Sir William Withey Gull and Theodore Dyke Acland (ed.), A Collection of the Published Writings of William Withey Gull (1896), xxvi.
[Elementary student, laying a cocoon on the teacher's desk:] That is serendipity. The caterpillar thinks it is dying but it is really being born.
As quoted, without citation, by Marcus Bach, 'Serendiptiy in the Business World', in The Rotarian (Oct 1981), 139, No. 4, 40.
[Recalling Professor Ira Remsen's remarks (1895) to a group of his graduate students about to go out with their degrees into the world beyond the university:]
He talked to us for an hour on what was ahead of us; cautioned us against giving up the desire to push ahead by continued study and work. He warned us against allowing our present accomplishments to be the high spot in our lives. He urged us not to wait for a brilliant idea before beginning independent research, and emphasized the fact the Lavoisier's first contribution to chemistry was the analysis of a sample of gypsum. He told us that the fields in which the great masters had worked were still fruitful; the ground had only been scratched and the gleaner could be sure of ample reward.
He talked to us for an hour on what was ahead of us; cautioned us against giving up the desire to push ahead by continued study and work. He warned us against allowing our present accomplishments to be the high spot in our lives. He urged us not to wait for a brilliant idea before beginning independent research, and emphasized the fact the Lavoisier's first contribution to chemistry was the analysis of a sample of gypsum. He told us that the fields in which the great masters had worked were still fruitful; the ground had only been scratched and the gleaner could be sure of ample reward.
Quoted in Frederick Hutton Getman, The Life of Ira Remsen (1980), 73.
[Responding to a student whose friend asked about studying Agricultural Chemistry at Johns Hopkins:]
We would be glad to have your friend come here to study, but tell him that we teach Chemistry here and not Agricultural Chemistry, nor any other special kind of chemistry. ... We teach Chemistry.
We would be glad to have your friend come here to study, but tell him that we teach Chemistry here and not Agricultural Chemistry, nor any other special kind of chemistry. ... We teach Chemistry.
In Frederick Hutton Getman, The Life of Ira Remsen, 71.
[Student describing Niels Bohr's main gift, the ability to synthesize:] Like Socrates, he wages a fight to bring harmony out of chaos and diversity.
Quoted in Bill Becker, 'Pioneer of the Atom', New York Times Sunday Magazine (20 Oct 1957), 52.
[Students or readers about teachers or authors.] They will listen with both ears to what is said by the men just a step or two ahead of them, who stand nearest to them, and within arm’s reach. A guide ceases to be of any use when he strides so far ahead as to be hidden by the curvature of the earth.
From Lecture (5 Apr 1917) at Hackley School, Tarrytown, N.Y., 'Choosing Books', collected in Canadian Stories (1918), 150.
A famous anecdote concerning Cuvier involves the tale of his visitation from the devil—only it was not the devil but one of his students dressed up with horns on his head and shoes shaped like cloven hooves. This frightening apparition burst into Cuvier’s bedroom when he was fast asleep and claimed:
“Wake up thou man of catastrophes. I am the Devil. I have come to devour you!”
Cuvier studied the apparition carefully and critically said,
“I doubt whether you can. You have horns and hooves. You eat only plants.”
“Wake up thou man of catastrophes. I am the Devil. I have come to devour you!”
Cuvier studied the apparition carefully and critically said,
“I doubt whether you can. You have horns and hooves. You eat only plants.”
Quoted in Glyn Daniel, The Idea of Pre-History (1962), 34.
Nun wie gehts?
How goes it?
[Werner’s perennial salutation to research students, hence his nickname, Professor Nunwiegehts.]
How goes it?
[Werner’s perennial salutation to research students, hence his nickname, Professor Nunwiegehts.]
Quoted in Ralph Oesper, The Human Side of Scientists (1975), 188.
To Wheeler's comment, If you haven't found something strange during the day, it hasn't been much of a day, a student responded, I can't believe that space is that crummy. Wheeler replied: To disagree leads to study, to study leads to understanding, to understand is to appreciate, to appreciate is to love. So maybe I'll end up loving your theory.
Quoted in Charles Birch, Biology and the Riddle of Life (1999), 10.
A century ago astronomers, geologists, chemists, physicists, each had an island of his own, separate and distinct from that of every other student of Nature; the whole field of research was then an archipelago of unconnected units. To-day all the provinces of study have risen together to form a continent without either a ferry or a bridge.
From chapter 'Jottings from a Note-book', in Canadian Stories (1918), 182-183.
A chemical compound once formed would persist for ever, if no alteration took place in surrounding conditions. But to the student of Life the aspect of nature is reversed. Here, incessant, and, so far as we know, spontaneous change is the rule, rest the exception—the anomaly to be accounted for. Living things have no inertia and tend to no equilibrium.
From Address (22 Jul 1854) delivered at St. Martin’s Hall, published as a pamphlet (1854), 7, and collected in 'Educational Value of Natural History Sciences', Lay Sermons, Addresses, and Reviews (1870), 75.
A favourite piece of advice [by William Gull] to his students was, “never disregard what a mother says;” he knew the mother’s instinct, and her perception, quickened by love, would make her a keen observer.
Stated in Sir William Withey Gull and Theodore Dyke Acland (ed.), A Collection of the Published Writings of William Withey Gull (1896), xxiii.
A good theoretical physicist today might find it useful to have a wide range of physical viewpoints and mathematical expressions of the same theory (for example, of quantum electrodynamics) available to him. This may be asking too much of one man. Then new students should as a class have this. If every individual student follows the same current fashion in expressing and thinking about electrodynamics or field theory, then the variety of hypotheses being generated to understand strong interactions, say, is limited. Perhaps rightly so, for possibly the chance is high that the truth lies in the fashionable direction. But, on the off-chance that it is in another direction—a direction obvious from an unfashionable view of field theory—who will find it?
In his Nobel Prize Lecture (11 Dec 1965), 'The Development of the Space-Time View of Quantum Electrodynamics'. Collected in Stig Lundqvist, Nobel Lectures: Physics, 1963-1970 (1998), 177.
A lecture is a process by which the notes of the professor become the notes of the student without passing through the minds of either.
Quoted, without source, in Des MacHale, Wit (1999, 2003), 30.
A parable: A man was examining the construction of a cathedral. He asked a stone mason what he was doing chipping the stones, and the mason replied, “I am making stones.” He asked a stone carver what he was doing. “I am carving a gargoyle.” And so it went, each person said in detail what they were doing. Finally he came to an old woman who was sweeping the ground. She said. “I am helping build a cathedral.”
...Most of the time each person is immersed in the details of one special part of the whole and does not think of how what they are doing relates to the larger picture.
[For example, in education, a teacher might say in the next class he was going to “explain Young's modulus and how to measure it,” rather than, “I am going to educate the students and prepare them for their future careers.”]
...Most of the time each person is immersed in the details of one special part of the whole and does not think of how what they are doing relates to the larger picture.
[For example, in education, a teacher might say in the next class he was going to “explain Young's modulus and how to measure it,” rather than, “I am going to educate the students and prepare them for their future careers.”]
In The Art of Doing Science and Engineering: Learning to Learn (1975, 2005), 195.
A professor … may be to produce a perfect mathematical work of art, having every axiom stated, every conclusion drawn with flawless logic, the whole syllabus covered. This sounds excellent, but in practice the result is often that the class does not have the faintest idea of what is going on. … The framework is lacking; students do not know where the subject fits in, and this has a paralyzing effect on the mind.
In A Concrete Approach to Abstract Algebra (1959), 1-2.
A professor of experimental science must sometimes grab at any, even senseless, means to impress scientific laws [on students]. Sometimes, one can only capture what is most important about beautiful drastic experiments with a joke. Nothing conveys it better!
Given as “fashioned from Boltzmann’s notes for his lecture on natural philosophy on November 3, 1903” and translated in John Blackmore (ed.), Ludwig Boltzmann: His Later Life and Philosophy, 1900-1906 (1995), 133. Blackmore indicates that since Boltzmann spoke freely, this may not be verbatim for what he actually said, because he did not read his lectures from his notes. However, it does “rather accurately represent his thinking” at the time he wrote his lecture. His Lectures on Natural Philosophy (1903-1906) were reconstructed from Boltzmann’s shorthand notes by Ilse M. Fasol-Boltzmann (ed.), in Ludwig Boltzmann Principien der Naturfolosofti (1990).
A student who wishes now-a-days to study geometry by dividing it sharply from analysis, without taking account of the progress which the latter has made and is making, that student no matter how great his genius, will never be a whole geometer. He will not possess those powerful instruments of research which modern analysis puts into the hands of modern geometry. He will remain ignorant of many geometrical results which are to be found, perhaps implicitly, in the writings of the analyst. And not only will he be unable to use them in his own researches, but he will probably toil to discover them himself, and, as happens very often, he will publish them as new, when really he has only rediscovered them.
From 'On Some Recent Tendencies in Geometrical Investigations', Rivista di Matematica (1891), 43. In Bulletin American Mathematical Society (1904), 443.
A taxonomy of abilities, like a taxonomy anywhere else in science, is apt to strike a certain type of impatient student as a gratuitous orgy of pedantry. Doubtless, compulsions to intellectual tidiness express themselves prematurely at times, and excessively at others, but a good descriptive taxonomy, as Darwin found in developing his theory, and as Newton found in the work of Kepler, is the mother of laws and theories.
From Intelligence: Its Structure, Growth and Action: Its Structure, Growth and Action (1987), 61.
A teacher … is never a giver of "truth”; he is a guide, a pointer to the truth that the student must discover for himself. … For example, a skillful teacher might spur his student’s growth by confronting him with certain frustrations. A good teacher is a catalyst.
In 'Liberate Yourself From Classical Karate', Black Belt (Sep 1971), 27.
A teacher of mathematics has a great opportunity. If he fills his allotted time with drilling his students in routine operations he kills their interest, hampers their intellectual development, and misuses his opportunity. But if he challenges the curiosity of his students by setting them problems proportionate to their knowledge, and helps them to solve their problems with stimulating questions, he may give them a taste for, and some means of, independent thinking.
In How to Solve It (1948), Preface.
A very sincere and serious freshman student came to my office with a question that had clearly been troubling him deeply. He said to me, ‘I am a devout Christian and have never had any reason to doubt evolution, an idea that seems both exciting and well documented. But my roommate, a proselytizing evangelical, has been insisting with enormous vigor that I cannot be both a real Christian and an evolutionist. So tell me, can a person believe both in God and in evolution?’ Again, I gulped hard, did my intellectual duty, a nd reassured him that evolution was both true and entirely compatible with Christian belief –a position that I hold sincerely, but still an odd situation for a Jewish agnostic.
…...
A wonderful exhilaration comes from holding in the mind the deepest questions we can ask. Such questions animate all scientists. Many students of science were first attracted to the field as children by popular accounts of important unsolved problems. They have been waiting ever since to begin working on a mystery. [With co-author Arthur Zajonc]
In George Greenstein and Arthur Zajonc, The Quantum Challenge: Modern Research on the Foundations of Quantum Mechanics (2006), xii.
Although my Aachen colleagues and students at first regarded the “pure mathematician” with suspicion, I soon had the satisfaction of being accepted a useful member not merely in teaching but also engineering practice; thus I was requested to render expert opinions and to participate in the Ingenieurverein [engineering association].
As quoted in Paul Forman and Armin Hermann, 'Sommerfeld, Arnold (Johannes Wilhelm)', Biography in Dictionary of Scientific Biography (1975), Vol. 12, 527. Cited from 'Autobiographische Skizze', Gesammelte Schriften, Vol 4, 673–682.
An author has always great difficulty in avoiding unnecessary and tedious detail on the one hand; while, on the other, he must notice such a number of facts as may convince a student, that he is not wandering in a wilderness of crude hypotheses or unsupported assumptions.
In A Geological Manual (1832), Preface, iii.
And science, we should insist, better than other discipline, can hold up to its students and followers an ideal of patient devotion to the search to objective truth, with vision unclouded by personal or political motive, not tolerating any lapse from precision or neglect of any anomaly, fearing only prejudice and preconception, accepting nature’s answers humbly and with courage, and giving them to the world with an unflinching fidelity. The world cannot afford to lose such a contribution to the moral framework of its civilisation.
Concluding statements of Pilgrim Trust Lecture (22 Oct 1946) delivered at National Academy of Science Washington, DC. Published in 'The Freedom of Science', Proceedings of the American Philosophical Society (25 Feb 1947), 91, No. 1, 72.
As a graduate student at Columbia University, I remember the a priori derision of my distinguished stratigraphy professor toward a visiting Australian drifter ... Today my own students would dismiss with even more derision anyone who denied the evident truth of continental drift–a prophetic madman is at least amusing; a superannuated fuddy-duddy is merely pitiful.
…...
As a second year high school chemistry student, I still have a vivid memory of my excitement when I first saw a chart of the periodic table of elements. The order in the universe seemed miraculous, and I wanted to study and learn as much as possible about the natural sciences.
In Tore Frängsmyr and Jan E. Lindsten (eds.), Nobel Lectures: Physiology Or Medicine: 1981-1990 (1993), 555.
As an exercise of the reasoning faculty, pure mathematics is an admirable exercise, because it consists of reasoning alone, and does not encumber the student with an exercise of judgment: and it is well to begin with learning one thing at a time, and to defer a combination of mental exercises to a later period.
In Annotations to Bacon’s Essays (1873), Essay 1, 493.
As long as museums and universities send out expeditions to bring to light new forms of living and extinct animals and new data illustrating the interrelations of organisms and their environments, as long as anatomists desire a broad comparative basis human for anatomy, as long as even a few students feel a strong curiosity to learn about the course of evolution and relationships of animals, the old problems of taxonomy, phylogeny and evolution will gradually reassert themselves even in competition with brilliant and highly fruitful laboratory studies in cytology, genetics and physiological chemistry.
'Genetics Versus Paleontology', The American Naturalist, 1917, 51, 623.
Attaching significance to invariants is an effort to recognize what, because of its form or colour or meaning or otherwise, is important or significant in what is only trivial or ephemeral. A simple instance of failing in this is provided by the poll-man at Cambridge, who learned perfectly how to factorize a²-b² but was floored because the examiner unkindly asked for the factors of p²–q².
In 'Recent Developments in Invariant Theory', The Mathematical Gazette (Dec 1926), 13, No. 185, 217. [Note: A poll-man is a student who takes the ordinary university degree, without honours. -Webmaster]
Basic research at universities comes in two varieties: research that requires big bucks and research that requires small bucks. Big bucks research is much like government research and in fact usually is government research but done for the government under contract. Like other government research, big bucks academic research is done to understand the nature and structure of the universe or to understand life, which really means that it is either for blowing up the world or extending life, whichever comes first. Again, that's the government's motivation. The universities' motivation for conducting big bucks research is to bring money in to support professors and graduate students and to wax the floors of ivy-covered buildings. While we think they are busy teaching and learning, these folks are mainly doing big bucks basic research for a living, all the while priding themselves on their terrific summer vacations and lack of a dress code.
Smalls bucks research is the sort of thing that requires paper and pencil, and maybe a blackboard, and is aimed primarily at increasing knowledge in areas of study that don't usually attract big bucks - that is, areas that don't extend life or end it, or both. History, political science, and romance languages are typically small bucks areas of basic research. The real purpose of small bucks research to the universities is to provide a means of deciding, by the quality of their small bucks research, which professors in these areas should get tenure.
Smalls bucks research is the sort of thing that requires paper and pencil, and maybe a blackboard, and is aimed primarily at increasing knowledge in areas of study that don't usually attract big bucks - that is, areas that don't extend life or end it, or both. History, political science, and romance languages are typically small bucks areas of basic research. The real purpose of small bucks research to the universities is to provide a means of deciding, by the quality of their small bucks research, which professors in these areas should get tenure.
Accidental Empires (1992), 78.
Be a physical chemist, an organic chemist, an analytical chemist, if you will; but above all be a Chemist.
[Admonishing his students to avoid over-specialization.]
[Admonishing his students to avoid over-specialization.]
F. H. Getman, The Life of Ira Remsen (1940), 71.
Berzelius' symbols are horrifying. A young student in chemistry might as soon learn Hebrew as make himself acquainted with them... They appear to me equally to perplex the adepts in science, to discourage the learner, as well as to cloud the beauty and simplicity of the atomic theory.
Quoted in H. E. Roscoe, 'Presidential Address', Reports of the British Association for the Advancement of Science, 57th report, 1887, 7.
Besides accustoming the student to demand, complete proof, and to know when he has not obtained it, mathematical studies are of immense benefit to his education by habituating him to precision. It is one of the peculiar excellencies of mathematical discipline, that the mathematician is never satisfied with à peu près. He requires the exact truth. Hardly any of the non-mathematical sciences, except chemistry, has this advantage. One of the commonest modes of loose thought, and sources of error both in opinion and in practice, is to overlook the importance of quantities. Mathematicians and chemists are taught by the whole course of their studies, that the most fundamental difference of quality depends on some very slight difference in proportional quantity; and that from the qualities of the influencing elements, without careful attention to their quantities, false expectation would constantly be formed as to the very nature and essential character of the result produced.
In An Examination of Sir William Hamilton’s Philosophy (1878), 611. [The French phrase, à peu près means “approximately”. —Webmaster]
Biological disciplines tend to guide research into certain channels. One consequence is that disciplines are apt to become parochial, or at least to develop blind spots, for example, to treat some questions as “interesting” and to dismiss others as “uninteresting.” As a consequence, readily accessible but unworked areas of genuine biological interest often lie in plain sight but untouched within one discipline while being heavily worked in another. For example, historically insect physiologists have paid relatively little attention to the behavioral and physiological control of body temperature and its energetic and ecological consequences, whereas many students of the comparative physiology of terrestrial vertebrates have been virtually fixated on that topic. For the past 10 years, several of my students and I have exploited this situation by taking the standard questions and techniques from comparative vertebrate physiology and applying them to insects. It is surprising that this pattern of innovation is not more deliberately employed.
In 'Scientific innovation and creativity: a zoologist’s point of view', American Zoologist (1982), 22, 233.
Biology as a discipline would benefit enormously if we could bring together the scientists working at the opposite ends of the biological spectrum. Students of organisms who know natural history have abundant questions to offer the students of molecules and cells. And molecular and cellular biologists with their armory of techniques and special insights have much to offer students of organisms and ecology.
In 'The role of natural history in contemporary biology', BioScience (1986), 36, 328-329.
But for the persistence of a student of this university in urging upon me his desire to study with me the modern algebra I should never have been led into this investigation; and the new facts and principles which I have discovered in regard to it (important facts, I believe), would, so far as I am concerned, have remained still hidden in the womb of time. In vain I represented to this inquisitive student that he would do better to take up some other subject lying less off the beaten track of study, such as the higher parts of the calculus or elliptic functions, or the theory of substitutions, or I wot not what besides. He stuck with perfect respectfulness, but with invincible pertinacity, to his point. He would have the new algebra (Heaven knows where he had heard about it, for it is almost unknown in this continent), that or nothing. I was obliged to yield, and what was the consequence? In trying to throw light upon an obscure explanation in our text-book, my brain took fire, I plunged with re-quickened zeal into a subject which I had for years abandoned, and found food for thoughts which have engaged my attention for a considerable time past, and will probably occupy all my powers of contemplation advantageously for several months to come.
In Johns Hopkins Commemoration Day Address, Collected Mathematical Papers, Vol. 3, 76.
But it is precisely mathematics, and the pure science generally, from which the general educated public and independent students have been debarred, and into which they have only rarely attained more than a very meagre insight. The reason of this is twofold. In the first place, the ascendant and consecutive character of mathematical knowledge renders its results absolutely insusceptible of presentation to persons who are unacquainted with what has gone before, and so necessitates on the part of its devotees a thorough and patient exploration of the field from the very beginning, as distinguished from those sciences which may, so to speak, be begun at the end, and which are consequently cultivated with the greatest zeal. The second reason is that, partly through the exigencies of academic instruction, but mainly through the martinet traditions of antiquity and the influence of mediaeval logic-mongers, the great bulk of the elementary text-books of mathematics have unconsciously assumed a very repellant form,—something similar to what is termed in the theory of protective mimicry in biology “the terrifying form.” And it is mainly to this formidableness and touch-me-not character of exterior, concealing withal a harmless body, that the undue neglect of typical mathematical studies is to be attributed.
In Editor’s Preface to Augustus De Morgan and Thomas J. McCormack (ed.), Elementary Illustrations of the Differential and Integral Calculus (1899), v.
By the year 2070 we cannot say, or it would be imbecile to do so, that any man alive could understand Shakespearean experience better than Shakespeare, whereas any decent eighteen-year-old student of physics will know more physics than Newton.
'The Case of Leavis and the Serious Case’, Times Literary Supplement (9 Jul 1970), 737-740. Collected in Public Affairs (1971), 95.
Cell and tissue, shell and bone, leaf and flower, are so many portions of matter, and it is in obedience to the laws of physics that their particles have been moved, moulded and confirmed. They are no exception to the rule that God always geometrizes. Their problems of form are in the first instance mathematical problems, their problems of growth are essentially physical problems, and the morphologist is, ipso facto, a student of physical science.
On Growth and Form (1917), 7-8.
Certain students of genetics inferred that the Mendelian units responsible for the selected character were genes producing only a single effect. This was careless logic. It took a good deal of hammering to get rid of this erroneous idea. As facts accumulated it became evident that each gene produces not a single effect, but in some cases a multitude of effects on the characters of the individual. It is true that in most genetic work only one of these character-effects is selected for study—the one that is most sharply defined and separable from its contrasted character—but in most cases minor differences also are recognizable that are just as much the product of the same gene as is the major effect.
'The Relation of Genetics to Physiology and Medicine', Nobel Lecture (4 Jun 1934). In Nobel Lectures, Physiology or Medicine 1922-1941 (1965), 317.
Connected by innumerable ties with abstract science, Physiology is yet in the most intimate relation with humanity; and by teaching us that law and order, and a definite scheme of development, regulate even the strangest and wildest manifestations of individual life, she prepares the student to look for a goal even amidst the erratic wanderings of mankind, and to believe that history offers something more than an entertaining chaos—a journal of a toilsome, tragi-comic march nowither.
In 'Educational Value of Natural History Sciences', Lay Sermons, Addresses, and Reviews (1870), 97.
Consider the plight of a scientist of my age. I graduated from the University of California at Berkeley in 1940. In the 41 years since then the amount of biological information has increased 16 fold; during these 4 decades my capacity to absorb new information has declined at an accelerating rate and now is at least 50% less than when I was a graduate student. If one defines ignorance as the ratio of what is available to be known to what is known, there seems no alternative to the conclusion that my ignorance is at least 25 times as extensive as it was when I got my bachelor’s degree. Although I am sure that my unfortunate condition comes as no surprise to my students and younger colleagues, I personally find it somewhat depressing. My depression is tempered, however, by the fact that all biologists, young or old, developing or senescing, face the same melancholy situation because of an interlocking set of circumstances.
In 'Scientific innovation and creativity: a zoologist’s point of view', American Zoologist (1982), 22, 228.
Considerable obstacles generally present themselves to the beginner, in studying the elements of Solid Geometry, from the practice which has hitherto uniformly prevailed in this country, of never submitting to the eye of the student, the figures on whose properties he is reasoning, but of drawing perspective representations of them upon a plane. ...I hope that I shall never be obliged to have recourse to a perspective drawing of any figure whose parts are not in the same plane.
Quoted in Adrian Rice, 'What Makes a Great Mathematics Teacher?' The American Mathematical Monthly, (June-July 1999), 540.
Doubly galling was the fact that at the same time my roommate was taking a history course … filled with excitement over a class discussion. … I was busy with Ampere’s law. We never had any fascinating class discussions about this law. No one, teacher or student, ever asked me what I thought about it.
In Understanding the Universe: An Inquiry Approach to Astronomy and the Nature of Scientific Research (2013), ix.
During the school period the student has been mentally bending over his desk; at the University he should stand up and look around. For this reason it is fatal if the first year at the University be frittered away in going over the old work in the old spirit. At school the boy painfully rises from the particular towards glimpses at general ideas; at the University he should start from general ideas and study their applications to concrete cases.
In 'The Rhythm of Education', The Aims of Education and Other Essays (1929), 26.
Einstein, my upset stomach hates your theory [of General Relativity]—it almost hates you yourself! How am I to provide for my students? What am I to answer to the philosophers?!!
Letter to Albert Einstein, 20 Nov 1919. In Martin J. Klein, Paul Ehrenfest: The Making of a Theoretical Physicist (1970), Vol. 1, 315.
Euclidean mathematics assumes the completeness and invariability of mathematical forms; these forms it describes with appropriate accuracy and enumerates their inherent and related properties with perfect clearness, order, and completeness, that is, Euclidean mathematics operates on forms after the manner that anatomy operates on the dead body and its members. On the other hand, the mathematics of variable magnitudes—function theory or analysis—considers mathematical forms in their genesis. By writing the equation of the parabola, we express its law of generation, the law according to which the variable point moves. The path, produced before the eyes of the student by a point moving in accordance to this law, is the parabola.
If, then, Euclidean mathematics treats space and number forms after the manner in which anatomy treats the dead body, modern mathematics deals, as it were, with the living body, with growing and changing forms, and thus furnishes an insight, not only into nature as she is and appears, but also into nature as she generates and creates,—reveals her transition steps and in so doing creates a mind for and understanding of the laws of becoming. Thus modern mathematics bears the same relation to Euclidean mathematics that physiology or biology … bears to anatomy.
If, then, Euclidean mathematics treats space and number forms after the manner in which anatomy treats the dead body, modern mathematics deals, as it were, with the living body, with growing and changing forms, and thus furnishes an insight, not only into nature as she is and appears, but also into nature as she generates and creates,—reveals her transition steps and in so doing creates a mind for and understanding of the laws of becoming. Thus modern mathematics bears the same relation to Euclidean mathematics that physiology or biology … bears to anatomy.
In Die Mathematik die Fackelträgerin einer neuen Zeit (1889), 38. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 112-113.
Even fairly good students, when they have obtained the solution of the problem and written down neatly the argument, shut their books and look for something else. Doing so, they miss an important and instructive phase of the work. ... A good teacher should understand and impress on his students the view that no problem whatever is completely exhausted.
In How to Solve It: A New Aspect of Mathematical Method (2004), 14.
Even today I still get letters from young students here and there who say, Why are you people trying to program intelligence? Why don’t you try to find a way to build a nervous system that will just spontaneously create it? Finally I decided that this was either a bad idea or else it would take thousands or millions of neurons to make it work and I couldn’t afford to try to build a machine like that.
As quoted in Jeremy Bernstein, 'A.I.', The New Yorker (14 Dec 1981), 57, 70.
Every schoolmaster knows that for every one person who wants to teach there are approximately 30 who don’t want to learn – much.
Found in a book, on a table at a campsite on Taveuni Island in Fiji. As recorded by Peter, in outdoor travel blog, 'Leaving the Teaching Profession', Atlas & Boots (13 Sep 2014).
Every sentence I utter must be understood not as an affirmation but as a question.
[A caution he gives his students, to be wary of dogmatism.]
[A caution he gives his students, to be wary of dogmatism.]
In Bill Becker, 'Pioneer of the Atom', New York Times Sunday Magazine (20 Oct 1957), 52.
Every student who enters upon a scientific pursuit, especially if at a somewhat advanced period of life, will find not only that he has much to learn, but much also to unlearn.
Outlines of Astronomy (1871), 11th edn., 1.
Evolutionists sometimes take as haughty an attitude toward the next level up the conventional ladder of disciplines: the human sciences. They decry the supposed atheoretical particularism of their anthropological colleagues and argue that all would be well if only the students of humanity regarded their subject as yet another animal and therefore yielded explanatory control to evolutionary biologists.
From book review, 'The Ghost of Protagoras', The New York Review of Books (22 Jan 1981), 27, No. 21 & 22. Collected in An Urchin in the Storm: Essays about Books and Ideas (1987, 2010), 64. The article reviewed two books: John Tyler Bonner, The Evolution of Culture and Peter J. Wilson, The Promising Primate.
First, as concerns the success of teaching mathematics. No instruction in the high schools is as difficult as that of mathematics, since the large majority of students are at first decidedly disinclined to be harnessed into the rigid framework of logical conclusions. The interest of young people is won much more easily, if sense-objects are made the starting point and the transition to abstract formulation is brought about gradually. For this reason it is psychologically quite correct to follow this course.
Not less to be recommended is this course if we inquire into the essential purpose of mathematical instruction. Formerly it was too exclusively held that this purpose is to sharpen the understanding. Surely another important end is to implant in the student the conviction that correct thinking based on true premises secures mastery over the outer world. To accomplish this the outer world must receive its share of attention from the very beginning.
Doubtless this is true but there is a danger which needs pointing out. It is as in the case of language teaching where the modern tendency is to secure in addition to grammar also an understanding of the authors. The danger lies in grammar being completely set aside leaving the subject without its indispensable solid basis. Just so in Teaching of Mathematics it is possible to accumulate interesting applications to such an extent as to stunt the essential logical development. This should in no wise be permitted, for thus the kernel of the whole matter is lost. Therefore: We do want throughout a quickening of mathematical instruction by the introduction of applications, but we do not want that the pendulum, which in former decades may have inclined too much toward the abstract side, should now swing to the other extreme; we would rather pursue the proper middle course.
Not less to be recommended is this course if we inquire into the essential purpose of mathematical instruction. Formerly it was too exclusively held that this purpose is to sharpen the understanding. Surely another important end is to implant in the student the conviction that correct thinking based on true premises secures mastery over the outer world. To accomplish this the outer world must receive its share of attention from the very beginning.
Doubtless this is true but there is a danger which needs pointing out. It is as in the case of language teaching where the modern tendency is to secure in addition to grammar also an understanding of the authors. The danger lies in grammar being completely set aside leaving the subject without its indispensable solid basis. Just so in Teaching of Mathematics it is possible to accumulate interesting applications to such an extent as to stunt the essential logical development. This should in no wise be permitted, for thus the kernel of the whole matter is lost. Therefore: We do want throughout a quickening of mathematical instruction by the introduction of applications, but we do not want that the pendulum, which in former decades may have inclined too much toward the abstract side, should now swing to the other extreme; we would rather pursue the proper middle course.
In Ueber den Mathematischen Unterricht an den hoheren Schulen; Jahresbericht der Deutschen Mathematiker Vereinigung, Bd. 11, 131.
Five centuries ago the printing press sparked a radical reshaping of the nature of education. By bringing a master’s words to those who could not hear a master’s voice, the technology of printing dissolved the notion that education must be reserved for those with the means to hire personal tutors. Today we are approaching a new technological revolution, one whose impact on education may be as far-reaching as that of the printing press: the emergence of powerful computers that are sufficiently inexpensive to be used by students for learning, play and exploration. It is our hope that these powerful but simple tools for creating and exploring richly interactive environments will dissolve the barriers to the production of knowledge as the printing press dissolved the barriers to its transmission.
As co-author with A.A. diSessa, from 'Preface', Turtle Geometry: The Computer as a Medium for Exploring Mathematics (1986), xiii.
FORTRAN —’the infantile disorder’—, by now nearly 20 years old, is hopelessly inadequate for whatever computer application you have in mind today: it is now too clumsy, too risky, and too expensive to use. PL/I —’the fatal disease’— belongs more to the problem set than to the solution set. It is practically impossible to teach good programming to students that have had a prior exposure to BASIC: as potential programmers they are mentally mutilated beyond hope of regeneration. The use of COBOL cripples the mind; its teaching should, therefore, be regarded as a criminal offence. APL is a mistake, carried through to perfection. It is the language of the future for the programming techniques of the past: it creates a new generation of coding bums.
…...
Four college students taking a class together, had done so well through the semester, and each had an “A”. They were so confident, the weekend before finals, they went out partying with friends. Consequently, on Monday, they overslept and missed the final. They explained to the professor that they had gone to a remote mountain cabin for the weekend to study, but, unfortunately, they had a flat tire on the way back, didn’t have a spare, and couldn’t get help for a long time. As a result, they missed the final. The professor kindly agreed they could make up the final the following day. When they arrived the next morning, he placed them each in separate rooms, handed each one a test booklet, and told them to begin. The the first problem was simple, worth 5 points. Turning the page they found the next question, written: “(For 95 points): Which tire?”
From him [Wilard Bennett] I learned how different a working laboratory is from a student laboratory. The answers are not known!
[While an undergraduate, doing experimental measurements in the laboratory of his professor, at Ohio State University.]
[While an undergraduate, doing experimental measurements in the laboratory of his professor, at Ohio State University.]
From autobiography on Nobel Prize website.
From the physician, as emphatically the student of Nature, is expected not only an inquiry into cause, but an investigation of the whole empire of Nature and a determination of the applicability of every species of knowledge to the improvement of his art.
In 'An Inquiry, Analogical and Experimental, into the Different Electrical conditions of Arterial and Venous Blood', New Orleans Medical and Surgical Journal (1853-4), 10, 584-602 & 738-757. As cited in George B. Roth, 'Dr. John Gorrie—Inventor of Artificial Ice and Mechanical Refrigeration', The Scientific Monthly (May 1936) 42 No. 5, 464-469.
From the point of view of the pure morphologist the recapitulation theory is an instrument of research enabling him to reconstruct probable lines of descent; from the standpoint of the student of development and heredity the fact of recapitulation is a difficult problem whose solution would perhaps give the key to a true understanding of the real nature of heredity.
Form and Function: A Contribution to the History of Animal Morphology (1916), 312-3.
Geology ... offers always some material for observation. ... [When] spring and summer come round, how easily may the hammer be buckled round the waist, and the student emerge from the dust of town into the joyous air of the country, for a few delightful hours among the rocks.
In The Story of a Boulder: or, Gleanings from the Note-book of a Field Geologist (1858), viii.
Good mathematicians when they make errors, which is not infrequently, soon perceive and correct them. As for me (and mine is the case of many mathematicians), I make many more of them than my students do; only I always correct them so that no trace of them remains in the final result.
In An Essay on the Psychology of Invention in the Mathematical Field (1954), 49.
GRAVE, n. A place in which the dead are laid to await the coming of the medical student.
The Collected Works of Ambrose Bierce (1911), Vol. 7, The Devil's Dictionary, 122.
He [a student] liked to look at the … remains of queer animals: funny little skulls and bones and disjointed skeletons of strange monsters that must have been remarkable when they were alive … [he] wondered if the long one with the flat, triangular head used to crawl, or hop, or what.
In 'The Great Paste-pot Handicap' Maroon Tales: University of Chicago Stories (1910), 289. Note: the fictional student is in the University of Chicago’s Walker Museum.
He never got drunk, he never got tired, and he never perspired.
[Harvard chemistry students’ axioms.]
[Harvard chemistry students’ axioms.]
As attributed in John D. Roberts, The Right Place at the Right Time (1990), 52.
He who would lead a Christ-like life is he who is perfectly and absolutely himself. He may be a great poet, or a great man of science, or a young student at the University, or one who watches sheep upon a moor, or a maker of dramas like Shakespeare, or a thinker about God, like Spinoza. or a child who plays in a garden, or a fisherman who throws his nets into the sea. It does not matter what he is as long as he realises the perfection of the soul that is within him.
In 'The Critic As Artist', Oscariana: Epigrams (1907), 27-28
High school counselors would try to railroad Hispanic students into the AD nursing programs. I’m proud of the fact that we’ve [National Association of Hispanic Nurses] been able to push more of our nurses on to earn doctoral degrees. We now have a number of Hispanic doctoral nurses who are very good at research and have been recognized worldwide for their studies. For example, Mary Lou de Leon Siantz has done work with Mexican migrant families that was truly ground-breaking.
As quoted in 'Minority Mental Health: Shining a Light on Unique Needs and Situations', Minority Nurse (30 Mar 2013) online at minoritynurse.com
His [J.J. Sylvester’s] lectures were generally the result of his thought for the preceding day or two, and often were suggested by ideas that came to him while talking. The one great advantage that this method had for his students was that everything was fresh, and we saw, as it were, the very genesis of his ideas. One could not help being inspired by such teaching.
As quoted by Florian Cajori, in Teaching and History of Mathematics in the United States (1890), 267-268.
Histology is an exotic meal, but can be as repulsive as a dose of medicine for students who are obliged to study it, and little loved by doctors who have finished their study of it all too hastily. Taken compulsorily in large doses it is impossible to digest, but after repeated tastings in small draughts it becomes completely agreeable and even addictive. Whoever possesses a refined sensitivity for artistic manifestations will appreciate that, in the science of histology, there exists an inherent focus of aesthetic emotions.
Opening remarks of paper, 'Art and Artifice in the Science of Histology' (1933), reprinted in Histopathology (1993), 22, 515-525. Quoted in Ross, Pawlina and Barnash, Atlas of Descriptive Histology (2009).
History without the history of science, to alter slightly an apothegm of Lord Bacon, resembles a statue of Polyphemus without his eye—that very feature being left out which most marks the spirit and life of the person. My own thesis is complementary: science taught ... without a sense of history is robbed of those very qualities that make it worth teaching to the student of the humanities and the social sciences.
'The History of Science and the Teaching of Science', in I. Bernard Cohen and Fletcher G. Watson (eds.), General Education in Science (1952), 71.
How to tell students what to look for without telling them what to see is the dilemma of teaching.
…...
I advise my students to listen carefully the moment they decide to take no more Mathematics courses. They might be able to hear the sound of closing doors.
From 'Everybody a Mathematician', CAIP Quarterly (Fall 1989), 2, as quoted and cited, as a space filler following article Reinhard C. Laubenbacher and Michael Siddoway, 'Great Problems of Mathematics: A Summer Workshop for High School Students', The College Mathematics Journal (Mar 1994), 25, No. 2, 114.
I am ashamed to say that C. P. Snow's “two cultures” debate smoulders away. It is an embarrassing and sterile debate, but at least it introduced us to Medawar's essays. Afterwards, not even the most bigoted aesthete doubted that a scientist could be every inch as cultivated and intellectually endowed as a student of the humanities.
From 'Words of Hope', The Times (17 May 1988). Quoted in Neil Calver, 'Sir Peter Medawar: Science, Creativity and the Popularization of Karl Popper', Notes and Records of the Royal Society (May 2013), 67, 303.
I am convinced that this is the only means of advancing science, of clearing the mind from a confused heap of contradictory observations, that do but perplex and puzzle the Student, when he compares them, or misguide him if he gives himself up to their authority; but bringing them under one general head, can alone give rest and satisfaction to an inquisitive mind.
From 'A Discourse Delivered to the Students of the Royal Academy, on the Distribution of Prizes' (11 Dec 1770), in Seven Discourses Delivered in the Royal Academy (1778), 98.
I am giving this winter two courses of lectures to three students, of which one is only moderately prepared, the other less than moderately, and the third lacks both preparation and ability. Such are the onera of a mathematical profession.
Letter to Friedrich Bessel (4 Dec 1808). In Gauss-Bessel Briefwechsel (1880), 107. In Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath's Quotation-book (1914), 158.
I am often amazed at how much more capability and enthusiasm for science there is among elementary school youngsters than among college students.
In Broca's Brain: Reflections on the Romance of Science (1974, 2011), 46.
I am told that the wall paintings which we had the happiness of admiring in all their beauty and freshness [in the chapel she discovered at Abu Simbel] are already much injured. Such is the fate of every Egyptian monument, great or small. The tourist carves it over with names and dates, and in some instances with caricatures. The student of Egyptology, by taking wet paper “squeezes” sponges away every vestige of the original colour. The “Collector” buys and carries off everything of value that he can, and the Arab steals it for him. The work of destruction, meanwhile goes on apace. The Museums of Berlin, of Turin, of Florence are rich in spoils which tell their lamentable tale. When science leads the way, is it wonderful that ignorance should follow?
Quoted in Margaret S. Drower, The Early Years, in T.G.H. James, (ed.), Excavating in Egypt: The Egypt Exploration Society, 1882-1982 (1982), 10. As cited in Wendy M.K. Shaw, Possessors and Possessed: Museums, Archaeology, and the Visualization of History in the Late Ottoman Empire (2003), 37. Also quoted in Margaret S. Drower, Flinders Petrie: A Life in Archaeology (1995), 57.
I believe … that we can still have a genre of scientific books suitable for and accessible alike to professionals and interested laypeople. The concepts of science, in all their richness and ambiguity, can be presented without any compromise, without any simplification counting as distortion, in language accessible to all intelligent people … I hope that this book can be read with profit both in seminars for graduate students and–if the movie stinks and you forgot your sleeping pills–on the businessman’s special to Tokyo.
In Wonderful Life: The Burgess Shale and the Nature of History (1990), Preface, 16.
I completed my formal education having been one of the first students in geophysics at three great universities. By today’s standards my studies were extremely casual, but I had learned to work hard, taking courses which it turned out were often irrelevant, old-fashioned, and frequently wrong. Nevertheless, the very casualness encouraged independence in thought and action.
In 'Early Days in University Geophysics', Annual Review of Earth and Planetary Sciences (1982), 10, 7.
I did try “to make things clear,” first to myself (an important point) and then to my students and somehow to make “these dry bones live.”
His response on his 80th birthday (1929) recognition of his mathematical contributions and teachings by his former students. As quoted by R.T. Glazebrook in Obituary Notices of Fellows of the Royal Society (Dec 1935), 392.
I do not intend to go deeply into the question how far mathematical studies, as the representatives of conscious logical reasoning, should take a more important place in school education. But it is, in reality, one of the questions of the day. In proportion as the range of science extends, its system and organization must be improved, and it must inevitably come about that individual students will find themselves compelled to go through a stricter course of training than grammar is in a position to supply. What strikes me in my own experience with students who pass from our classical schools to scientific and medical studies, is first, a certain laxity in the application of strictly universal laws. The grammatical rules, in which they have been exercised, are for the most part followed by long lists of exceptions; accordingly they are not in the habit of relying implicitly on the certainty of a legitimate deduction from a strictly universal law. Secondly, I find them for the most part too much inclined to trust to authority, even in cases where they might form an independent judgment. In fact, in philological studies, inasmuch as it is seldom possible to take in the whole of the premises at a glance, and inasmuch as the decision of disputed questions often depends on an aesthetic feeling for beauty of expression, or for the genius of the language, attainable only by long training, it must often happen that the student is referred to authorities even by the best teachers. Both faults are traceable to certain indolence and vagueness of thought, the sad effects of which are not confined to subsequent scientific studies. But certainly the best remedy for both is to be found in mathematics, where there is absolute certainty in the reasoning, and no authority is recognized but that of one’s own intelligence.
In 'On the Relation of Natural Science to Science in general', Popular Lectures on Scientific Subjects, translated by E. Atkinson (1900), 25-26.
I fancy that Dr. Sabin’s impulsive sincerity has helped greatly to open the way to the hearts of her pupils and friends.
As quoted in Vincent T. Andriole, 'Florence Rena Sabin—Teacher, Scientist, Citizen', Journal of the History of Medicine and Allied Sciences (Jul 1959), 14, No. 3, (July 1959), 325. Cited as from W. H. Howell, 'Presentation to the University of the Portrait of Dr. Florence Rena Sabin', Bulletin of Johns Hopkins Hospital (1920), 31, 151.
I find four great classes of students: The dumb who stay dumb. The dumb who become wise. The wise who go dumb. The wise who remain wise.
I had at one time a very bad fever of which I almost died. In my fever I had a long consistent delirium. I dreamt that I was in Hell, and that Hell is a place full of all those happenings that are improbable but not impossible. The effects of this are curious. Some of the damned, when they first arrive below, imagine that they will beguile the tedium of eternity by games of cards. But they find this impossible, because, whenever a pack is shuffled, it comes out in perfect order, beginning with the Ace of Spades and ending with the King of Hearts. There is a special department of Hell for students of probability. In this department there are many typewriters and many monkeys. Every time that a monkey walks on a typewriter, it types by chance one of Shakespeare's sonnets. There is another place of torment for physicists. In this there are kettles and fires, but when the kettles are put on the fires, the water in them freezes. There are also stuffy rooms. But experience has taught the physicists never to open a window because, when they do, all the air rushes out and leaves the room a vacuum.
'The Metaphysician's Nightmare', Nightmares of Eminent Persons and Other Stories (1954), 38-9.
I have lived much of my life among molecules. They are good company. I tell my students to try to know molecules, so well that when they have some question involving molecules, they can ask themselves, What would I do if I were that molecule? I tell them, Try to feel like a molecule; and if you work hard, who knows? Some day you may get to feel like a big molecule!
Nobel banquet speech (10 Dec 1967). In Ragnar Granit (ed.), Les Prix Nobel en 1967 (1968).
I have never had any student or pupil under me to aid me with assistance; but have always prepared and made my experiments with my own hands, working & thinking at the same time. I do not think I could work in company, or think aloud, or explain my thoughts at the time. Sometimes I and my assistant have been in the Laboratory for hours & days together, he preparing some lecture apparatus or cleaning up, & scarcely a word has passed between us; — all this being a consequence of the solitary & isolated system of investigation; in contradistinction to that pursued by a Professor with his aids & pupils as in your Universities.
Letter to C. Ransteed, 16 Dec 1857. In L. Pearce Williams (ed.), The Selected Correspondence of Michael Faraday (1971), Vol. 2, 888.
I have seen many phases of life; I have moved in imperial circles, I have been a Minister of State; but if I had to live my life again, I would always remain in my laboratory, for the greatest joy of my life has been to accomplish original scientific work, and, next to that, to lecture to a set of intelligent students.
Quoted in Ralph Oesper, The Human Side of Scientists (1975), 55.
I have spent much time in the study of the abstract sciences; but the paucity of persons with whom you can communicate on such subjects disgusted me with them. When I began to study man, I saw that these abstract sciences are not suited to him, and that in diving into them, I wandered farther from my real object than those who knew them not, and I forgave them for not having attended to these things. I expected then, however, that I should find some companions in the study of man, since it was so specifically a duty. I was in error. There are fewer students of man than of geometry.
Thoughts of Blaise Pascal (1846), 137.
I learned what research was all about as a research student [with] Stoppani ... Max Perutz, and ... Fred Sanger... From them, I always received an unspoken message which in my imagination I translated as “Do good experiments, and don’t worry about the rest.”
From Nobel Lecture (8 Dec 1984), collected in Tore Frängsmyr and Jan Lindsten (eds.), Nobel Lectures in Physiology Or Medicine: 1981-1990 (1993), 268.
I like to find mavericks, students who don’t know what they’re looking for, who are sensitive and vulnerable and have unusual pasts. If you do enough work with these students you can often transform their level of contribution. After all, the real breakthroughs come from the mavericks.
As quoted in interview with Frances Glennon, 'Student and Teacher of Human Ways', Life (14 Sep 1959), 143. Mead attributes her own pioneering approach to being educated at home by her grandmother, a retired schoolteacher, whom she said “was about 50 years ahead of her time—for instance, she taught me algebra before arithmetic.”
I like to tell students that the jobs I took [at NASA] after my Ph.D. were not in existence only a few years before. New opportunities can open up for you in this ever changing field.
From interview, 'Happy 90th Birthday, Nancy', on NASA website (30 May 2017).
I once knew an otherwise excellent teacher who compelled his students to perform all their demonstrations with incorrect figures, on the theory that it was the logical connection of the concepts, not the figure, that was essential.
In Ernst Mach and Thomas Joseph McCormack, Space and Geometry (1906), 93.
I remember vividly my student days, spending hours at the light microscope, turning endlessly the micrometric screw, and gazing at the blurred boundary which concealed the mysterious ground substance where the secret mechanisms of cell life might be found.
Nobel Lecture, The Coming Age of the Cell, 12 Dec 1974
I should like to draw attention to the inexhaustible variety of the problems and exercises which it [mathematics] furnishes; these may be graduated to precisely the amount of attainment which may be possessed, while yet retaining an interest and value. It seems to me that no other branch of study at all compares with mathematics in this. When we propose a deduction to a beginner we give him an exercise in many cases that would have been admired in the vigorous days of Greek geometry. Although grammatical exercises are well suited to insure the great benefits connected with the study of languages, yet these exercises seem to me stiff and artificial in comparison with the problems of mathematics. It is not absurd to maintain that Euclid and Apollonius would have regarded with interest many of the elegant deductions which are invented for the use of our students in geometry; but it seems scarcely conceivable that the great masters in any other line of study could condescend to give a moment’s attention to the elementary books of the beginner.
In Conflict of Studies (1873), 10-11.
I should rejoice to see … Euclid honourably shelved or buried “deeper than did ever plummet sound” out of the schoolboys’ reach; morphology introduced into the elements of algebra; projection, correlation, and motion accepted as aids to geometry; the mind of the student quickened and elevated and his faith awakened by early initiation into the ruling ideas of polarity, continuity, infinity, and familiarization with the doctrines of the imaginary and inconceivable.
From Presidential Address (1869) to the British Association, Exeter, Section A, collected in Collected Mathematical Papers of Lames Joseph Sylvester (1908), Vol. 2, 657. Also in George Edward Martin, The Foundations of Geometry and the Non-Euclidean Plane (1982), 93. [Note: “plummet sound” refers to ocean depth measurement (sound) from a ship using a line dropped with a weight (plummet). —Webmaster]
I strive that in public dissection the students do as much as possible so that if even the least trained of them must dissect a cadaver before a group of spectators, he will be able to perform it accurately with his own hands; and by comparing their studies one with another they will properly understand, this part of medicine.
In De Humani Corporis Fabrica Libri Septem [Seven Books on the Structure of the Human Body] (1543), 547. Quoted and trans. in Charles Donald O'Malley, Andreas Vesalius of Brussels, 1514-1564 (1964), 144.
I tell [medical students] that they are the luckiest persons on earth to be in medical school, and to forget all this worry about H.M.O.’s and keep your eye on helping the patient. It’s the best time ever to be a doctor because you can heal and treat conditions that were untreatable even a couple of years ago.
From Cornelia Dean, 'A Conversation with Joseph E. Murray', New York Times (25 Sep 2001), F5.
I tell my students, with a feeling of pride that I hope they will share, that the carbon, nitrogen, and oxygen that make up ninety-nine per cent of our living substance were cooked in the deep interiors of earlier generations of dying stars. Gathered up from the ends of the universe, over billions of years, eventually they came to form, in part, the substance of our sun, its planets, and ourselves. Three billion years ago, life arose upon the earth. It is the only life in the solar system.
From speech given at an anti-war teach-in at the Massachusetts Institute of Technology, (4 Mar 1969) 'A Generation in Search of a Future', as edited by Ron Dorfman for Chicago Journalism Review, (May 1969).
I think I know what is bothering the students. I think that what we are up against is a generation that is by no means sure that it has a future.
From speech given at an anti-war teach-in at the Massachusetts Institute of Technology, (4 Mar 1969) 'A Generation in Search of a Future', as edited by Ron Dorfman for Chicago Journalism Review, (May 1969).
I think it’s a very valuable thing for a doctor to learn how to do research, to learn how to approach research, something there isn't time to teach them in medical school. They don't really learn how to approach a problem, and yet diagnosis is a problem; and I think that year spent in research is extremely valuable to them.
On mentoring a medical student.
On mentoring a medical student.
Quoted in interview by Mary Ellen Avery (1997)
I venture to maintain, that, if the general culture obtained in the Faculty of Arts were what it ought to be, the student would have quite as much knowledge of the fundamental principles of Physics, of Chemistry, and of Biology, as he needs, before he commenced his special medical studies. Moreover, I would urge, that a thorough study of Human Physiology is, in itself, an education broader and more comprehensive than much that passes under that name. There is no side of the intellect which it does not call into play, no region of human knowledge into which either its roots, or its branches, do not extend; like the Atlantic between the Old and the New Worlds, its waves wash the shores of the two worlds of matter and of mind; its tributary streams flow from both; through its waters, as yet unfurrowed by the keel of any Columbus, lies the road, if such there be, from the one to the other; far away from that Northwest Passage of mere speculation, in which so many brave souls have been hopelessly frozen up.
'Universities: Actual and Ideal' (1874). In Collected Essays (1893), Vol. 3, 220.
I was a reasonably good student in college ... My chief interests were scientific. When I entered college, I was devoted to out-of-doors natural history, and my ambition was to be a scientific man of the Audubon, or Wilson, or Baird, or Coues type—a man like Hart Merriam, or Frank Chapman, or Hornaday, to-day.
In Theodore Roosevelt: An Autobiography (1913), 23.
I've always felt that maybe one of the reasons that I did well as a student and made such good grades was because I lacked ... self-confidence, and I never felt that I was prepared to take an examination, and I had to study a little bit extra. So that sort of lack of confidence helped me, I think, to make a good record when I was a student.
If any student comes to me and says he wants to be useful to mankind and go into research to alleviate human suffering, I advise him to go into charity instead. Research wants real egotists who seek their own pleasure and satisfaction, but find it in solving the puzzles of nature.
In Science Today (May 1980), 35. In Vladimir Burdyuzha, The Future of Life and the Future of Our Civilization (2006), 374.
If it is good to teach students about the chemical industry then why is it not good to assign ethical qualities to substances along with their physical and chemical ones? We might for instance say that CS [gas] is a bad chemical because it can only ever be used by a few people with something to protect against many people with nothing to lose. Terylene or indigotin are neutral chemicals. Under capitalism their production is an exploitive process, under socialism they are used for the common good. Penicillin is a good chemical.
Quoted in T. Pateman (ed.), Countercourse (1972), 215.
Imagination is a contagious disease. It cannot be measured by the yard, or weighed by the pound, and then delivered to the students by members of the faculty. It can only be communicated by a faculty whose members themselves wear their learning with imagination.
In 'Universities and Their Function', The Aims of Education: & Other Essays (1917), 139.
In all our academies we attempt far too much. ... In earlier times lectures were delivered upon chemistry and botany as branches of medicine, and the medical student learned enough of them. Now, however, chemistry and botany are become sciences of themselves, incapable of comprehension by a hasty survey, and each demanding the study of a whole life, yet we expect the medical student to understand them. He who is prudent, accordingly declines all distracting claims upon his time, and limits himself to a single branch and becomes expert in one thing.
Quoted in Johann Hermann Baas, Henry Ebenezer Handerson (trans.), Outlines of the History of Medicine and the Medical Profession (1889), 842-843.
In college I largely wasted my opportunities. My worst subjects were drawing and science. Almost my only memory of the chemistry class was of making some sulfuric acid into a foul-smelling concoction and dropping it into another student's pocket.
From My Own Story (1957), 55.
In entering upon any scientific pursuit, one of the student’s first endeavours ought to be, to prepare his mind for the reception of truth, by dismissing, or at least loosening his hold on, all such crude and hastily adopted notions respecting the objects and relations he is about to examine as may tend to embarrass or mislead him.
From opening paragraph, J.F.W. Herschel, 'Introduction', A Treatise on Astronomy (1833), 1.
In every case the awakening touch has been the mathematical spirit, the attempt to count, to measure, or to calculate. What to the poet or the seer may appear to be the very death of all his poetry and all his visions—the cold touch of the calculating mind,—this has proved to be the spell by which knowledge has been born, by which new sciences have been created, and hundreds of definite problems put before the minds and into the hands of diligent students. It is the geometrical figure, the dry algebraical formula, which transforms the vague reasoning of the philosopher into a tangible and manageable conception; which represents, though it does not fully describe, which corresponds to, though it does not explain, the things and processes of nature: this clothes the fruitful, but otherwise indefinite, ideas in such a form that the strict logical methods of thought can be applied, that the human mind can in its inner chamber evolve a train of reasoning the result of which corresponds to the phenomena of the outer world.
In A History of European Thought in the Nineteenth Century (1896), Vol. 1, 314.
In my life as an architect, I found that the single thing which inhibits young professionals, new students most severely, is their acceptance of standards that are too low.
In 'Foreword' written for Richard P. Gabriel, Patterns of Software: Tales from the Software Community (1996), vii.
In the beginning, there was benzene!
[Written over Thiele’s office door. His former student Heinrich Otto Wieland said it expressed Thiele’s disdain for the chemistry of natural products.]
[Written over Thiele’s office door. His former student Heinrich Otto Wieland said it expressed Thiele’s disdain for the chemistry of natural products.]
Quoted in R. Huisgen, 'The Wieland Memorial Lecture: Heinrich Wieland', Proceedings of the Chemical Society (1958), 214.
In the light of knowledge attained, the happy achievement seems almost a matter of course, and any intelligent student can grasp it without too much trouble. But the years of anxious searching in the dark, with their intense longing, their alternations of confidence and exhaustion, and the final emergence into the light—only those who have experienced it can understand that.
Quoted in Banesh Hoffmann and Helen Dukas, Albert Einstein: Creator and Rebel (1972), 124.
Index-learning turns no student pale,
Yet holds the eel of Science by the tail.
Index-learning is a term used to mock pretenders who acquire superficial knowledge merely by consulting indexes.
Yet holds the eel of Science by the tail.
Index-learning is a term used to mock pretenders who acquire superficial knowledge merely by consulting indexes.
The Dunciad (1728), Book 1, 279. Reference from The Oxford English Dictionary.
Instead of adjusting students to docile membership in whatever group they happen to be placed, we should equip them to cope with their environment, not be adjusted to it, to be willing to stand alone, if necessary, for what is right and true.
In speech, 'Education for Creativity in the Sciences', Conference at New York University, Washington Square. As quoted by Gene Currivan in 'I.Q. Tests Called Harmful to Pupil', New York Times (16 Jun 1963), 66.
Intelligence is important in psychology for two reasons. First, it is one of the most scientifically developed corners of the subject, giving the student as complete a view as is possible anywhere of the way scientific method can be applied to psychological problems. Secondly, it is of immense practical importance, educationally, socially, and in regard to physiology and genetics.
From Intelligence: Its Structure, Growth and Action: Its Structure, Growth and Action (1987), 1.
It can hardly be pressed forcibly enough on the attention of the student of nature, that there is scarcely any natural phenomenon which can be fully and completely explained, in all its circumstances, without a union of several, perhaps of all, the sciences.
In A Preliminary Discourse on the Study of Natural Philosophy (1831), 174.
It is a misfortune to pass at once from observation to conclusion, and to regard both as of equal value; but it befalls many a student.
In The Maxims and Reflections of Goethe (1906), 183.
It is above all the duty of the methodical text-book to adapt itself to the pupil’s power of comprehension, only challenging his higher efforts with the increasing development of his imagination, his logical power and the ability of abstraction. This indeed constitutes a test of the art of teaching, it is here where pedagogic tact becomes manifest. In reference to the axioms, caution is necessary. It should be pointed out comparatively early, in how far the mathematical body differs from the material body. Furthermore, since mathematical bodies are really portions of space, this space is to be conceived as mathematical space and to be clearly distinguished from real or physical space. Gradually the student will become conscious that the portion of the real space which lies beyond the visible stellar universe is not cognizable through the senses, that we know nothing of its properties and consequently have no basis for judgments concerning it. Mathematical space, on the other hand, may be subjected to conditions, for instance, we may condition its properties at infinity, and these conditions constitute the axioms, say the Euclidean axioms. But every student will require years before the conviction of the truth of this last statement will force itself upon him.
In Methodisches Lehrbuch der Elementar-Mathemalik (1904), Teil I, Vorwort, 4-5.
It is clear that the chief end of mathematical study must be to make the pupil think.
In Lectures on Fundamental Concepts of Algebra and Geometry (1911), 4.
It is important that students bring a certain ragamuffin, barefoot irreverence to their studies; they are not here to worship what is known, but to question it.
The Ascent of Man (1973), 360.
It is impossible not to feel stirred at the thought of the emotions of man at certain historic moments of adventure and discovery—Columbus when he first saw the Western shore, Pizarro when he stared at the Pacific Ocean, Franklin when the electric spark came from the string of his kite, Galileo when he first turned his telescope to the heavens. Such moments are also granted to students in the abstract regions of thought, and high among them must be placed the morning when Descartes lay in bed and invented the method of co-ordinate geometry.
Quoted in James Roy Newman, The World of Mathematics (2000), Vol. 1, 239.
It is not always the truth that tells us where to look for new knowledge. We don’t search for the penny under the lamp post where the light is. We know we are more likely to find it out there in the darkness. My favorite way of expressing this notion to graduate students who are trying to do very hard experiments is to remind them that “God loves the noise as much as he does the signal.”
In 'Physics and the APS in 1979', Physics Today (Apr 1980), 33, No. 4, 50.
It is not an easy paper to follow, for the items that require retention throughout the analysis are many, and it is fatal to one's understanding to lose track of any of them. Mastery of this paper, however, can give one the strong feeling of being ableto master anything else [one] might have to wrestle within biology.
Describing the paper 'A Correlation of Cytological and Genetic Crossings-over in Zea mays' published by Barbara McClintock and her student Harriet Creighton in the Proceedings of the National Academy of Sciences (1931).
Describing the paper 'A Correlation of Cytological and Genetic Crossings-over in Zea mays' published by Barbara McClintock and her student Harriet Creighton in the Proceedings of the National Academy of Sciences (1931).
Classic Papers in Genetics (1959), 156.
It is not easy to imagine how little interested a scientist usually is in the work of any other, with the possible exception of the teacher who backs him or the student who honors him.
Pensées d'un Biologiste (1939). Translated in The Substance of Man (1962), 195.
It is not enough to teach man a specialty. Through it he may become a kind of useful machine, but not a harmoniously developed personality. It is essential that the student acquire an understanding of and a lively feeling for values. He must acquire a vivid sense of the beautiful and of the morally good. Otherwise he—with his specialized knowledge—more closely resembles a well-trained dog than a harmoniously developed person.
From interview with Benjamin Fine, 'Einstein Stresses Critical Thinking', New York Times (5 Oct 1952), 37.
It is of great advantage to the student of any subject to read the original memoirs on that subject, for science is always most completely assimilated when it is in the nascent state.
A Treatise on Electricity and Magnetism (1873), Vol. 1, Preface, xiii-xiv.
It is perhaps difficult for a modern student of Physics to realize the basic taboo of the past period (before 1956) … it was unthinkable that anyone would question the validity of symmetries under “space inversion,” “charge conjugation” and “time reversal.” It would have been almost sacrilegious to do experiments to test such unholy thoughts.
In paper presented to the International Conference on the History of Original Ideas and Basic Discoveries, Erice, Sicily (27 Jul-4 Aug 1994), 'Parity Violation' collected in Harvey B. Newman, Thomas Ypsilantis History of Original Ideas and Basic Discoveries in Particle Physics (1996), 381.
It is still true, even at the graduate level, that students study to avoid the consequences of not studying.
In 'B.F. Skinner Addresses Standing-Room-Only Crowd at Conference', Engineering Education News (Aug 1980), 7, No. 2, 3.
It is very desirable to have a word to express the Availability for work of the heat in a given magazine; a term for that possession, the waste of which is called Dissipation. Unfortunately the excellent word Entropy, which Clausius has introduced in this connexion, is applied by him to the negative of the idea we most naturally wish to express. It would only confuse the student if we were to endeavour to invent another term for our purpose. But the necessity for some such term will be obvious from the beautiful examples which follow. And we take the liberty of using the term Entropy in this altered sense ... The entropy of the universe tends continually to zero.
Sketch of Thermodynamics (1868), 100-2.
It must happen that in some cases the author is not understood, or is very imperfectly understood; and the question is what is to be done. After giving a reasonable amount of attention to the passage, let the student pass on, reserving the obscurity for future efforts. … The natural tendency of solitary students, I believe, is not to hurry away prematurely from a hard passage, but to hang far too long over it; the just pride that does not like to acknowledge defeat, and the strong will that cannot endure to be thwarted, both urge to a continuance of effort even when success seems hopeless. It is only by experience we gain the conviction that when the mind is thoroughly fatigued it has neither the power to continue with advantage its course in .an assigned direction, nor elasticity to strike out a new path; but that, on the other hand, after being withdrawn for a time from the pursuit, it may return and gain the desired end.
In 'Private Study of Mathematics', Conflict of Studies and other Essays (1873), 68.
It seems to me that the older subjects, classics and mathematics, are strongly to be recommended on the ground of the accuracy with which we can compare the relative performance of the students. In fact the definiteness of these subjects is obvious, and is commonly admitted. There is however another advantage, which I think belongs in general to these subjects, that the examinations can be brought to bear on what is really most valuable in these subjects.
In Conflict of Studies and other Essays (1873), 6-7.
It’s important for students to be put in touch with real-world problems. The curriculum should include computer science. Mathematics should include statistics. The curriculums should really adjust.
From address at a conference on Google campus, co-hosted with Common Sense Media and the Joan Ganz Cooney Center at Sesame Workshop 'Breakthrough Learning in the Digital Age'. As quoted in Technology blog report by Dan Fost, 'Google co-founder Sergey Brin wants more computers in schools', Los Angeles Times (28 Oct 2009). On latimesblogs.latimes.com website.
As quoted, without citation, in Can Akdeniz, Fast MBA (2014), 280.
Knowledge does not keep any better than fish. You may be dealing with knowledge of the old species, with some old truth; but somehow or other it must come to the students, as it were, just drawn out of the sea and with the freshness of its immediate importance.
In 'Universities and Their Function', The Aims of Education and Other Essays (1929), 98.
Language is a guide to 'social reality.' Though language is not ordinarily thought of as essential interest to the students of social science, it powerfully conditions all our thinking about social problems and processes. Human beings do not live in the objective world alone, nor alone in the world of social activity as ordinarily understood, but are very much at the mercy of the particular language which has become the medium of expression for their society. It is quite an illusion to imagine that one adjusts to reality essentially without the use of language and that language is merely an incidental means of solving specific problems of communication or reflection. The fact of the matter is that the 'real world' is to a large extent unconsciously built up on the language habits of the group. No two languages are ever sufficiently similar to be considered as representing the same social reality. The worlds in which different societies live are distinct worlds, not merely the same world with different labels attached.
'The Status of Linguistics as a Science', Language (1929), 5, 207-14. In David Mandelbaum (ed.), Selected Writings of Edward Sapir in Language, Culture, and Personality (1949), 162.
Lectures with demonstrations are certainly valuable—more valuable than the lectures with text-books alone. Yet analyzing the object itself is infinitely more valuable than to watch the results exposed by another. Wrestling with the part which is being studied, handling it and viewing it from all sides, and tabulating and classifying the parts worked out, give us the greatest reward. All this can be accomplished by practical laboratory work. If we can make the student work thoroughly and carefully, a great result is achieved. It makes of him an artist, an actor, an expert, not a dilettante. He is upon the stage, not in the audience.
As quoted from a paper by Mall (1896), in Florence R. Sabin, Franklin Paine Mall: The Story of a Mind. (1934), 142.
Let each social order … give the scientist a free hand and provide him with the environment and tools he needs; make him accessible to students, for he is essentially a teacher, make the university his home, and otherwise, for humanity’s sake, leave him alone.
Address upon receiving the Passano award in Baltimore, MD. In 'Medicine: The Egg & He', Time (27 May 1946). The author of the article described (not as direct quote) that Goodpasture deplored the fact that researchers are too often hamstrung by special “projects,” and not permitted to follow their own keen noses. Goodpasture acknowledged that exploratory research does entail relatively great financial risk, but these risks must be met if medicine is to serve humanity and not a social order. The author wrote that the ceremony was “last week”.
Let every student of nature take this as his rule, that whatever the mind seizes upon with particular satisfaction is to be held in suspicion.
Novum Organum (1620). In Jerome Kagan, Three Seductive Ideas (1998).
Liebig taught the world two great lessons. The first was that in order to teach chemistry it was necessary that students should be taken into a laboratory. The second lesson was that he who is to apply scientific thought and method to industrial problems must have a thorough knowledge of the sciences. The world learned the first lesson more readily than it learned the second.
Ira Remsen, Address to the Industrial Chemistry Society, Glasgow (1910). Quoted in Frederick Hutton Getman, The Life of Ira Remsen (1980), 121-122.
Liebig was not a teacher in the ordinary sense of the word. Scientifically productive himself in an unusual degree, and rich in chemical ideas, he imparted the latter to his advanced pupils, to be put by them to experimental proof; he thus brought his pupils gradually to think for themselves, besides showing and explaining to them the methods by which chemical problems might be solved experimentally.
As quoted in G. H. Getman, The Life of Ira Remsen (1980), 18-19.
Like all things of the mind, science is a brittle thing: it becomes absurd when you look at it too closely. It is designed for few at a time, not as a mass profession. But now we have megascience: an immense apparatus discharging in a minute more bursts of knowledge than humanity is able to assimilate in a lifetime. Each of us has two eyes, two ears, and, I hope, one brain. We cannot even listen to two symphonies at the same time. How do we get out of the horrible cacophony that assails our minds day and night? We have to learn, as others did, that if science is a machine to make more science, a machine to grind out so-called facts of nature, not all facts are equally worth knowing. Students, in other words, will have to learn to forget most of what they have learned. This process of forgetting must begin after each exam, but never before. The Ph.D. is essentially a license to start unlearning.
Voices In the Labyrinth: Nature, Man, and Science (1979), 2.
Like so many aging college people, Pnin had long ceased to notice the existence of students on the campus.
In Pnin (1957), 53
Mathematics … above all other subjects, makes the student lust after knowledge, fills him, as it were, with a longing to fathom the cause of things and to employ his own powers independently; it collects his mental forces and concentrates them on a single point and thus awakens the spirit of individual inquiry, self-confidence and the joy of doing; it fascinates because of the view-points which it offers and creates certainty and assurance, owing to the universal validity of its methods. Thus, both what he receives and what he himself contributes toward the proper conception and solution of a problem, combine to mature the student and to make him skillful, to lead him away from the surface of things and to exercise him in the perception of their essence. A student thus prepared thirsts after knowledge and is ready for the university and its sciences. Thus it appears, that higher mathematics is the best guide to philosophy and to the philosophic conception of the world (considered as a self-contained whole) and of one’s own being.
In Die Mathematik die Fackelträgerin einer neuen Zeit (1889), 40. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 49.
Mathematics gives the young man a clear idea of demonstration and habituates him to form long trains of thought and reasoning methodically connected and sustained by the final certainty of the result; and it has the further advantage, from a purely moral point of view, of inspiring an absolute and fanatical respect for truth. In addition to all this, mathematics, and chiefly algebra and infinitesimal calculus, excite to a high degree the conception of the signs and symbols—necessary instruments to extend the power and reach of the human mind by summarizing an aggregate of relations in a condensed form and in a kind of mechanical way. These auxiliaries are of special value in mathematics because they are there adequate to their definitions, a characteristic which they do not possess to the same degree in the physical and mathematical [natural?] sciences.
There are, in fact, a mass of mental and moral faculties that can be put in full play only by instruction in mathematics; and they would be made still more available if the teaching was directed so as to leave free play to the personal work of the student.
There are, in fact, a mass of mental and moral faculties that can be put in full play only by instruction in mathematics; and they would be made still more available if the teaching was directed so as to leave free play to the personal work of the student.
In 'Science as an Instrument of Education', Popular Science Monthly (1897), 253.
Mathematics is indeed dangerous in that it absorbs students to such a degree that it dulls their senses to everything else.
While a student, an observation made about his teacher, Professor Karl Schellbach. Quoted, without citation, in Howard W. Eves, Mathematical Circles Adieu, (1977).
May every young scientist remember … and not fail to keep his eyes open for the possibility that an irritating failure of his apparatus to give consistent results may once or twice in a lifetime conceal an important discovery.
Commenting on the discovery of thoron gas because one of Rutherford’s students had found his measurements of the ionizing property of thorium were variable. His results even seemed to relate to whether the laboratory door was closed or open. After considering the problem, Rutherford realized a radioactive gas was emitted by thorium, which hovered close to the metal sample, adding to its radioactivity—unless it was dissipated by air drafts from an open door. (Thoron was later found to be argon.)
Commenting on the discovery of thoron gas because one of Rutherford’s students had found his measurements of the ionizing property of thorium were variable. His results even seemed to relate to whether the laboratory door was closed or open. After considering the problem, Rutherford realized a radioactive gas was emitted by thorium, which hovered close to the metal sample, adding to its radioactivity—unless it was dissipated by air drafts from an open door. (Thoron was later found to be argon.)
In Barbara Lovett Cline, Men Who Made a New Physics (1987), 21.
Maybe the situation is hopeless. Television is just the wrong medium, at least in prime time, to teach science. I think it is hopeless if it insists on behaving like television… The people who produce these programs always respond to such complaints by insisting that no one would watch a program consisting of real scientists giving real lectures to real students. If they are right, then this sort of program is just another form of entertainment.
(1986).
Meanwhile I flatter myself with so much success, that: students... will not be so easily mistaken in the subjects of the mineral kingdom, as has happened with me and others in following former systems; and I also hope to obtain some protectors against those who are so possessed with the figuromania, and so addicted to the surface of things, that they are shocked at the boldness of calling a marble a limestone, and of placing the Porphyry amongst the Saxa.
An Essay Towards a System of Mineralogy (1770), trans. G. Von Engestrom, xxi.
Medical education does not exist to provide student with a way of making a living, but to ensure the health of the community.
Epigraph, without citation, in Robert Perlman, Evolution and Medicine (2013), xiii. Webmaster has not yet found the primary source; can you help?
Medicine is essentially a learned profession. Its literature is ancient, and connects it with the most learned periods of antiquity; and its terminology continues to be Greek or Latin. You cannot name a part of the body, and scarcely a disease, without the use of a classical term. Every structure bears upon it the impress of learning, and is a silent appeal to the student to cultivate an acquaintance with the sources from which the nomenclature of his profession is derived.
From Address (Oct 1874) delivered at Guy’s Hospital, 'On The Study of Medicine', printed in British Medical journal (1874), 2, 425. Collected in Sir William Withey Gull and Theodore Dyke Acland (ed.), A Collection of the Published Writings of William Withey Gull (1896), 11.
Most students treat knowledge as a liquid to be swallowed rather than as a solid to be chewed, and then wonder why it provides so little nourishment.
Seen around the web, but without citation. Webmaster has so far been unable to authenticate. Please contact Webmaster if you know the primary source.
Most writing online is devolving toward SMS and tweets that involve quick, throwaway notes with abbreviations and threaded references. This is not a form of lasting communication. In 2020 there is unlikely to be a list of classic tweets and blog posts that every student and educated citizen should have read.
Written response to the Pew Research Center and Elon University's 'Imagining the Internet' research initiative asking their survey question (2010), “Share your view of the Internet’s influence on the future of knowledge-sharing in 2020.” From 'Imagining the Internet' on elon.edu website.
Much have I learned from my teachers, more from my colleagues, but most from my students.
— Talmud
…...
My interest in chemistry was started by reading Robert Kennedy Duncan’s popular books while a high school student in Des Moines, Iowa, so that after some delay when it was possible for me to go to college I had definitely decided to specialize in chemistry.
Letter (4 Apr 1932) to Pauline G. Beery. Hagley Museum and Library Collection, Wilmington, Delaware. 1784.) As cited in Matthew E. Hermes, Enough for One Lifetime: Wallace Carothers, Inventor of Nylon (1996), 13.
My young friend, I wish that science would intoxicate you as much as our good Göttingen beer! Upon seeing a student staggering down a street.
Attributed. Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 416.
Nearly all the great inventions which distinguish the present century are the results, immediately or remotely, of the application of scientific principles to practical purposes, and in most cases these applications have been suggested by the student of nature, whose primary object was the discovery of abstract truth.
In 'Report of the Secretary', Annual Report of the Board of Regents of the Smithsonian Institution for 1859 (1860), 15.
Nearly every subject has a shadow, or imitation. It would, I suppose, be quite possible to teach a deaf and dumb child to play the piano. When it played a wrong note, it would see the frown of its teacher, and try again. But it would obviously have no idea of what it was doing, or why anyone should devote hours to such an extraordinary exercise. It would have learnt an imitation of music. and it would fear the piano exactly as most students fear what is supposed to be mathematics.
In Mathematician's Delight (1943), 8.
Newton lectured now and then to the few students who chose to hear him; and it is recorded that very frequently he came to the lecture-room and found it empty. On such occasions he would remain fifteen minutes, and then, if no one came, return to his apartments.
In 'Sir Isaac Newton', People’s Book of Biography: Or, Short Lives of the Most Interesting Persons of All Ages and Countries (1868), 250.
Ninety-nine [students] out of a hundred are automata, careful to walk in prescribed paths, careful to follow the prescribed custom. This is not an accident but the result of substantial education, which, scientifically defined, is the subsumption of the individual.
As quoted in various 21st century books, each time cited only as from the The Philosophy of Education (1906), with no page number. For example, in John Taylor Gatto, A Different Kind of Teacher: Solving the Crisis of American Schooling (2000), 61. Note: Webmaster is suspicious of the attribution of this quote. The Library of Congress lists no such title by Harris in 1906. The LOC does catalog this title by Harris for 1893, which is a 9-page pamphlet printing the text of a series of five lectures. These lectures do not contain this quote. William Torrey Harris was editor of the International Education Series of books, of which Vol. 1 was the translation by Anna Callender Bracket of The Philosophy of Education by Johann Karl Friedrich Rosenkranz (2nd ed. rev. 1886). The translation was previously published in The Journal of Speculative Philosophy (1872, -73, -74), Vols vi-viii. Webmaster does not find the quote in that book, either. Webmaster has so far been unable to verify this quote, in these words, or even find the quote in any 19th or 20th century publication (which causes more suspicion). If you have access to the primary source for this quote, please contact Webmaster.
No scientist or student of science, need ever read an original work of the past. As a general rule, he does not think of doing so. Rutherford was one of the greatest experimental physicists, but no nuclear scientist today would study his researches of fifty years ago. Their substance has all been infused into the common agreement, the textbooks, the contemporary papers, the living present.
Attempting to distinguish between science and the humanities in which original works like Shakespeare's must be studied verbatim. 'The Case of Leavis and the Serious Case', (1970), reprinted in Public Affairs (1971), 94.
No serious student of human behavior denies the potent influence of evolved biology upon our cultural lives. Our struggle is to figure out how biology affects us, not whether it does.
In An Urchin in the Storm: Essays about Books and Ideas (1988, 2010), 152.
No video, no photographs, no verbal descriptions, no lectures can provide the enchantment that a few minutes out-of-doors can: watch a spider construct a web; observe a caterpillar systematically ravaging the edge of a leaf; close your eyes, cup your hands behind your ears, and listen to aspen leaves rustle or a stream muse about its pools and eddies. Nothing can replace plucking a cluster of pine needles and rolling them in your fingers to feel how they’re put together, or discovering that “sedges have edges and grasses are round,” The firsthand, right-and-left-brain experience of being in the out-of-doors involves all the senses including some we’ve forgotten about, like smelling water a mile away. No teacher, no student, can help but sense and absorb the larger ecological rhythms at work here, and the intertwining of intricate, varied and complex strands that characterize a rich, healthy natural world.
Into the Field: A Guide to Locally Focused Teaching
Nothing can be more fatal to progress than a too confident reliance upon mathematical symbols; for the student is only too apt to take the easier course, and consider the formula and not the fact as the physical reality.
In William Thomson and Peter Guthrie Tait, Treatise on Natural Philosophy (1867), Vol. 1, viii.
Now, the causes being four, it is the business of the student of nature to know about them all, and if he refers his problems back to all of them, he will assign the “why” in the way proper to his science—the matter, the form, the mover, that for the sake of which.
Physics, 198a, 22-4. In Jonathan Barnes (ed.), The Complete Works of Aristotle (1984), Vol. I, 338.
On all levels primary, and secondary and undergraduate - mathematics is taught as an isolated subject with few, if any, ties to the real world. To students, mathematics appears to deal almost entirely with things whlch are of no concern at all to man.
In editorial in Focus, a Journal of the Mathematical Association of America (1986), quoted in obituary by Eric Pace, New York Times (11 Jun 1992).
On May 15, 1957 Linus Pauling made an extraordinary speech to the students of Washington University. ... It was at this time that the idea of the scientists' petition against nuclear weapons tests was born. That evening we discussed it at length after dinner at my house and various ones of those present were scribbling and suggesting paragraphs. But it was Linus Pauling himself who contributed the simple prose of the petition that was much superior to any of the suggestions we were making.
Speech, "The 1962 Nobel Peace Prize," at Unitarian Church, Boulder, Colorado (20 Oct 1963). On Oregon State University Library website.
On my tests I used to always give as my first question, define chemistry, because I thought every student should know what they were taking. I do this quite often.
In address, to the Economic Club of Detroit (14 Jan 1990), 'Where Do We Go From Here?' on the massiechairs.com website.
One could say you can't do any experiment which exceeds the lifetime of a Ph.D. student.
In transcript of video interview story No. 45, 'Evolution experiments' on webofstories.com website.
One morning a great noise proceeded from one of the classrooms [of the Braunsberger gymnasium] and on investigation it was found that Weierstrass, who was to give the recitation, had not appeared. The director went in person to Weierstrass’ dwelling and on knocking was told to come in. There sat Weierstrass by a glimmering lamp in a darkened room though it was daylight outside. He had worked the night through and had not noticed the approach of daylight. When the director reminded him of the noisy throng of students who were waiting for him, his only reply was that he could impossibly interrupt his work; that he was about to make an important discovery which would attract attention in scientific circles.
In Karl Weierstrass: Jahrbuch der Deutschen Mathematiker Vereinigung (1897), 6), 88-89. As quoted, cited and translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 180.
One of the big misapprehensions about mathematics that we perpetrate in our classrooms is that the teacher always seems to know the answer to any problem that is discussed. This gives students the idea that there is a book somewhere with all the right answers to all of the interesting questions, and that teachers know those answers. And if one could get hold of the book, one would have everything settled. That’s so unlike the true nature of mathematics.
As quoted in L.A. Steen and D.J. Albers (eds.), Teaching Teachers, Teaching Students (1981), 89.
One of the first and foremost duties of the teacher is not to give his students the impression that mathematical problems have little connection with each other, and no connection at all with anything else. We have a natural opportunity to investigate the connections of a problem when looking back at its solution.
In How to Solve It: A New Aspect of Mathematical Method (2004), 15.
One of the things I hope to bring back into the classroom is to make that connection with the students that they too are part of history, the space program belongs to them and to try to bring them up with the space age.
As quoted in BBC website article.
One rarely hears of the mathematical recitation as a preparation for public speaking. Yet mathematics shares with these studies [foreign languages, drawing and natural science] their advantages, and has another in a higher degree than either of them.
Most readers will agree that a prime requisite for healthful experience in public speaking is that the attention of the speaker and hearers alike be drawn wholly away from the speaker and concentrated upon the thought. In perhaps no other classroom is this so easy as in the mathematical, where the close reasoning, the rigorous demonstration, the tracing of necessary conclusions from given hypotheses, commands and secures the entire mental power of the student who is explaining, and of his classmates. In what other circumstances do students feel so instinctively that manner counts for so little and mind for so much? In what other circumstances, therefore, is a simple, unaffected, easy, graceful manner so naturally and so healthfully cultivated? Mannerisms that are mere affectation or the result of bad literary habit recede to the background and finally disappear, while those peculiarities that are the expression of personality and are inseparable from its activity continually develop, where the student frequently presents, to an audience of his intellectual peers, a connected train of reasoning. …
One would almost wish that our institutions of the science and art of public speaking would put over their doors the motto that Plato had over the entrance to his school of philosophy: “Let no one who is unacquainted with geometry enter here.”
Most readers will agree that a prime requisite for healthful experience in public speaking is that the attention of the speaker and hearers alike be drawn wholly away from the speaker and concentrated upon the thought. In perhaps no other classroom is this so easy as in the mathematical, where the close reasoning, the rigorous demonstration, the tracing of necessary conclusions from given hypotheses, commands and secures the entire mental power of the student who is explaining, and of his classmates. In what other circumstances do students feel so instinctively that manner counts for so little and mind for so much? In what other circumstances, therefore, is a simple, unaffected, easy, graceful manner so naturally and so healthfully cultivated? Mannerisms that are mere affectation or the result of bad literary habit recede to the background and finally disappear, while those peculiarities that are the expression of personality and are inseparable from its activity continually develop, where the student frequently presents, to an audience of his intellectual peers, a connected train of reasoning. …
One would almost wish that our institutions of the science and art of public speaking would put over their doors the motto that Plato had over the entrance to his school of philosophy: “Let no one who is unacquainted with geometry enter here.”
In A Scrap-book of Elementary Mathematics: Notes, Recreations, Essays (1908), 210-211.
One striking peculiarity of mathematics is its unlimited power of evolving examples and problems. A student may read a book of Euclid, or a few chapters of Algebra, and within that limited range of knowledge it is possible to set him exercises as real and as interesting as the propositions themselves which he has studied; deductions which might have pleased the Greek geometers, and algebraic propositions which Pascal and Fermat would not have disdained to investigate.
In 'Private Study of Mathematics', Conflict of Studies and other Essays (1873), 82.
One word characterises the most strenuous of the efforts for the advancement of science that I have made perseveringly during fifty-five years; that word is failure. I know no more of electric and magnetic force, or of the relation between ether, electricity and ponderable matter, or of chemical affinity, than I knew and tried to teach to my students of natural philosophy fifty years ago in my first session as Professor.
Address (16 Jun 1896), at Celebration for his Jubilee as Professor, at Glasgow University. Printed in The Electrician (19 Jun 1896), 37, 247.
Originally a pupil of Liebig, I became a pupil of Dumas, Gerhardt and Williamson: I no longer belonged to any school.
J. R. Partington, A History of Chemistry (1970), Vol. 4, 533.
Our abiding belief is that just as the workmen in the tunnel of St. Gothard, working from either end, met at last to shake hands in the very central root of the mountain, so students of nature and students of Christianity will yet join hands in the unity of reason and faith, in the heart of their deepest mysteries.
…...
Our failure to discern a universal good does not record any lack of insight or ingenuity, but merely demonstrates that nature contains no moral messages framed in human terms. Morality is a subject for philosophers, theologians, students of the humanities, indeed for all thinking people. The answers will not be read passively from nature; they do not, and cannot, arise from the data of science. The factual state of the world does not teach us how we, with our powers for good and evil, should alter or preserve it in the most ethical manner.
…...
Out of the interaction of form and content in mathematics grows an acquaintance with methods which enable the student to produce independently within certain though moderate limits, and to extend his knowledge through his own reflection. The deepening of the consciousness of the intellectual powers connected with this kind of activity, and the gradual awakening of the feeling of intellectual self-reliance may well be considered as the most beautiful and highest result of mathematical training.
In 'Ueber Wert und angeblichen Unwert der Mathematik', Jahresbericht der Deutschen Mathematiker Vereinigung (1904), 374.
Over the years it has become clear that adjustments to the physical environment are behavioral as well as physiological and are inextricably intertwined with ecology and evolution. Consequently, a student of the physiology of adaptation should not only be a technically competent physiologist, but also be familiar with the evolutionary and ecological setting of the phenomenon that he or she is studying.
From 'Interspecific comparison as a tool for ecological physiologists', collected in M.E. Feder, A.F. Bennett, W.W. Burggren, and R.B. Huey, (eds.), New Directions in Ecological Physiology (1987), 17.
Perhaps I occasionally sought to give, or inadvertently gave, to the student a sense of battle on the intellectual battlefield. If all you do is to give them a faultless and complete and uninhabited architectural masterpiece, then you do not help them to become builders of their own.
National Academy of Sciences, Biographical Memoirs Vol. 66 (1995), 86-87.
Perhaps the earliest memories I have are of being a stubborn, determined child. Through the years my mother has told me that it was fortunate that I chose to do acceptable things, for if I had chosen otherwise no one could have deflected me from my path. ... The Chairman of the Physics Department, looking at this record, could only say 'That A- confirms that women do not do well at laboratory work'. But I was no longer a stubborn, determined child, but rather a stubborn, determined graduate student. The hard work and subtle discrimination were of no moment.
Autobiography, Nobel Foundation
Plainly, then, these are the causes, and this is how many they are. They are four, and the student of nature should know them all, and it will be his method, when stating on account of what, to get back to them all: the matter, the form, the thing which effects the change, and what the thing is for.
From Physics, Book II, Part 7, 198a21-26. As quoted in Stephen Everson, 'Aristotle on the Foundations of the State', Political Studies (1988), 36, 89-101. Reprinted in Lloyd P. Gerson (ed.), Aristotle: Politics, Rhetoric and Aesthetics (1999), 74.
Poor is the pupil who does not surpass his master.
'Aphorisms', in The Notebooks of Leonardo da Vinci, trans. E. MacCurdy (1938 ), Vol. 1, 98.
Professor Brown: “Since this slide was made,” he opined, “My students have re-examined the errant points and I am happy to report that all fall close to the [straight] line.” Questioner: “Professor Brown, I am delighted that the points which fell off the line proved, on reinvestigation, to be in compliance. I wonder, however, if you have had your students reinvestigate all these points that previously fell on the line to find out how many no longer do so?”
Quoted in D. A. Davenport, 'The Invective Effect', Chemtech, September 1987, 530.
Professor Sylvester’s first high class at the new university Johns Hopkins consisted of only one student, G. B. Halsted, who had persisted in urging Sylvester to lecture on the modem algebra. The attempt to lecture on this subject led him into new investigations in quantics.
In Teaching and History of Mathematics in the United States (1890), 264.
Professors have a tendency to think that independent, creative thinking cannot be done by non-science students, and that only advanced science majors have learned enough of the material to think critically about it. I believe this attitude is false. … [Ask] students to use their native intelligence to actually confront subtle scientific issues.
In Understanding the Universe: An Inquiry Approach to Astronomy and the Nature of Scientific Research (2013), ix.
Quite distinct from the theoretical question of the manner in which mathematics will rescue itself from the perils to which it is exposed by its own prolific nature is the practical problem of finding means of rendering available for the student the results which have been already accumulated, and making it possible for the learner to obtain some idea of the present state of the various departments of mathematics. … The great mass of mathematical literature will be always contained in Journals and Transactions, but there is no reason why it should not be rendered far more useful and accessible than at present by means of treatises or higher text-books. The whole science suffers from want of avenues of approach, and many beautiful branches of mathematics are regarded as difficult and technical merely because they are not easily accessible. … I feel very strongly that any introduction to a new subject written by a competent person confers a real benefit on the whole science. The number of excellent text-books of an elementary kind that are published in this country makes it all the more to be regretted that we have so few that are intended for the advanced student. As an example of the higher kind of text-book, the want of which is so badly felt in many subjects, I may mention the second part of Prof. Chrystal’s Algebra published last year, which in a small compass gives a great mass of valuable and fundamental knowledge that has hitherto been beyond the reach of an ordinary student, though in reality lying so close at hand. I may add that in any treatise or higher text-book it is always desirable that references to the original memoirs should be given, and, if possible, short historic notices also. I am sure that no subject loses more than mathematics by any attempt to dissociate it from its history.
In Presidential Address British Association for the Advancement of Science, Section A (1890), Nature, 42, 466.
Religious creeds are a great obstacle to any full sympathy between the outlook of the scientist and the outlook which religion is so often supposed to require … The spirit of seeking which animates us refuses to regard any kind of creed as its goal. It would be a shock to come across a university where it was the practice of the students to recite adherence to Newton's laws of motion, to Maxwell's equations and to the electromagnetic theory of light. We should not deplore it the less if our own pet theory happened to be included, or if the list were brought up to date every few years. We should say that the students cannot possibly realise the intention of scientific training if they are taught to look on these results as things to be recited and subscribed to. Science may fall short of its ideal, and although the peril scarcely takes this extreme form, it is not always easy, particularly in popular science, to maintain our stand against creed and dogma.
Swarthmore Lecture (1929), Science and the Unseen World (1929), 54-56.
Sample recommendation letter:
Dear Search Committee Chair,
I am writing this letter for Mr. John Smith who has applied for a position in your department. I should start by saying that I cannot recommend him too highly.
In fact, there is no other student with whom I can adequately compare him, and I am sure that the amount of mathematics he knows will surprise you.
His dissertation is the sort of work you don’t expect to see these days.
It definitely demonstrates his complete capabilities.
In closing, let me say that you will be fortunate if you can get him to work for you.
Sincerely,
A. D. Visor (Prof.)
Dear Search Committee Chair,
I am writing this letter for Mr. John Smith who has applied for a position in your department. I should start by saying that I cannot recommend him too highly.
In fact, there is no other student with whom I can adequately compare him, and I am sure that the amount of mathematics he knows will surprise you.
His dissertation is the sort of work you don’t expect to see these days.
It definitely demonstrates his complete capabilities.
In closing, let me say that you will be fortunate if you can get him to work for you.
Sincerely,
A. D. Visor (Prof.)
In A Mathematician Reads the Newspaper (1995), 43
Science and engineering students presumably are left to learn about their literature in the same way they learn about sex.
'Learning for Life', Journal of Chemical Information and Computer Sciences (1981), 21 (4), 2A.
Science is able to make cooperate catholics and mechanics, students and Nobel prize winners, because a common faith distributes the functions of workmanship despite all differences of rational formulation.
In 'The Scientific Grammar of Michael Faraday’s Diaries', Part I, 'The Classic of Science', A Classic and a Founder (1937), collected in Rosenstock-Huessy Papers (1981), Vol. 1, 8.
Science itself is badly in need of integration and unification. The tendency is more and more the other way ... Only the graduate student, poor beast of burden that he is, can be expected to know a little of each. As the number of physicists increases, each specialty becomes more self-sustaining and self-contained. Such Balkanization carries physics, and indeed, every science further away, from natural philosophy, which, intellectually, is the meaning and goal of science.
Science, The Center of Culture (1970), 92. Quoted by Victor F. Weisskopf, 'One Hundred Years of the Physical Review', in H. Henry Stroke, Physical Review: The First Hundred Years: a Selection of Seminal Papers and Commentaries, Vol. 1, 15.
Science must be taught well, if a student is to understand the coming decades he must live through.
Epigraph in Isaac Asimov’s Book of Science and Nature Quotations (1988), 255.
Science should be taught the way mathematics is taught today. Science education should begin in kindergarten. In the first grade one would learn a little more, in the second grade, a little more, and so on. All students should get this basic science training.
From interview with Neil A. Campbell, in 'Crossing the Boundaries of Science', BioScience (Dec 1986), 36, No. 11, 738.
Scientific education is catholic; it embraces the whole field of human learning. No student can master all knowledge in the short years of his academic life, but a young man of ability and industry may reasonably hope to master the outlines of science, obtain a deep insight into the methods of scientific research, and at the same time secure an initiation into some one of the departments of science, in such a manner that he may fully appreciate the multitude of facts upon which scientific conclusions rest, and be prepared to enter the field of scientific research himself and make additions to the sum of human knowledge.
From address (1 Oct 1884), at inauguration of the Corcoran School of Science and Arts, Columbian University, Washington, D.C. Published in 'The Larger Import of Scientific Education', Popular Science Monthly (Feb 1885), 26, 453.
Scientists and particularly the professional students of evolution are often accused of a bias toward mechanism or materialism, even though believers in vitalism and in finalism are not lacking among them. Such bias as may exist is inherent in the method of science. The most successful scientific investigation has generally involved treating phenomena as if they were purely materialistic, rejecting any metaphysical hypothesis as long as a physical hypothesis seems possible. The method works. The restriction is necessary because science is confined to physical means of investigation and so it would stultify its own efforts to postulate that its subject is not physical and so not susceptible to its methods.
The Meaning of Evolution: A Study of the History of Life and of its Significance for Man (1949), 127.
Sociological researchers maintain a mask of objectivity. But … when students in these movements report facts that contradict the tenets of their group's creed, they are … punished for their heresy. … forcing them “to leave the movement.” A similar mechanism of repression is at work in every scientific discipline that I know.
In 'The Conformity Police', Global Brain: The Evolution of Mass Mind from the Big Bang to the 21st Century (2000), 86.
Some of the men stood talking in this room, and at the right of the door a little knot had formed round a small table, the center of which was the mathematics student, who was eagerly talking. He had made the assertion that one could draw through a given point more than one parallel to a straight line; Frau Hagenström had cried out that this was impossible, and he had gone on to prove it so conclusively that his hearers were constrained to behave as though they understood.
In Little Herr Friedemann (1961), 25.
Standard mathematics has recently been rendered obsolete by the discovery that for years we have been writing the numeral five backward. This has led to reevaluation of counting as a method of getting from one to ten. Students are taught advanced concepts of Boolean algebra, and formerly unsolvable equations are dealt with by threats of reprisals.
Getting Even (1978), 44.
Students of the heavens are separable into astronomers and astrologers as readily as the minor domestic ruminants into sheep and goats, but the separation of philosophers into sages and cranks seems to be more sensitive to frames of reference.
Theories and Things (1981), 192.
Students should learn to study at an early stage the great works of the great masters instead of making their minds sterile through the everlasting exercises of college, which are of no use whatever, except to produce a new Arcadia where indolence is veiled under the form of useless activity. … Hard study on the great models has ever brought out the strong; and of such must be our new scientific generation if it is to be worthy of the era to which it is born and of the struggles to which it is destined.
In Giornale di matematiche, Vol. 11, 153.
Students using astrophysical textbooks remain essentially ignorant of even the existence of plasma concepts, despite the fact that some of them have been known for half a century. The conclusion is that astrophysics is too important to be left in the hands of astrophysicists who have gotten their main knowledge from these textbooks. Earthbound and space telescope data must be treated by scientists who are familiar with laboratory and magnetospheric physics and circuit theory, and of course with modern plasma theory.
[Lamenting the traditional neglect of plasma physics]
[Lamenting the traditional neglect of plasma physics]
Quoted in Anthony L. Peratt, 'Dean of the Plasma Dissidents', Washington Times, supplement: The World and I (May 1988),197.
![Thomas Clifford Allbutt quote: Students who have attended my [medical] lectures may remember that I try not only to teach them w](https://todayinsci.com/A/Allbutt_Thomas/AllbuttThomas-Doubt500x250px.jpg)
Students who have attended my [medical] lectures may remember that I try not only to teach them what we know, but also to realise how little this is: in every direction we seem to travel but a very short way before we are brought to a stop; our eyes are opened to see that our path is beset with doubts, and that even our best-made knowledge comes but too soon to an end.
In Notes on the Composition of Scientific Papers (1904), 3.
Sufficient knowledge and a solid background in the basic sciences are essential for all medical students. But that is not enough. A physician is not only a scientist or a good technician. He must be more than that—he must have good human qualities. He has to have a personal understanding and sympathy for the suffering of human beings.
From interview with Benjamin Fine, 'Einstein Stresses Critical Thinking', New York Times (5 Oct 1952), 37.
Suppose [an] imaginary physicist, the student of Niels Bohr, is shown an experiment in which a virus particle enters a bacterial cell and 20 minutes later the bacterial cell is lysed and 100 virus particles are liberated. He will say: “How come, one particle has become 100 particles of the same kind in 20 minutes? That is very interesting. Let us find out how it happens! How does the particle get in to the bacterium? How does it multiply? Does it multiply like a bacterium, growing and dividing, or does it multiply by an entirely different mechanism ? Does it have to be inside the bacterium to do this multiplying, or can we squash the bacterium and have the multiplication go on as before? Is this multiplying a trick of organic chemistry which the organic chemists have not yet discovered ? Let us find out. This is so simple a phenomenon that the answers cannot be hard to find. In a few months we will know. All we have to do is to study how conditions will influence the multiplication. We will do a few experiments at different temperatures, in different media, with different viruses, and we will know. Perhaps we may have to break into the bacteria at intermediate stages between infection and lysis. Anyhow, the experiments only take a few hours each, so the whole problem can not take long to solve.”
[Eight years later] he has not got anywhere in solving the problem he set out to solve. But [he may say to you] “Well, I made a slight mistake. I could not do it in a few months. Perhaps it will take a few decades, and perhaps it will take the help of a few dozen other people. But listen to what I have found, perhaps you will be interested to join me.”
[Eight years later] he has not got anywhere in solving the problem he set out to solve. But [he may say to you] “Well, I made a slight mistake. I could not do it in a few months. Perhaps it will take a few decades, and perhaps it will take the help of a few dozen other people. But listen to what I have found, perhaps you will be interested to join me.”
From 'Experiments with Bacterial Viruses (Bacteriophages)', Harvey Lecture (1946), 41, 161-162. As cited in Robert Olby, The Path of the Double Helix: The Discovery of DNA (1974, 1994), 237.
The advanced course in physics began with Rutherford’s lectures. I was the only woman student who attended them and the regulations required that women should sit by themselves in the front row. There had been a time when a chaperone was necessary but mercifully that day was past. At every lecture Rutherford would gaze at me pointedly, as I sat by myself under his very nose, and would begin in his stentorian voice: “Ladies and Gentlemen”. All the boys regularly greeted this witticism with thunderous applause, stamping with their feet in the traditional manner, and at every lecture I wished I could sink into the earth. To this day I instinctively take my place as far back as possible in a lecture room.
In Cecilia Payne-Gaposchkin: An Autobiography and Other Recollections (1996), 118.
The ancients devoted a lifetime to the study of arithmetic; it required days to extract a square root or to multiply two numbers together. Is there any harm in skipping all that, in letting the school boy learn multiplication sums, and in starting his more abstract reasoning at a more advanced point? Where would be the harm in letting the boy assume the truth of many propositions of the first four books of Euclid, letting him assume their truth partly by faith, partly by trial? Giving him the whole fifth book of Euclid by simple algebra? Letting him assume the sixth as axiomatic? Letting him, in fact, begin his severer studies where he is now in the habit of leaving off? We do much less orthodox things. Every here and there in one’s mathematical studies one makes exceedingly large assumptions, because the methodical study would be ridiculous even in the eyes of the most pedantic of teachers. I can imagine a whole year devoted to the philosophical study of many things that a student now takes in his stride without trouble. The present method of training the mind of a mathematical teacher causes it to strain at gnats and to swallow camels. Such gnats are most of the propositions of the sixth book of Euclid; propositions generally about incommensurables; the use of arithmetic in geometry; the parallelogram of forces, etc., decimals.
In Teaching of Mathematics (1904), 12.
The authors of literary works may not have intended all the subtleties, complexities, undertones, and overtones that are attributed to them by critics and by students writing doctoral theses.” That’s what God says about geologists, I told him...
Basin and Range
The average English author [of mathematical texts] leaves one under the impression that he has made a bargain with his reader to put before him the truth, the greater part of the truth, and nothing but the truth; and that if he has put the facts of his subject into his book, however difficult it may be to unearth them, he has fulfilled his contract with his reader. This is a very much mistaken view, because effective teaching requires a great deal more than a bare recitation of facts, even if these are duly set forth in logical order—as in English books they often are not. The probable difficulties which will occur to the student, the objections which the intelligent student will naturally and necessarily raise to some statement of fact or theory—these things our authors seldom or never notice, and yet a recognition and anticipation of them by the author would be often of priceless value to the student. Again, a touch of humour (strange as the contention may seem) in mathematical works is not only possible with perfect propriety, but very helpful; and I could give instances of this even from the pure mathematics of Salmon and the physics of Clerk Maxwell.
In Perry, Teaching of Mathematics (1902), 59-61.
The best part of working at a university is the students. They come in fresh, enthusiastic, open to ideas, unscarred by the battles of life. They don't realize it, but they're the recipients of the best our society can offer. If a mind is ever free to be creative, that's the time. They come in believing textbooks are authoritative but eventually they figure out that textbooks and professors don't know everything, and then they start to think on their own. Then, I begin learning from them.
As quoted in autobiography of Stephen Chu in Gösta Ekspong (ed.), Nobel Lectures: Physics 1996-2000 (2002), 120.
The central task of education is to implant a will and facility for learning; it should produce not learned but learning people. The truly human society is a learning society, where grandparents, parents, and children are students together.
In Reflections on the Human Condition (1973), 22.
The contributions of physiological knowledge to an understanding of distribution are necessarily inferential. Distribution is a historical phenomenon, and the data ordinarily obtained by students of physiology are essentially instantaneous. However, every organism has a line of ancestors which extends back to the beginning of life on earth and which, during this immensity of time, has invariably been able to avoid, to adapt to, or to compensate for environmental changes.
From 'The role of physiology in the distribution of terrestrial vertebrates', collected in C.L. Hubbs (ed.), Zoogeography: Publ. 51 (1958), 84.
The crippling of individuals I consider the worst evil of capitalism. Our whole educational system suffers from this evil. An exaggerated competitive attitude is inculcated into the student, who is trained to worship acquisitive success as a preparation for his future career.
…...
The dispute between evolutionists and creation scientists offers textbook writers and teachers a wonderful opportunity to provide students with insights into the philosophy and methods of science. … What students really need to know is … how scientists judge the merit of a theory. Suppose students were taught the criteria of scientific theory evaluation and then were asked to apply these criteria … to the two theories in question. Wouldn’t such a task qualify as authentic science education? … I suspect that when these two theories are put side by side, and students are given the freedom to judge their merit as science, creation theory will fail ignominiously (although natural selection is far from faultless). … It is not only bad science to allow disputes over theory to go unexamined, but also bad education.
In Building a Bridge to the 18th Century: How the Past Can Improve Our Future (1999), 168.
The examples which a beginner should choose for practice should be simple and should not contain very large numbers. The powers of the mind cannot be directed to two things at once; if the complexity of the numbers used requires all the student’s attention, he cannot observe the principle of the rule which he is following.
In Study and Difficulties of Mathematics (1902), chap. 3.
The experienced observer does more than merely report and recite. He guides the eager student to an understanding of the earth. He may chart the scientist’s steep, barren road of sober observation and strict deduction, or the artist’s gentle road of contemplation and empathy. And, finally, he may point out his own unique way, the path of the initiated, which leads him from the laboratories and libraries to the meadows and flower gardens of the living earth.
In 'Prologue', Conversation with the Earth (1954), 7. As translated by E.B. Garside from Gespräch mit der Erde (1947).
The feeling of understanding is as private as the feeling of pain. The act of understanding is at the heart of all scientific activity; without it any ostensibly scientific activity is as sterile as that of a high school student substituting numbers into a formula. For this reason, science, when I push the analysis back as far as I can, must be private.
Reflections of a Physicist (1950), 72.
The first business of a teacher … should be to excite … curiosity. … This process saves a student from being (as many are) intellectually damaged by having a very good memory.
From Annotation to Essay 50, 'Of Studies', in Bacon’s Essays: With Annotations (1856), 446.
The first principle for the student to recognise, and one to which in after life he will often have to recur, is that his work lies not in the fluctuating balance of men’s opinion, but with the unchangeable facts of nature.
From Address (Oct 1874) delivered at Guy’s Hospital, 'On The Study of Medicine', printed in British Medical journal (1874), 2, 425. Collected in Sir William Withey Gull and Theodore Dyke Acland (ed.), A Collection of the Published Writings of William Withey Gull (1896), 4.
The first step in all physical investigations, even in those which admit of the application of mathematical reasoning and the deductive method afterwards, is the observation of natural phenomena; and the smallest error in such observation in the beginning is sufficient to vitiate the whole investigation afterwards. The necessity of strict and minute observation, then, is the first thing which the student of the physical sciences has to learn; and it is easy to see with what great advantage the habit thus acquired may be carried into everything else afterwards.
Presidential Address to Anniversary meeting of the Royal Society (30 Nov 1859), Proceedings of the Royal Society of London (1860), 10, 164-165.
The following is one of the many stories told of “old Donald McFarlane” the faithful assistant of Sir William Thomson.
The father of a new student when bringing him to the University, after calling to see the Professor [Thomson] drew his assistant to one side and besought him to tell him what his son must do that he might stand well with the Professor. “You want your son to stand weel with the Profeessorr?” asked McFarlane. “Yes.” “Weel, then, he must just have a guid bellyful o’ mathematics!”
The father of a new student when bringing him to the University, after calling to see the Professor [Thomson] drew his assistant to one side and besought him to tell him what his son must do that he might stand well with the Professor. “You want your son to stand weel with the Profeessorr?” asked McFarlane. “Yes.” “Weel, then, he must just have a guid bellyful o’ mathematics!”
As given in Life of Lord Kelvin (1910), Vol. 1, 420, footnote. [Note: William Thomson, later became Lord Kelvin. —Webmaster]
The genius of Laplace was a perfect sledge hammer in bursting purely mathematical obstacles; but, like that useful instrument, it gave neither finish nor beauty to the results. In truth, in truism if the reader please, Laplace was neither Lagrange nor Euler, as every student is made to feel. The second is power and symmetry, the third power and simplicity; the first is power without either symmetry or simplicity. But, nevertheless, Laplace never attempted investigation of a subject without leaving upon it the marks of difficulties conquered: sometimes clumsily, sometimes indirectly, always without minuteness of design or arrangement of detail; but still, his end is obtained and the difficulty is conquered.
In 'Review of “Théorie Analytique des Probabilites” par M. le Marquis de Laplace, 3eme edition. Paris. 1820', Dublin Review (1837), 2, 348.
The Good Spirit never cared for the colleges, and though all men and boys were now drilled in Greek, Latin, and Mathematics, it had quite left these shells high on the beach, and was creating and feeding other matters [science] at other ends of the world.
The Prose Works of Ralph Waldo Emerson (1870), 553.
The history of mathematics may be instructive as well as agreeable; it may not only remind us of what we have, but may also teach us to increase our store. Says De Morgan, “The early history of the mind of men with regards to mathematics leads us to point out our own errors; and in this respect it is well to pay attention to the history of mathematics.” It warns us against hasty conclusions; it points out the importance of a good notation upon the progress of the science; it discourages excessive specialization on the part of the investigator, by showing how apparently distinct branches have been found to possess unexpected connecting links; it saves the student from wasting time and energy upon problems which were, perhaps, solved long since; it discourages him from attacking an unsolved problem by the same method which has led other mathematicians to failure; it teaches that fortifications can be taken by other ways than by direct attack, that when repulsed from a direct assault it is well to reconnoiter and occupy the surrounding ground and to discover the secret paths by which the apparently unconquerable position can be taken.
In History of Mathematics (1897), 1-2.
The idea that something in food might be of advantage to patients with pernicious anemia was in my mind in 1912, when I was a house officer at the Massachusetts General Hospital…. Ever since my student days, when I had the opportunity, in my father’s wards at the Massachusetts General Hospital, … I have taken a deep interest in this disease. … Prolonged observation permitted me to become acquainted with the multiple variations and many aspects of the disease, and to realize that from a few cases it was difficult to determine the effect of therapeutic procedures.
From Nobel Prize Lecture (12 Dec 1934), collected in Nobel Lectures, Physiology or Medicine 1922-1941 (1965).
The laboratory work was the province of Dr Searle, an explosive, bearded Nemesis who struck terror into my heart. If one made a blunder one was sent to ‘stand in the corner’ like a naughty child. He had no patience with the women students. He said they disturbed the magnetic equipment, and more than once I heard him shout ‘Go and take off your corsets!’ for most girls wore these garments then, and steel was beginning to replace whalebone as a stiffening agent. For all his eccentricities, he gave us excellent training in all types of precise measurement and in the correct handling of data.
In Cecilia Payne-Gaposchkin: An Autobiography and Other Recollections (1996), 116.
The leading idea which is present in all our [geological] researches, and which accompanies every fresh observation, the sound of which to the ear of the student of Nature seems echoed from every part of her works, is—Time!—Time!—Time!
The Geology and Extinct Volcanoes of Central France (2nd ed., 1858), 208-9.
The main difficulty the student of groups meets is not that of following the argument, which is nearly always straightforward, but of grasping the purpose of the investigation.
In 'On Groups', Prelude to Mathematics (1955), 201.
The majority of mathematical truths now possessed by us presuppose the intellectual toil of many centuries. A mathematician, therefore, who wishes today to acquire a thorough understanding of modern research in this department, must think over again in quickened tempo the mathematical labors of several centuries. This constant dependence of new truths on old ones stamps mathematics as a science of uncommon exclusiveness and renders it generally impossible to lay open to uninitiated readers a speedy path to the apprehension of the higher mathematical truths. For this reason, too, the theories and results of mathematics are rarely adapted for popular presentation … This same inaccessibility of mathematics, although it secures for it a lofty and aristocratic place among the sciences, also renders it odious to those who have never learned it, and who dread the great labor involved in acquiring an understanding of the questions of modern mathematics. Neither in the languages nor in the natural sciences are the investigations and results so closely interdependent as to make it impossible to acquaint the uninitiated student with single branches or with particular results of these sciences, without causing him to go through a long course of preliminary study.
In Mathematical Essays and Recreations (1898), 32.
The modern physicist is a quantum theorist on Monday, Wednesday, and Friday and a student of gravitational relativity theory on Tuesday, Thursday, and Saturday. On Sunday he is neither, but is praying to his God that someone, preferably himself, will find the reconciliation between the two views.
In I Am a Mathematician, the Later Life of a Prodigy (1956), 109.
The most striking characteristic of the written language of algebra and of the higher forms of the calculus is the sharpness of definition, by which we are enabled to reason upon the symbols by the mere laws of verbal logic, discharging our minds entirely of the meaning of the symbols, until we have reached a stage of the process where we desire to interpret our results. The ability to attend to the symbols, and to perform the verbal, visible changes in the position of them permitted by the logical rules of the science, without allowing the mind to be perplexed with the meaning of the symbols until the result is reached which you wish to interpret, is a fundamental part of what is called analytical power. Many students find themselves perplexed by a perpetual attempt to interpret not only the result, but each step of the process. They thus lose much of the benefit of the labor-saving machinery of the calculus and are, indeed, frequently incapacitated for using it.
In 'Uses of Mathesis', Bibliotheca Sacra (Jul 1875), 32, 505.
The number of mathematical students … would be much augmented if those who hold the highest rank in science would condescend to give more effective assistance in clearing the elements of the difficulties which they present.
In Study and Difficulties of Mathematics (1902), Preface.
The one who stays in my mind as the ideal man of science is, not Huxley or Tyndall, Hooker or Lubbock, still less my friend, philosopher and guide Herbert Spencer, but Francis Galton, whom I used to observe and listen to—I regret to add, without the least reciprocity—with rapt attention. Even to-day. I can conjure up, from memory’s misty deep, that tall figure with its attitude of perfect physical and mental poise; the clean-shaven face, the thin, compressed mouth with its enigmatical smile; the long upper lip and firm chin, and, as if presiding over the whole personality of the man, the prominent dark eyebrows from beneath which gleamed, with penetrating humour, contemplative grey eyes. Fascinating to me was Francis Galton’s all-embracing but apparently impersonal beneficence. But, to a recent and enthusiastic convert to the scientific method, the most relevant of Galton’s many gifts was the unique contribution of three separate and distinct processes of the intellect; a continuous curiosity about, and rapid apprehension of individual facts, whether common or uncommon; the faculty for ingenious trains of reasoning; and, more admirable than either of these, because the talent was wholly beyond my reach, the capacity for correcting and verifying his own hypotheses, by the statistical handling of masses of data, whether collected by himself or supplied by other students of the problem.
In My Apprenticeship (1926), 134-135.
The peculiar character of mathematical truth is, that it is necessarily and inevitably true; and one of the most important lessons which we learn from our mathematical studies is a knowledge that there are such truths, and a familiarity with their form and character.
This lesson is not only lost, but read backward, if the student is taught that there is no such difference, and that mathematical truths themselves are learned by experience.
This lesson is not only lost, but read backward, if the student is taught that there is no such difference, and that mathematical truths themselves are learned by experience.
In Thoughts on the Study of Mathematics. Principles of English University Education (1838).
The position of the anthropologist of to-day resembles in some sort the position of classical scholars at the revival of learning. To these men the rediscovery of ancient literature came like a revelation, disclosing to their wondering eyes a splendid vision of the antique world, such as the cloistered of the Middle Ages never dreamed of under the gloomy shadow of the minster and within the sound of its solemn bells. To us moderns a still wider vista is vouchsafed, a greater panorama is unrolled by the study which aims at bringing home to us the faith and the practice, the hopes and the ideals, not of two highly gifted races only, but of all mankind, and thus at enabling us to follow the long march, the slow and toilsome ascent, of humanity from savagery to civilization. And as the scholar of the Renaissance found not merely fresh food for thought but a new field of labour in the dusty and faded manuscripts of Greece and Rome, so in the mass of materials that is steadily pouring in from many sides—from buried cities of remotest antiquity as well as from the rudest savages of the desert and the jungle—we of to-day must recognise a new province of knowledge which will task the energies of generations of students to master.
'Author’s Introduction' (1900). In Dr Theodor H. Gaster (ed.), The New Golden Bough (1959), xxv-xxvi.
The present state of electrical science seems peculiarly unfavorable to speculation … to appreciate the requirements of the science, the student must make himself familiar with a considerable body of most intricate mathematics, the mere retention of which in the memory materially interferes with further progress. The first process therefore in the effectual study of the science, must be one of simplification and reduction of the results of previous investigation to a form in which the mind can grasp them.
First sentence of Maxwell’s first paper (read 10 Dec 1855), 'On Faraday’s Lines of Force', Transactions of the Cambridge Philosophical Society (1857), Vol. X, part I. Collected in William Davidson Niven (ed.), The Scientific Papers of James Clerk Maxwell (1890), Vol. 1, 155.
The problem for a writer of a text-book has come now, in fact, to be this—to write a book so neatly trimmed and compacted that no coach, on looking through it, can mark a single passage which the candidate for a minimum pass can safely omit. Some of these text-books I have seen, where the scientific matter has been, like the lady’s waist in the nursery song, compressed “so gent and sma’,” that the thickness barely, if at all, surpasses what is devoted to the publisher’s advertisements. We shall return, I verily believe, to the Compendium of Martianus Capella. The result of all this is that science, in the hands of specialists, soars higher and higher into the light of day, while educators and the educated are left more and more to wander in primeval darkness.
In Presidential Address British Association for the Advancement of Science (1885), Nature, 32, 448. [Martianus Capella, who flourished c.410-320, wrote a compendium of the seven liberal arts. —Webmaster]
The professor may choose familiar topics as a starting point. The students collect material, work problems, observe regularities, frame hypotheses, discover and prove theorems for themselves. … the student knows what he is doing and where he is going; he is secure in his mastery of the subject, strengthened in confidence of himself. He has had the experience of discovering mathematics. He no longer thinks of mathematics as static dogma learned by rote. He sees mathematics as something growing and developing, mathematical concepts as something continually revised and enriched in the light of new knowledge. The course may have covered a very limited region, but it should leave the student ready to explore further on his own.
In A Concrete Approach to Abstract Algebra (1959), 1-2.
The rigid career path of a professor at a modern university is that One Must Build the Big Research Group, recruit doctoral students more vigorously than the head football coach, bombard the federal agencies with grant applications more numerous than the pollen falling from the heavens in spring, and leave the paper writing and the research to the postdocs, research associates, and students who do all the bench work and all the computer programming. A professor is chained to his previous topics by his Big Group, his network of contacts built up laboriously over decades, and the impossibility of large funding except in areas where the grantee has grown the group from a corner of the building to an entire floor. The senior tenure-track faculty at a research university–the “silverbacks” in anthropological jargon–are bound by invisible chains stronger than the strongest steel to a narrow range of what the Prevailing Consensus agrees are Very Important Problems. The aspiring scientist is confronted with the reality that his mentors are all business managers.
In his Foreword to Cornelius Lanczos, Discourse on Fourier Series, ix-x.
The safest thing for a patient is to be in the hands of a man engaged in teaching medicine. In order to be a teacher of medicine the doctor must always be a student.
Proceedings of the Staff Meetings of the Mayo Clinic (1927).
The stories of Whitney’s love for experimenting are legion. At one time he received a letter asking if insects could live in a vacuum. Whitney took the letter to one of the members of his staff and asked the man if he cared to run an experiment on the subject. The man replied that there was no point in it, since it was well established that life could not exist without a supply of oxygen. Whitney, who was an inveterate student of wild life, replied that on his farm he had seen turtles bury themselves in mud each fall, and, although the mud was covered with ice and snow for months, emerge again in the spring. The man exclaimed, “Oh, you mean hibernation!” Whitney answered, “I don’t know what I mean, but I want to know if bugs can live in a vacuum.”
He proceeded down the hall and broached the subject to another member of the staff. Faced with the same lack of enthusiasm for pursuing the matter further, Whitney tried another illustration. “I’ve been told that you can freeze a goldfish solidly in a cake of ice, where he certainly can’t get much oxygen, and can keep him there for a month or two. But if you thaw him out carefully he seems none the worse for his experience.” The second scientist replied, “Oh, you mean suspended animation.” Whitney once again explained that his interest was not in the terms but in finding an answer to the question.
Finally Whitney returned to his own laboratory and set to work. He placed a fly and a cockroach in a bell jar and removed the air. The two insects promptly keeled over. After approximately two hours, however, when he gradually admitted air again, the cockroach waved its feelers and staggered to its feet. Before long, both the cockroach and the fly were back in action.
He proceeded down the hall and broached the subject to another member of the staff. Faced with the same lack of enthusiasm for pursuing the matter further, Whitney tried another illustration. “I’ve been told that you can freeze a goldfish solidly in a cake of ice, where he certainly can’t get much oxygen, and can keep him there for a month or two. But if you thaw him out carefully he seems none the worse for his experience.” The second scientist replied, “Oh, you mean suspended animation.” Whitney once again explained that his interest was not in the terms but in finding an answer to the question.
Finally Whitney returned to his own laboratory and set to work. He placed a fly and a cockroach in a bell jar and removed the air. The two insects promptly keeled over. After approximately two hours, however, when he gradually admitted air again, the cockroach waved its feelers and staggered to its feet. Before long, both the cockroach and the fly were back in action.
'Willis Rodney Whitney', National Academy of Sciences, Biographical Memoirs (1960), 357-358.
The story is told of Lord Kelvin, a famous Scotch physicist of the last century, that after he had given a lecture on atoms and molecules, one of his students came to him with the question, “Professor, what is your idea of the structure of the atom.”
“What,” said Kelvin, “The structure of the atom? Why, don’t you know, the very word ‘atom’ means the thing that can’t be cut. How then can it have a structure?”
“That,” remarked the facetious young man, “shows the disadvantage of knowing Greek.”
“What,” said Kelvin, “The structure of the atom? Why, don’t you know, the very word ‘atom’ means the thing that can’t be cut. How then can it have a structure?”
“That,” remarked the facetious young man, “shows the disadvantage of knowing Greek.”
As described in 'Assault on Atoms' (Read 23 Apr 1931 at Symposium—The Changing World) Proceedings of the American Philosophical Society (1931), 70, No. 3, 219.
The student of biology is often struck with the feeling that historians, when dealing with the rise and fall of nations, do not generally view the phenomena from a sufficiently high biological standpoint. To me, at least, they seem to attach too much importance to individual rulers and soldiers, and to particular wars, policies, religions, and customs; while at the same time they make little attempt to extract the fundamental causes of national success or failure.
Introduction written by Ross for William Henry Samuel Jones, Malaria, a Neglected Factor in the History of Greece and Rome (1907), 1.
The student of mathematics often finds it hard to throw off the uncomfortable feeling that his science, in the person of his pencil, surpasses him in intelligence,—an impression which the great Euler confessed he often could not get rid of. This feeling finds a sort of justification when we reflect that the majority of the ideas we deal with were conceived by others, often centuries ago. In a great measure it is really the intelligence of other people that confronts us in science.
In Popular Scientific Lectures (1910), 196.
The student of medicine can no more hope to advance in the mastery of his subject with a loose and careless mind than the student of mathematics. If the laws of abstract truth require such rigid precision from those who study them, we cannot believe the laws of nature require less. On the contrary, they would seem to require more; for the facts are obscure, the means of inquiry imperfect, and in every exercise of the mind there are peculiar facilities to err.
From Address (Oct 1874) delivered at Guy’s Hospital, 'On The Study of Medicine', printed in British Medical journal (1874), 2, 425. Collected in Sir William Withey Gull and Theodore Dyke Acland (ed.), A Collection of the Published Writings of William Withey Gull (1896), 6.
The student of palaetiological sciences is a scientist and a historian. The former tries to be as uniformitarian as possible, the latter has to recognize the contingency of events which will ever be a 'skandalon' to the scientist. Verily, the geologist 'lives in a divided world'.
Natural Law and Divine Miracle: The Principle of Uniformity in Geology, Biology and Theology (1963), 151.
The student should not lose any opportunity of exercising himself in numerical calculation and particularly in the use of logarithmic tables. His power of applying mathematics to questions of practical utility is in direct proportion to the facility which he possesses in computation.
In Study and Difficulties of Mathematics (1902), chap. 12.
The student should read his author with the most sustained attention, in order to discover the meaning of every sentence. If the book is well written, it will endure and repay his close attention: the text ought to be fairly intelligible, even without illustrative examples. Often, far too often, a reader hurries over the text without any sincere and vigorous effort to understand it; and rushes to some example to clear up what ought not to have been obscure, if it had been adequately considered. The habit of scrupulously investigating the text seems to me important on several grounds. The close scrutiny of language is a very valuable exercise both for studious and practical life. In the higher departments of mathematics the habit is indispensable: in the long investigations which occur there it would be impossible to interpose illustrative examples at every stage, the student must therefore encounter and master, sentence by sentence, an extensive and complicated argument.
In 'Private Study of Mathematics', Conflict of Studies and other Essays (1873), 67.
The student skit at Christmas contained a plaintive line: “Give us Master’s exams that our faculty can pass, or give us a faculty that can pass our Master’s exams.”
In I Want to be a Mathematician: An Automathography (1985), 146.
The study of … simple cases would, I think, often be of advantage even to students whose mathematical attainments are sufficient to enable them to follow the solution of the more general cases. For in these simple cases the absence of analytical difficulties allows attention to be more easily concentrated on the physical aspects of the question, and thus gives the student a more vivid idea and a more manageable grasp of the subject than he would be likely to attain if he merely regarded electrical phenomena through a cloud of analytical symbols.
Elements of the Mathematical Theory of Electricity and Magnetism (189S), v-vi.
The teacher can seldom afford to miss the questions: What is the unknown? What are the data? What is the condition? The student should consider the principal parts of the problem attentively, repeatedly, and from various sides.
In How to Solve It: A New Aspect of Mathematical Method (2004), 77
The tendency of the sciences has long been an increasing proclivity of separation and dismemberment … The mathematician turns away from the chemist; the chemist from the naturalist; the mathematician, left to himself divides himself into a pure mathematician and a mixed mathematician, who soon part company … And thus science, even mere physical science, loses all traces of unity. A curious illustration of this result may be observed in the want of any name by which we can designate the students of the knowledge of the material world collectively. We are informed that this difficulty was felt very oppressively by the members of the British Association for the Advancement of Science, at their meetings at York, Oxford and Cambridge, in the last three summers. There was no general term by which these gentlemen could describe themselves with reference to their pursuits … some ingenious gentleman [William Whewell] proposed that, by analogy with artist, they might form Scientist, and added that there could be no scruple … when we have words such as sciolist, economist, and atheist—but this was not generally palatable.
In Review of Mrs Somerville, 'On the Connexion of the Physical Sciences', The Quarterly Review (1834), 51, 58-61.
The theoretical side of physical chemistry is and will probably remain the dominant one; it is by this peculiarity that it has exerted such a great influence upon the neighboring sciences, pure and applied, and on this ground physical chemistry may be regarded as an excellent school of exact reasoning for all students of the natural sciences.
In Theories of Solutions (1912), xx.
The traditional method of confronting the student not with the problem but with the finished solution means depriving him of all excitement, to shut off the creative impulse, to reduce the adventure of mankind to a dusty heap of theorems.
In The Act of Creation (1964), 266.
The truth is, when all is said and done, one does not teach a subject, one teaches a student how to learn it.
Begin Here: The Forgotten Conditions of Teaching and Learning (1991), 35. In Richard J. Cox, Managing Records as Evidence and Information (2001), 217.
The University is a Mecca to which students come with something less than perfect faith. It is important that students bring a certain ragamuffin, barefoot irreverence to their studies; they are not here to worship what is known, but to question it.
From The Ascent of Man (1973,2011), 275.
The value of fundamental research does not lie only in the ideas it produces. There is more to it. It affects the whole intellectual life of a nation by determining its way of thinking and the standards by which actions and intellectual production are judged. If science is highly regarded and if the importance of being concerned with the most up-to-date problems of fundamental research is recognized, then a spiritual climate is created which influences the other activities. An atmosphere of creativity is established which penetrates every cultural frontier. Applied sciences and technology are forced to adjust themselves to the highest intellectual standards which are developed in the basic sciences. This influence works in many ways: some fundamental students go into industry; the techniques which are applied to meet the stringent requirements of fundamental research serve to create new technological methods. The style, the scale, and the level of scientific and technical work are determined in pure research; that is what attracts productive people and what brings scientists to those countries where science is at the highest level. Fundamental research sets the standards of modern scientific thought; it creates the intellectual climate in which our modern civilization flourishes. It pumps the lifeblood of idea and inventiveness not only into the technological laboratories and factories, but into every cultural activity of our time. The case for generous support for pure and fundamental science is as simple as that.
In 'Why Pure Science?' in Bulletin of the Atomic Scientists, 1965.
There are no better terms available to describe the difference between the approach of the natural and the social sciences than to call the former ‘objective’ and the latter ‘subjective.’ ... While for the natural scientist the contrast between objective facts and subjective opinions is a simple one, the distinction cannot as readily be applied to the object of the social sciences. The reason for this is that the object, the ‘facts’ of the social sciences are also opinions—not opinions of the student of the social phenomena, of course, but opinions of those whose actions produce the object of the social scientist.
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There can be but one opinion as to the beauty and utility of this analysis of Laplace; but the manner in which it has been hitherto presented has seemed repulsive to the ablest mathematicians, and difficult to ordinary mathematical students.[Co-author with Peter Guthrie Tait.]
In William Thomson Baron Kelvin, Peter Guthrie Tait, Treatise on Natural Philosophy (1879), Vol. 1, Preface, vii.
There is an influence which is getting strong and stronger day by day, which shows itself more and more in all departments of human activity, and influence most fruitful and beneficial—the influence of the artist. It was a happy day for the mass of humanity when the artist felt the desire of becoming a physician, an electrician, an engineer or mechanician or—whatnot—a mathematician or a financier; for it was he who wrought all these wonders and grandeur we are witnessing. It was he who abolished that small, pedantic, narrow-grooved school teaching which made of an aspiring student a galley-slave, and he who allowed freedom in the choice of subject of study according to one's pleasure and inclination, and so facilitated development.
'Roentgen Rays or Streams', Electrical Review (12 Aug 1896). Reprinted in The Nikola Tesla Treasury (2007), 307.
By Nikola Tesla
There is no such thing as chemistry for medical students! Chemistry is chemistry!
In G. B. Kauffman, Alfred Werner (1966), 60.
There was a golden period that I look back upon with great regret, in which the cheapest of experimental animals were medical students. Graduate students were even better. In the old days, if you offered a graduate student a thiamine-deficient diet, he gladly went on it, for that was the only way he could eat. Science is getting to be more and more difficult.
In talk, 'Origin of Death' (1970).
There was a seminar for advanced students in Zürich that I was teaching and von Neumann was in the class. I came to a certain theorem, and I said it is not proved and it may be difficult. Von Neumann didn’t say anything but after five minutes he raised his hand. When I called on him he went to the blackboard and proceeded to write down the proof. After that I was afraid of von Neumann.
In George Pólya and Gerald L. Alexanderson (ed.) The Pólya Picture Album: Encounters of a Mathematician (1987), 154. Also footnoted in Matti Tedre, The Development of Computer Science: a Sociocultural Perspective (2006), 198, cited as from How to Solve It: A New Aspect of Mathematical Method (1957), xv.
There’s a touch of the priesthood in the academic world, a sense that a scholar should not be distracted by the mundane tasks of day-to-day living. I used to have great stretches of time to work. Now I have research thoughts while making peanut butter and jelly sandwiches. Sure it’s impossible to write down ideas while reading “Curious George” to a two-year-old. On the other hand, as my husband was leaving graduate school for his first job, his thesis advisor told him, “You may wonder how a professor gets any research done when one has to teach, advise students, serve on committees, referee papers, write letters of recommendation, interview prospective faculty. Well, I take long showers.”
In 'In Her Own Words: Six Mathematicians Comment on Their Lives and Careers: Susan Landau', Notices of the AMS (Sep 1991), 38, No. 7, 704.
Therefore O students study mathematics and do not build without foundations.
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They tend to be suspicious, bristly, paranoid-type people with huge egos they push around like some elephantiasis victim with his distended testicles in a wheelbarrow terrified no doubt that some skulking ingrate of a clone student will sneak into his very brain and steal his genius work.
…...
This science, Geometry, is one of indispensable use and constant reference, for every student of the laws of nature; for the relations of space and number are the alphabet in which those laws are written. But besides the interest and importance of this kind which geometry possesses, it has a great and peculiar value for all who wish to understand the foundations of human knowledge, and the methods by which it is acquired. For the student of geometry acquires, with a degree of insight and clearness which the unmathematical reader can but feebly imagine, a conviction that there are necessary truths, many of them of a very complex and striking character; and that a few of the most simple and self-evident truths which it is possible for the mind of man to apprehend, may, by systematic deduction, lead to the most remote and unexpected results.
In The Philosophy of the Inductive Sciences Part 1, Bk. 2, chap. 4, sect. 8 (1868).
Those of us who were familiar with the state of inorganic chemistry in universities twenty to thirty years ago will recall that at that time it was widely regarded as a dull and uninteresting part of the undergraduate course. Usually, it was taught almost entirely in the early years of the course and then chiefly as a collection of largely unconnected facts. On the whole, students concluded that, apart from some relationships dependent upon the Periodic table, there was no system in inorganic chemistry comparable with that to be found in organic chemistry, and none of the rigour and logic which characterised physical chemistry. It was widely believed that the opportunities for research in inorganic chemistry were few, and that in any case the problems were dull and uninspiring; as a result, relatively few people specialized in the subject... So long as inorganic chemistry is regarded as, in years gone by, as consisting simply of the preparations and analysis of elements and compounds, its lack of appeal is only to be expected. The stage is now past and for the purpose of our discussion we shall define inorganic chemistry today as the integrated study of the formation, composition, structure and reactions of the chemical elements and compounds, excepting most of those of carbon.
Inaugural Lecture delivered at University College, London (1 Mar 1956). In The Renaissance of Inorganic Chemistry (1956), 4-5.
Those…more fortunate in their mental equipment and eager to learn and to progress, have been chained to the dull and to the average and have been allowed to proceed only so fast as they were able to drag this burden with them. Search where we will,… there can be found few organized endeavors to facilitate the progress and early emergence of the brilliant students.
Co-author with Louis Jay Heath, in A New Basis for Social Progress (1917), 152.
Three engineering students were discussing who designed the human body. One said, “It was a mechanical engineer. Just look at all the joints and levers.” The second said, “No, it was an electrical engineer. The nervous system has thousands of electrical connections.” The last said, “Obviously, it was a civil engineer. Who else would run a toxic waste pipeline through a major recreation area?”
Through art and science in their broadest senses it is possible to make a permanent contribution towards the improvement and enrichment of human life and it is these pursuits that we students are engaged in.
From Nobel Banquet Speech (10 Dec 1980).
To educate means to influence the whole personality of the student.
Quoted as an epigraph, without citation, in Stanley Gudder, A Mathematical Journey (1976), xi.
To eliminate the discrepancy between men's plans and the results achieved, a new approach is necessary. Morphological thinking suggests that this new approach cannot be realized through increased teaching of specialized knowledge. This morphological analysis suggests that the essential fact has been overlooked that every human is potentially a genius. Education and dissemination of knowledge must assume a form which allows each student to absorb whatever develops his own genius, lest he become frustrated. The same outlook applies to the genius of the peoples as a whole.
Halley Lecture for 1948, delivered at Oxford (12 May 1948). In "Morphological Astronomy", The Observatory (1948), 68, 143.
To teach effectively a teacher must develop a feeling for his subject; he cannot make his students sense its vitality if he does not sense it himself. He cannot share his enthusiasm when he has no enthusiasm to share. How he makes his point may be as important as the point he makes; he must personally feel it to be important.
Mathematical Methods in Science (1963, 1977), 1.
Train yourselves. Don’t wait to be fed knowledge out of a book. Get out and seek it. Make explorations. Do your own research work. Train your hands and your mind. Become curious. Invent your own problems and solve them. You can see things going on all about you. Inquire into them. Seek out answers to your own questions. There are many phenomena going on in nature the explanation of which cannot be found in books. Find out why these phenomena take place. Information a boy gets by himself is enormously more valuable than that which is taught to him in school.
In 'Dr. Irving Langmuir', Boys' Life (Jul 1941), 12.
We don’t teach our students enough of the intellectual content of experiments—their novelty and their capacity for opening new fields… . My own view is that you take these things personally. You do an experiment because your own philosophy makes you want to know the result. It’s too hard, and life is too short, to spend your time doing something because someone else has said it’s important. You must feel the thing yourself—feel that it will change your outlook and your way of life.
In Bernstein, 'Profiles: Physicists: I', The New Yorker (13 Oct 1975), 108.
We must not only prepare [students] in sciences, we must prepare them in other areas. For example, I teach Chemistry but on every test I give I have an English question. And I give a simple question. I say, “Discuss your understanding of this topic.”
In address, to the Economic Club of Detroit (14 Jan 1990), 'Where Do We Go From Here?' on the massiechairs.com website.
We pass with admiration along the great series of mathematicians, by whom the science of theoretical mechanics has been cultivated, from the time of Newton to our own. There is no group of men of science whose fame is higher or brighter. The great discoveries of Copernicus, Galileo, Newton, had fixed all eyes on those portions of human knowledge on which their successors employed their labors. The certainty belonging to this line of speculation seemed to elevate mathematicians above the students of other subjects; and the beauty of mathematical relations and the subtlety of intellect which may be shown in dealing with them, were fitted to win unbounded applause. The successors of Newton and the Bernoullis, as Euler, Clairaut, D’Alembert, Lagrange, Laplace, not to introduce living names, have been some of the most remarkable men of talent which the world has seen.
In History of the Inductive Sciences, Vol. 1, Bk. 4, chap. 6, sect. 6.
What I am going to tell you about is what we teach our physics students in the third or fourth year of graduate school… It is my task to convince you not to turn away because you don’t understand it. You see my physics students don’t understand it… That is because I don’t understand it. Nobody does.
From Lecture, the first in the first series of Alix G. Mauntner Lectures, trascribed and editted by Ralph Leighton, 'Introduction', QED, The Strange Theory of Light and Matter (1985, 1988), 9.
What made von Liebig and his students “different” from other chemists was their effort to apply their fundamental discoveries to the development of specific chemical processes and products.
In 'The Origins of Academic Chemical Engineering', collected in Nicholas A. Peppas (ed.), One Hundred Years of Chemical Engineering: From Lewis M. Norton (M.I.T. 1888) to Present (2012), 2.
Whatever be the detail with which you cram your student, the chance of his meeting in after life exactly that detail is almost infinitesimal; and if he does meet it, he will probably have forgotten what you taught him about it. The really useful training yields a comprehension of a few general principles with a thorough grounding in the way they apply to a variety of concrete details. In subsequent practice the men will have forgotten your particular details; but they will remember by an unconscious common sense how to apply principles to immediate circumstances. Your learning is useless to you till you have lost your textbooks, burnt your lecture notes, and forgotten the minutiae which you learned by heart for the examination. What, in the way of detail, you continually require will stick in your memory as obvious facts like the sun and the moon; and what you casually require can be looked up in any work of reference. The function of a University is to enable you to shed details in favor of principles. When I speak of principles I am hardly even thinking of verbal formulations. A principle which has thoroughly soaked into you is rather a mental habit than a formal statement. It becomes the way the mind reacts to the appropriate stimulus in the form of illustrative circumstances. Nobody goes about with his knowledge clearly and consciously before him. Mental cultivation is nothing else than the satisfactory way in which the mind will function when it is poked up into activity.
In 'The Rhythm of Education', The Aims of Education: & Other Essays (1917), 41.
When Galileo caused balls, the weights of which he had himself previously determined, to roll down an inclined plane; when Torricelli made the air carry a weight which he had calculated beforehand to be equal to that of a definite volume of water; or in more recent times, when Stahl changed metal into lime, and lime back into metal, by withdrawing something and then restoring it, a light broke upon all students of nature. They learned that reason has insight only into that which it produces after a plan of its own, and that it must not allow itself to be kept, as it were, in nature's leading-strings, but must itself show the way with principles of judgement based upon fixed laws, constraining nature to give answer to questions of reason's own determining. Accidental observations, made in obedience to no previously thought-out plan, can never be made to yield a necessary law, which alone reason is concerned to discover.
Critique of Pure Reason (1781), trans. Norman Kemp Smith (1929), 20.
When I was growing up, I always knew I’d be in the top of my class in math, and that gave me a lot of self-confidence. [But now that students can see beyond their own school, they see that] there are always going to be a million people better than you at times, or someone will always be far better than you. I feel there’s an existential angst among young people. I didn’t have that. They see enormous mountains, where I only saw one little hill to climb.
From address at a conference on Google campus, co-hosted with Common Sense Media and the Joan Ganz Cooney Center at Sesame Workshop 'Breakthrough Learning in the Digital Age'. As quoted in Technology blog report by Dan Fost, 'Google co-founder Sergey Brin wants more computers in schools', Los Angeles Times (28 Oct 2009). On latimesblogs.latimes.com website.
As quoted, without citation, in Can Akdeniz, Fast MBA (2014), 280.
When it was first proposed to establish laboratories at Cambridge, Todhunter, the mathematician, objected that it was unnecessary for students to see experiments performed, since the results could be vouched for by their teachers, all of them of the highest character, and many of them clergymen of the Church of England.
In The Scientific Outlook (1931, 2009), 49.
When students hear the story of Andrew J. Wiles’ proof of Fermat’s Last Theorem, it is not the result itself that stirs their emotions, but the revelation that a mathematician was driven by the same passion as any creative artist.
In 'Loving Math Infinitely', The Chronicle of Higher Education (19 Jan 2001).
When you start in science, you are brainwashed into believing how careful you must be, and how difficult it is to discover things. There’s something that might be called the “graduate student syndrome”; graduate students hardly believe they can make a discovery.
Quotation supplied by Professor Francis Crick.
When young Galileo, then a student at Pisa, noticed one day during divine service a chandelier swinging backwards and forwards, and convinced himself, by counting his pulse, that the duration of the oscillations was independent of the arc through which it moved, who could know that this discovery would eventually put it in our power, by means of the pendulum, to attain an accuracy in the measurement of time till then deemed impossible, and would enable the storm-tossed seaman in the most distant oceans to determine in what degree of longitude he was sailing?
Hermann von Helmholtz, Edmund Atkinson (trans.), Popular Lectures on Scientific Subjects: First Series (1883), 29.
Whenever a textbook is written of real educational worth, you may be quite certain that some reviewer will say that it will be difficult to teach from it. Of course it will be difficult to teach from it. It it were easy, the book ought to be burned; for it cannot be educational. In education as elsewhere, the broad primrose path leads to a nasty place. This evil path is represented by a book or a set of lectures which will practically enable the student to learn by heart all the questions likely to be asked at the next external examination.
In 'The Aims of Education', The Aims of Education: & Other Essays (1917), 6-7.
Where there are three students of nature, there are two atheists.
Epigraph in Ludwig Büchner, Force and Matter: Or, Principles of the Natural Order of the Universe (1891), 1. It is given in parentheses, without attribution, but in the Preface Buchner states that if the name of a “poet” is not given, it is a contribution by the author.
Whoever ceases to be a student has never been a student.
From chapter 'Jottings from a Note-Book', in Canadian Stories (1918), 169.
Working is beautiful and rewarding, but acquisition of wealth for its own sake is disgusting.
A comment Bunsen often told his students.
A comment Bunsen often told his students.
Quoted in Ralph Oesper, The Human Side of Scientists (1975), 28.
You can prepare yourself for work. The paintings of the great masters, the compositions of great musicians, the sermons of great preachers, the policies of great statesmen, and the campaigns of great generals, do not spring full bloom from barren rock. … If you are a true student you will be more dissatisfied with yourself when you graduate than you are now.
From Cameron Prize Lecture (1928), delivered before the University of Edinburgh. As quoted in J.B. Collip 'Frederick Grant Banting, Discoverer of Insulin', The Scientific Monthly (May 1941), 52, No. 5, 473-474.
You can recognize truth by its beauty and simplicity. When you get it right, it is obvious that it is right—at least if you have any experience—because usually what happens is that more comes out than goes in. … The inexperienced, the crackpots, and people like that, make guesses that are simple, but you can immediately see that they are wrong, so that does not count. Others, the inexperienced students, make guesses that are very complicated, and it sort of looks as if it is all right, but I know it is not true because the truth always turns out to be simpler than you thought.
In The Character of Physical Law (1965), 171.
You don’t know who he was? Half the particles in the universe obey him!
[Reply by a physics professor when a student asked who Bose was.]
[Reply by a physics professor when a student asked who Bose was.]
Quoted in 'Original Vision, Forgotten Hero', The Calcutta Telegraph (3 Jan 2012)
You have all heard of that celebrated painter who would never allow any one to mix his colors for him. He always insisted on doing that himself, and at last one of his students, whose curiosity had been aroused, said: “Professor, what do you mix your colors with?” “With brains, sir,” said the professor. Now, that is what we have to do with our observations.
From Address (22 May 1914) to the graduating class of the Friends’ School, Washington, D.C. Printed in 'Discovery and Invention', The National Geographic Magazine (1914), 25, 650.
Young children were sooner allured by love, than driven by beating, to attain good learning.
The Scholemaster (1570), Book 1, Preface.
Young men, trust those certain and powerful methods, only the first secrets of which we yet know. And all of you, whatever your career, … do not allow yourselves to be discouraged by the gloom of certain hours which pass a nation.
Advice in Speech (27 Dec 1892) to young scientists at the Golden Jubilee celebration for Pasteur's 70th birthday. As translated in Nature (1893), 47, 205. Also translated as “Young men, have faith in those powerful and safe methods, of which we do not yet know all the secrets. And, whatever your career may be, do not let yourselves be discouraged by the sadness of certain hours which pass over nations.” By René J. Dubos, quoted and cited in Maurice B. Strauss, Familiar Medical Quotations (1968), 526.
Your aim is no better than your knowledge of chemistry.
[On being shot at by a Polish student whom Werner had failed in an examination.]
[On being shot at by a Polish student whom Werner had failed in an examination.]
In G. B. Kauffman, Alfred Werner (1966), 59.
In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion.
(1987) -- 
