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Who said: “A change in motion is proportional to the motive force impressed and takes place along the straight line in which that force is impressed.”
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Problem Quotes (180 quotes)


'Yes,' he said. 'But these things (the solutions to problems in solid geometry such as the duplication of the cube) do not seem to have been discovered yet.' 'There are two reasons for this,' I said. 'Because no city holds these things in honour, they are investigated in a feeble way, since they are difficult; and the investigators need an overseer, since they will not find the solutions without one. First, it is hard to get such an overseer, and second, even if one did, as things are now those who investigate these things would not obey him, because of their arrogance. If however a whole city, which did hold these things in honour, were to oversee them communally, the investigators would be obedient, and when these problems were investigated continually and with eagerness, their solutions would become apparent.'
Plato
The Republic 7 528bc, trans. R. W. Sharples.
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Quand les physiciens nous demandent la solution d'un problème, ce n'est pas une corvée qu'ils nous impsent, c'est nous au contraire qui leur doivent des remercîments.
When the physicists ask us for the solution of a problem, it is not drudgery that they impose on us, on the contrary, it is us who owe them thanks.
La valeur de la science. In Anton Bovier, Statistical Mechanics of Disordered Systems (2006), 111.
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A central lesson of science is that to understand complex issues (or even simple ones), we must try to free our minds of dogma and to guarantee the freedom to publish, to contradict, and to experiment. Arguments from authority are unacceptable.
Billions and Billions: Thoughts on Life and Death at the Brink of the Millenium (1998), 190.
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A chess problem is genuine mathematics, but it is in some way “trivial” mathematics. However, ingenious and intricate, however original and surprising the moves, there is something essential lacking. Chess problems are unimportant. The best mathematics is serious as well as beautiful—“important” if you like, but the word is very ambiguous, and “serious” expresses what I mean much better.
'A Mathematician's Apology', in James Roy Newman, The World of Mathematics (2000), 2029.
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A designer must always think about the unfortunate production engineer who will have to manufacture what you have designed; try to understand his problems.
On the official Raymond Loewry website.
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A good deal of my research in physics has consisted in not setting out to solve some particular problem, but simply examining mathematical equations of a kind that physicists use and trying to fit them together in an interesting way, regardless of any application that the work may have. It is simply a search for pretty mathematics. It may turn out later to have an application. Then one has good luck. At age 78.
International Journal of Theoretical Physics (1982), 21, 603. In A. Pais, 'Playing With Equations, the Dirac Way'. Behram N. Kursunoglu (Ed.) and Eugene Paul Wigner (Ed.), Paul Adrien Maurice Dirac: Reminiscences about a Great Physicist (1990), 110.
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A great discovery solves a great problem, but there is a grain of discovery in the solution of any problem. Your problem may be modest, but if it challenges your curiosity and brings into play your inventive faculties, and if you solve it by your own means, you may experience the tension and enjoy the triumph of discovery.
From Preface to the first printing, reprinted in How to Solve It: A New Aspect of Mathematical Method (2004), v.
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A multidisciplinary study group ... estimated that it would be 1980 before developments in artificial intelligence make it possible for machines alone to do much thinking or problem solving of military significance. That would leave, say, five years to develop man-computer symbiosis and 15 years to use it. The 15 may be 10 or 500, but those years should be intellectually the most creative and exciting in the history of mankind.
From article 'Man-Computer Symbiosis', in IRE Transactions on Human Factors in Electronics (Mar 1960), Vol. HFE-1, 4-11.
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A problem well stated is a problem half-solved.
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A research problem is not solved by apparatus; it is solved in a man's head.
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A strong feeling of adventure is animating those who are working on bacterial viruses, a feeling that they have a small part in the great drive towards a fundamental problem in biology.
From 'Experiments with Bacterial Viruses (Bacteriophages)', Harvey Lecture (1946), 41, 187. As cited in Robert Olby, The Path of the Double Helix: The Discovery of DNA (1974, 1994), 238.
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Accordingly, we find Euler and D'Alembert devoting their talent and their patience to the establishment of the laws of rotation of the solid bodies. Lagrange has incorporated his own analysis of the problem with his general treatment of mechanics, and since his time M. Poinsôt has brought the subject under the power of a more searching analysis than that of the calculus, in which ideas take the place of symbols, and intelligent propositions supersede equations.
J. C. Maxwell on Louis Poinsôt (1777-1859) in 'On a Dynamical Top' (1857). In W. D. Niven (ed.), The Scientific Papers of James Clerk Maxwell (1890), Vol. 1, 248.
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After Gibbs, one the most distinguished [American scientists] was Langley, of the Smithsonian. … He had the physicist's heinous fault of professing to know nothing between flashes of intense perception. … Rigidly denying himself the amusement of philosophy, which consists chiefly in suggesting unintelligible answers to insoluble problems, and liked to wander past them in a courteous temper, even bowing to them distantly as though recognizing their existence, while doubting their respectibility.
The Education of Henry Adams: An Autobiography? (1918), 377.
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After the discovery of spectral analysis no one trained in physics could doubt the problem of the atom would be solved when physicists had learned to understand the language of spectra. So manifold was the enormous amount of material that has been accumulated in sixty years of spectroscopic research that it seemed at first beyond the possibility of disentanglement. An almost greater enlightenment has resulted from the seven years of Röntgen spectroscopy, inasmuch as it has attacked the problem of the atom at its very root, and illuminates the interior. What we are nowadays hearing of the language of spectra is a true 'music of the spheres' in order and harmony that becomes ever more perfect in spite of the manifold variety. The theory of spectral lines will bear the name of Bohr for all time. But yet another name will be permanently associated with it, that of Planck. All integral laws of spectral lines and of atomic theory spring originally from the quantum theory. It is the mysterious organon on which Nature plays her music of the spectra, and according to the rhythm of which she regulates the structure of the atoms and nuclei.
Atombau und Spektrallinien (1919), viii, Atomic Structure and Spectral Lines, trans. Henry L. Brose (1923), viii.
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All interpretations made by a scientist are hypotheses, and all hypotheses are tentative. They must forever be tested and they must be revised if found to be unsatisfactory. Hence, a change of mind in a scientist, and particularly in a great scientist, is not only not a sign of weakness but rather evidence for continuing attention to the respective problem and an ability to test the hypothesis again and again.
The Growth of Biological Thought: Diversity, Evolution and Inheritance (1982), 831.
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All Nature bristles with the marks of interrogation—among the grass and the petals of flowers, amidst the feathers of birds and the hairs of mammals, on mountain and moorland, in sea and sky-everywhere. It is one of the joys of life to discover those marks of interrogation, these unsolved and half-solved problems and try to answer their questions.
In Riddles of Science (1932), 5.
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All that can be said upon the number and nature of elements is, in my opinion, confined to discussions entirely of a metaphysical nature. The subject only furnishes us with indefinite problems, which may be solved in a thousand different ways, not one of which, in all probability, is consistent with nature. I shall therefore only add upon this subject, that if, by the term elements, we mean to express those simple and indivisible atoms of which matter is composed, it is extremely probable we know nothing at all about them; but, if we apply the term elements, or principles of bodies, to express our idea of the last point which analysis is capable of reaching, we must admit, as elements, all the substances into which we are capable, by any means, to reduce bodies by decomposition.
Elements of Chemistry (1790), trans. R. Kerr, Preface, xxiv.
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Almost every major systematic error which has deluded men for thousands of years relied on practical experience. Horoscopes, incantations, oracles, magic, witchcraft, the cures of witch doctors and of medical practitioners before the advent of modern medicine, were all firmly established through the centuries in the eyes of the public by their supposed practical successes. The scientific method was devised precisely for the purpose of elucidating the nature of things under more carefully controlled conditions and by more rigorous criteria than are present in the situations created by practical problems.
Personal Knowledge (1958), 183.
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Almost everyone... seems to be quite sure that the differences between the methodologies of history and of the natural sciences are vast. For, we are assured, it is well known that in the natural sciences we start from observation and proceed by induction to theory. And is it not obvious that in history we proceed very differently? Yes, I agree that we proceed very differently. But we do so in the natural sciences as well.
In both we start from myths—from traditional prejudices, beset with error—and from these we proceed by criticism: by the critical elimination of errors. In both the role of evidence is, in the main, to correct our mistakes, our prejudices, our tentative theories—that is, to play a part in the critical discussion, in the elimination of error. By correcting our mistakes, we raise new problems. And in order to solve these problems, we invent conjectures, that is, tentative theories, which we submit to critical discussion, directed towards the elimination of error.
The Myth of the Framework: In Defence of Science and Rationality (1993), 140.
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Any problem can be solved using the materials in the room.
In Peter C. Wensberg, Land's Polaroid: A Company and the Man Who Invented It (1987).
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As soon as we touch the complex processes that go on in a living thing, be it plant or animal, we are at once forced to use the methods of this science [chemistry]. No longer will the microscope, the kymograph, the scalpel avail for the complete solution of the problem. For the further analysis of these phenomena which are in flux and flow, the investigator must associate himself with those who have labored in fields where molecules and atoms, rather than multicellular tissues or even unicellular organisms, are the units of study.
'Experimental and Chemical Studies of the Blood with an Appeal for More Extended Chemical Training for the Biological and Medical Investigator', Science (6 Aug 1915), 42, 176.
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As the world of science has grown in size and in power, its deepest problems have changed from the epistemological to the social.
Scientific Knowledge and its Social Problems (1971), 10.
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At a given instant everything the surgeon knows suddenly becomes important to the solution of the problem. You can't do it an hour later, or tomorrow. Nor can you go to the library and look it up.
Quoted in 'The Best Hope of All', Time (3 May 1963)
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Atoms for peace. Man is still the greatest miracle and the greatest problem on earth. [Message tapped out by Sarnoff using a telegraph key in a tabletop circuit demonstrating an RCA atomic battery as a power source.]
The Wisdom of Sarnoff and the World of RCA (1967), 251.
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Behold the mighty dinosaur,
Famous in prehistoric lore,
Not only for his power and strength
But for his intellectual length.
You will observe by these remains
The creature had two sets of brains—
One in his head (the usual place),
The other at his spinal base.
Thus he could reason 'A priori'
As well as 'A posteriori'.
No problem bothered him a bit
He made both head and tail of it.
So wise was he, so wise and solemn,
Each thought filled just a spinal column.
If one brain found the pressure strong
It passed a few ideas along.
If something slipped his forward mind
'Twas rescued by the one behind.
And if in error he was caught
He had a saving afterthought.
As he thought twice before he spoke
He had no judgment to revoke.
Thus he could think without congestion
Upon both sides of every question.
Oh, gaze upon this model beast
Defunct ten million years at least.
'The Dinosaur: A Poem' (1912). In E. H. Colbert (ed.), The Dinosaur Book (1951), 78.
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Beware of the problem of testing too many hypotheses; the more you torture the data, the more likely they are to confess, but confessions obtained under duress may not be admissible in the court of scientific opinion.
'Testing Hypotheses or fitting Models? Another Look at Mass Extinctions'. In Matthew H. Nitecki and Antoni Hoffman (eds.), Neutral Models in Biology (1987), 148.
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Biology occupies a position among the sciences both marginal and central. Marginal because, the living world, constituting only a tiny and very “special” part of the universe, it does not seem likely that the study of living beings will ever uncover general laws applicable outside the biosphere. But if the ultimate aim of the whole of science is indeed, as I believe, to clarify man's relationship to the universe, then biology must be accorded a central position, since of all the disciplines it is the one that endeavours to go most directly to the heart of the problems that must be resolved before that of “human nature” can even be framed in other than metaphysical terms.
In Jacques Monod and Austryn Wainhouse (trans.), Chance and Necessity: An Essay on the Natural Philosophy of Modern Biology (1971), xi.
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Cancer is a biological, not a statistical problem.
Anonymous
'Shoot Out in Marlboro Country', Mother Jones Magazine (Jan 1979), 36.
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Chess problems are the hymn-tunes of mathematics.
'A Mathematician's Apology', in James Roy Newman, The World of Mathematics (2000), 2028.
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Consider a cow. A cow doesn’t have the problem-solving skill of a chimpanzee, which has discovered how to get termites out of the ground by putting a stick into a hole. Evolution has developed the brain’s ability to solve puzzles, and at the same time has produced in our brain a pleasure of solving problems.
In John Tierney, 'For Decades, Puzzling People With Mathematics', New York Times (20 Oct 2009), D2.
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During the time that [Karl] Landsteiner gave me an education in the field of imununology, I discovered that he and I were thinking about the serologic problem in very different ways. He would ask, What do these experiments force us to believe about the nature of the world? I would ask, What is the most. simple and general picture of the world that we can formulate that is not ruled by these experiments? I realized that medical and biological investigators were not attacking their problems the same way that theoretical physicists do, the way I had been in the habit of doing.
‘Molecular Disease’, Pfizer Spectrum (1958), 6:9, 234.
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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.
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Even mistaken hypotheses and theories are of use in leading to discoveries. This remark is true in all the sciences. The alchemists founded chemistry by pursuing chimerical problems and theories which are false. In physical science, which is more advanced than biology, we might still cite men of science who make great discoveries by relying on false theories. It seems, indeed, a necessary weakness of our mind to be able to reach truth only across a multitude of errors and obstacles.
An Introduction to the Study of Experimental Medicine (1865, translation 1927, 1957), 170.
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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.
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He who seeks for methods without having a definite problem in mind seeks for the most part in vain.
'Mathematical Problems', Bulletin of the American Mathematical Society (Jul 1902), 8, 444.
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Here I shall present, without using Analysis [mathematics], the principles and general results of the Théorie, applying them to the most important questions of life, which are indeed, for the most part, only problems in probability. One may even say, strictly speaking, that almost all our knowledge is only probable; and in the small number of things that we are able to know with certainty, in the mathematical sciences themselves, the principal means of arriving at the truth—induction and analogy—are based on probabilities, so that the whole system of human knowledge is tied up with the theory set out in this essay.
Philosophical Essay on Probabilities (1814), 5th edition (1825), trans. Andrew I. Dale (1995), 1.
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How is it that there are so many minds that are incapable of understanding mathematics? ... the skeleton of our understanding, ... and actually they are the majority. ... We have here a problem that is not easy of solution, but yet must engage the attention of all who wish to devote themselves to education.
Science and Method (1914, 2003), 117-118.
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I carried this problem around in my head basically the whole time. I would wake up with it first thing in the morning, I would be thinking about it all day, and I would be thinking about it when I went to sleep. Without distraction I would have the same thing going round and round in my mind.
Recalling the degree of focus and determination that eventually yielded the proof of Fermat's Last Theorem.
Quoted in interview for PBS TV program Nova. In William Byers, How Mathematicians Think (2007), 1.
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I have been able to solve a few problems of mathematical physics on which the greatest mathematicians since Euler have struggled in vain ... But the pride I might have held in my conclusions was perceptibly lessened by the fact that I knew that the solution of these problems had almost always come to me as the gradual generalization of favorable examples, by a series of fortunate conjectures, after many errors. I am fain to compare myself with a wanderer on the mountains who, not knowing the path, climbs slowly and painfully upwards and often has to retrace his steps because he can go no further—then, whether by taking thought or from luck, discovers a new track that leads him on a little till at length when he reaches the summit he finds to his shame that there is a royal road by which he might have ascended, had he only the wits to find the right approach to it. In my works, I naturally said nothing about my mistake to the reader, but only described the made track by which he may now reach the sa,e heights without difficulty.
In L. Koenigsberger, Hermann von Helmholtz, 180-1.
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I have yet to see any problem, however complicated, which, when you looked at it in the right way, did not become still more complicated.
Quoted in William Thorpe, 'Reduction v. Organicism,' New Scientist, 25 Sep 1969, 43, No 66, 638. In Carl C. Gaither, Statistically Speaking: A Dictionary of Quotations (1996), 187.
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I know that most men, including those at ease with problems of the greatest complexity, can seldom accept even the simplest and most obvious truth if it be such as would oblige them to admit the falsity of conclusions which they have delighted in explaining to colleagues, which they have proudly taught to others, and which they have woven, thread by thread, into the fabric of their lives.
Attributed. Quoted in James GleickChaos (1988), 38. Contact webmaster if you know a primary print source.
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If a problem is clearly stated, it has no further interest to the physicist.
In Richard Hamming, Numerical Methods for Scientists and Engineers (1973), 704, footnote, without citation.
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If there is a problem you can’t solve, then there is an easier problem you can solve: find it.
Quoted in Preface, How to Solve It: A New Aspect of Mathematical Method (2004), xxi.
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If thou art able, O stranger, to find out all these things and gather them together in your mind, giving all the relations, thou shalt depart crowned with glory and knowing that thou hast been adjudged perfect in this species of wisdom.
From a letter to Eratosthenes, the chief librarian at Alexandria, containing the Cattle Problem, an exceedingly difficult calculation involving huge numbers (which was not solved exactly until the use of a supercomputer in 1981). In David J. Darling, The Universal Book of Mathematics (2004), 23. The debate by scholars regarding whether Archimedes is the true author is in T. L. Heath (ed.), The Works of Archimedes (1897), xxxiv.
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If we want to solve a problem that we have never solved before, we must leave the door to the unknown ajar.
In 'The Value of Science,' What Do You Care What Other People Think? (1988, 2001), 247. Collected in The Pleasure of Finding Things Out (2000), 149.
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If you walk along the street you will encounter a number of scientific problems. Of these, about 80 per cent are insoluble, while 19½ per cent are trivial. There is then perhaps half a per cent where skill, persistence, courage, creativity and originality can make a difference. It is always the task of the academic to swim in that half a per cent, asking the questions through which some progress can be made.
'The Making of a Scientist', Journal of the Royal Society of Arts, June 1983, 406.
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Ignorance more frequently begets confidence than does knowledge: it is those who know little, and not those who know much, who so positively assert that this or that problem will never be solved by science.
The Descent of Man (1871), Vol. 1, 3.
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In a sense Shapley’s telling me that space was transparent, which I shouldn’t have believed, illustrates a fundamental problem in science, believing what people tell you. Go and find it out for yourself. That same error has persisted in my life and in many other people’s. Authorities are not always authorities on everything; they often cling to their own mistakes.
Oral History Transcript of interview with Dr. Jesse Greenstein by Paul Wright (31 Jul 1974), on website of American Institute of Physics.
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In fact a favourite problem of [Tyndall] is—Given the molecular forces in a mutton chop, deduce Hamlet or Faust therefrom. He is confident that the Physics of the Future will solve this easily.
Letter to Herbert Spencer (3 Aug 1861). In L. Huxley, The Life and Letters of Thomas Henry Huxley (1900), Vol. 1, 249.
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In less than eight years “The Origin of Species” has produced conviction in the minds of a majority of the most eminent living men of science. New facts, new problems, new difficulties as they arise are accepted, solved, or removed by this theory; and its principles are illustrated by the progress and conclusions of every well established branch of human knowledge.
From a review of four books on the subject 'Mimicry, and Other Protective Resemblances Among Animals', in The Westminster Review (Jul 1867), 88, 1. Wallace is identified as the author in the article as reprinted in William Beebe, The Book of Naturalists: An Anthology of the Best Natural History (1988), 108.
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In short, the greatest contribution to real security that science can make is through the extension of the scientific method to the social sciences and a solution of the problem of complete avoidance of war.
In "Science and Security", Science (25 Jun 1948), 107, 665. Written while Director of the U.S. National Bureau of Standards.
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In so far as such developments utilise the natural energy running to waste, as in water power, they may be accounted as pure gain. But in so far as they consume the fuel resources of the globe they are very different. The one is like spending the interest on a legacy, and the other is like spending the legacy itself. ... [There is] a still hardly recognised coming energy problem.
Matter and Energy (1911), 139.
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In the end, poverty, putridity and pestilence; work, wealth and worry; health, happiness and hell, all simmer down into village problems.
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In the modern world, science and society often interact in a perverse way. We live in a technological society, and technology causes political problems. The politicians and the public expect science to provide answers to the problems. Scientific experts are paid and encouraged to provide answers. The public does not have much use for a scientist who says, “Sorry, but we don’t know.” The public prefers to listen to scientists who give confident answers to questions and make confident predictions of what will happen as a result of human activities. So it happens that the experts who talk publicly about politically contentious questions tend to speak more clearly than they think. They make confident predictions about the future, and end up believing their own predictions. Their predictions become dogmas which they do not question. The public is led to believe that the fashionable scientific dogmas are true, and it may sometimes happen that they are wrong. That is why heretics who question the dogmas are needed.
Frederick S. Pardee Distinguished Lecture (Oct 2005), Boston University. Collected in 'Heretical Thoughts About Science and Society', A Many-Colored Glass: Reflections on the Place of Life in the Universe (2007), 43-44.
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Intelligence is an extremely subtle concept. It’s a kind of understanding that flourishes if it's combined with a good memory, but exists anyway even in the absence of good memory. It’s the ability to draw consequences from causes, to make correct inferences, to foresee what might be the result, to work out logical problems, to be reasonable, rational, to have the ability to understand the solution from perhaps insufficient information. You know when a person is intelligent, but you can be easily fooled if you are not yourself intelligent.
In Irv Broughton (ed.), The Writer's Mind: Interviews with American Authors (1990), Vol. 2, 57.
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Investigation may be likened to the long months of pregnancy, and solving a problem to the day of birth. To investigate a problem is, indeed, to solve it.
In Winberg Chai, The Foreign Relations of the People's Republic of China (1972), 46.
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It appears that the solution of the problem of time and space is reserved to philosophers who, like Leibniz, are mathematicians, or to mathematicians who, like Einstein, are philosophers.
Collected in Paul Arthur Schilpp (ed.), Albert Einstein: Philosopher-Scientist (1959), Vol. 1, 307. Also, in James Louis Jarrett and Sterling M. McMurrin (eds.), Contemporary Philosophy: A Book of Readings (1954), 71.
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It appears, nevertheless, that all such simple solutions of the problem of vertebrate ancestry are without warrant. They arise from a very common tendency of the mind, against which the naturalist has to guard himself,—a tendency which finds expression in the very widespread notion that the existing anthropoid apes, and more especially the gorilla, must be looked upon as the ancestors of mankind, if once the doctrine of the descent of man from ape-like forefathers is admitted. A little reflexion suffices to show that any given living form, such as the gorilla, cannot possibly be the ancestral form from which man was derived, since ex-hypothesi that ancestral form underwent modification and development, and in so doing, ceased to exist.
'Vertebrata', entry in Encyclopaedia Britannica, 9th edition (1899), Vol. 24, 180.
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It has been recognized that hydrogen bonds restrain protein molecules to their native configurations, and I believe that as the methods of structural chemistry are further applied to physiological problems it will be found that the significance of the hydrogen bond for physiology is greater than that of any other single structural feature.
Nature of the Chemical Bond and the Structure of Molecules and Crystals (1939), 265.
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It is a curious property of research activity that after the problem has been solved the solution seems obvious. This is true not only for those who have not previously been acquainted with the problem, but also for those who have worked over it for years.
Address at the Franklin Institute (1937). Journal of the Franklin Institute (1937), 224, 277. Also see Paul C. Wensberg, Land's Polaroid: A Company and the Man who Invented It (1987), 31.
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It is an occupational risk of biologists to claim, towards the end of their careers, that the problems which they have not solved are insoluble.
'Popper's World', The London Review of Books (18-31 August 1983), 12.
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It is better to do the right problem the wrong way than the wrong problem the right way.
Quoted in Julie K. Petersen, Fiber Optics Illustrated Dictionary (2003), 435.
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It is evident, therefore, that one of the most fundamental problems of psychology is that of investigating the laws of mental growth. When these laws are known, the door of the future will in a measure be opened; determination of the child's present status will enable us to forecast what manner of adult he will become.
In The Intelligence of School Children: How Children Differ in Ability, the Use of Mental Tests in School Grading and the Proper Education of Exceptional Children (1919), 136
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It is science alone that can solve the problems of hunger and poverty, of insanitation and illiteracy, of superstition and deadening custom and tradition, of vast resources running to waste, of a rich country inhabited by starving people... Who indeed could afford to ignore science today? At every turn we have to seek its aid... the future belongs to science and those who make friends with science.
Quoted in Atma Ram, 'The Making of Optical Glass in India: Its Lessons for Industrial Development', Proceedings of ihe National Institute of Sciences of India (1961), 27, 564-5.
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It is the business of science to offer rational explanations for all the events in the real world, and any scientist who calls on God to explain something is falling down on his job. This applies as much to the start of the expansion as to any other event. If the explanation is not forthcoming at once, the scientist must suspend judgment: but if he is worth his salt he will always maintain that a rational explanation will eventually be found. This is the one piece of dogmatism that a scientist can allow himself—and without it science would be in danger of giving way to superstition every time that a problem defied solution for a few years.
The Mystery of the Expanding Universe (1964), 122.
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It isn't that they can't see the solution. It is that they can't see the problem.
'The Point of a Pin', in The Scandal of Father Brown (1935,2000), 142.
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It sometimes seems necessary to suspend one's normal critical faculties not to find the problems of fusion overwhelming.
Science (1976). In Ervan G. Garrison, A History of Engineering and Technology
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It was Plato, according to Sosigenes, who set this as a problem for those concerned with these things, through what suppositions of uniform and ordered movements the appearances concerning the movements of the wandering heavenly bodies could be preserved.
Plato
Simplicius, On Aristotle's On the Heavens, 488.21. Trans. R. W. Sharples.
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It's much more effective to allow solutions to problems to emerge from the people close to the problem rather than to impose them from higher up.
Interviewed in 'Simple, Yet Complex', CIO (15 Apr 1998), 64.
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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.
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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.
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Life arose as a living molecule or protogene, the progression from this stage to that of the ameba is at least as great as from ameba to man. All the essential problems of living organisms are already solved in the one-celled (or, as many now prefer to say, noncellular) protozoan and these are only elaborated in man or the other multicellular animals. The step from nonlife to life may not have been so complex, after all, and that from cell to multicellular organism is readily comprehensible. The change from protogene to protozoan was probably the most complex that has occurred in evolution, and it may well have taken as long as the change from protozoan to man.
The Meaning of Evolution: A Study of the History of Life and of its Significance for Man (1949), 16
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Littlewood, on Hardy's own estimate, is the finest mathematician he has ever known. He was the man most likely to storm and smash a really deep and formidable problem; there was no one else who could command such a combination of insight, technique and power. (1943)
In Béla Bollobás, Littlewood's Miscellany (1986), Foreward, 22.
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Man is born, not to solve the problems of the universe, but to find out where the problem applies, and then to restrain himself within the limits of the comprehensible.
Wed. 12 Oct 1825. Johann Peter Eckermann, Conversations with Goethe, ed. J. K. Moorhead and trans. J. Oxenford (1971), 120.

Man is not a machine, ... although man most certainly processes information, he does not necessarily process it in the way computers do. Computers and men are not species of the same genus. .... No other organism, and certainly no computer, can be made to confront genuine human problems in human terms. ... However much intelligence computers may attain, now or in the future, theirs must always be an intelligence alien to genuine human problems and concerns.
Computer Power and Human Reason: From Judgment to Calculation, (1976) 203 and 223. Also excerpted in Ronald Chrisley (ed.), Artificial Intelligence: Critical Concepts (2000), Vol. 3, 313 and 321. Note that the second ellipsis spans 8 pages.
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Marxists are more right than wrong when they argue that the problems scientists take up,. the way they go about solving them, and even the solutions they arc inclined to accept, arc conditioned by the intellectual, social, and economic environments in which they live and work.
In Mankind Evolving: The Evolution of the Human Species, 128. As cited in Ted Woods & Alan Grant, Reason in Revolt - Dialectical Philosophy and Modern Science (2003), Vol. 2, 183.
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More and more of out colleagues fail to understand our work because of the high specialization of research problems. We must not be discouraged if the products of our labor are not read or even known to exist. The joy of research must be found in doing since every other harvest is uncertain.
Letter to Dr. E. B. Krumhaar (11 Oct 1933), in Journal of Bacteriology (Jan 1934), 27, No. 1, 20.
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New scientific ideas never spring from a communal body, however organized, but rather from the head of an individually inspired researcher who struggles with his problems in lonely thought and unites all his thought on one single point which is his whole world for the moment.
Address on the 25th anniversary of the Kaiser-Wilhelm Gesellschaft (Jan 1936). Quoted in Surviving the Swastika: Scientific Research in Nazi Germany (1993), 97.
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No research will answer all queries that the future may raise. It is wiser to praise the work for what it has accomplished and then to formulate the problems still to be solved.
Letter to Dr. E. B. Krumhaar (11 Oct 1933), in Journal of Bacteriology (Jan 1934), 27, No. 1, 19.
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Often the great scientists, by turning the problem around a bit, changed a defect to an asset. For example, many scientists when they found they couldn't do a problem finally began to study why not. They then turned it around the other way and said, “But of course, this is what it is” and got an important result.
'You and Your Research', Bell Communications Research Colloquium Seminar, 7 Mar 1986.
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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.
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Our atom of carbon enters the leaf, colliding with other innumerable (but here useless) molecules of nitrogen and oxygen. It adheres to a large and complicated molecule that activates it, and simultaneously receives the decisive message from the sky, in the flashing form of a packet of solar light; in an instant, like an insect caught by a spider, it is separated from its oxygen, combined with hydrogen and (one thinks) phosphous, and finally inserted in a chain, whether long or short does not matter, but it is the chain of life. All this happens swiftly, in silence, at the temperature and pressure of the atmosphere, and gratis: dear colleagues, when we learn to do likewise we will be sicut Deus [like God], and we will have also solved the problem of hunger in the world.
Levi Primo and Raymond Rosenthal (trans.), The Periodic Table (1975, 1984), 227-228. In this final section of his book, Levi imagines the life of a carbon atom. He calls this his first “literary dream”. It came to him at Auschwitz.
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Our contemporary culture, primed by population growth and driven by technology, has created problems of environmental degradation that directly affect all of our senses: noise, odors and toxins which bring physical pain and suffering, and ugliness, barrenness, and homogeneity of experience which bring emotional and psychological suffering and emptiness. In short, we are jeopardizing our human qualities by pursuing technology as an end rather than a means. Too often we have failed to ask two necessary questions: First, what human purpose will a given technology or development serve? Second, what human and environmental effects will it have?
Report of the Subcommittee on Air and Water Pollution (7 Aug 1969). 'Environmental Quality: Summary and Discussion of Major Provisions', U.S. Environmental Protection Agency, Legal Compilation, (Jan 1973), Water, Vol. 3, 1365. EPA website.
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Our present work sets forth mathematical principles of philosophy. For the basic problem of philosophy seems to be to discover the forces of nature from the phenomena of motions and then to demonstrate the other phenomena from these forces. It is to these ends that the general propositions in books 1 and 2 are directed, while in book 3 our explanation of the system of the world illustrates these propositions.
The Principia: Mathematical Principles of Natural Philosophy (1687), 3rd edition (1726), trans. I. B. Cohen and Anne Whitman (1999), Preface to the first edition, 382.
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Perhaps the central problem we face in all of computer science is how we are to get to the situation where we build on top of the work of others rather than redoing so much of it in a trivially different way.
From Turing Award lecture (1968), 'One Man's View of Computer Science', collected in ACM Turing Award Lectures: The First Twenty Years, 1966 to 1985 (1987), 216. ACM is the Association for Computing Machinery. The lecture is also published in Journal of the ACM (Jan 1969), 16, No. 1, 10.
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Perhaps the problem is the seeming need that people have of making black-and-white cutoffs when it comes to certain mysterious phenomena, such as life and consciousness. People seem to want there to be an absolute threshold between the living and the nonliving, and between the thinking and the “merely mechanical,” ... But the onward march of science seems to force us ever more clearly into accepting intermediate levels of such properties.
‘Shades of Gray Along the Consciousness Continuum’, Fluid Concepts & Creative Analogies: Computer Models of the Fundamental Mechanisms of Thought (1995), 310.
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Philosophy is that part of science which at present people chose to have opinions about, but which they have no knowledge about. Therefore every advance in knowledge robs philosophy of some problems which formerly it had …and will belong to science.
'The Philosophy of Logical Atomism' (1918). In Betrand Russell and Robert Charles Marsh (Ed.), Logic and Knowledge: Essays, 1901-1950 (1988), 281.
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Physics is becoming so unbelievably complex that it is taking longer and longer to train a physicist. It is taking so long, in fact, to train a physicist to the place where he understands the nature of physical problems that he is already too old to solve them.
As quoted by Colin Pittendrigh (1971). In George C. Beakley, Ernest G. Chilton, Introduction to Engineering Design and Graphics (1973), 40
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Probably the most important skill that children learn is how to learn. … Too often we give children answers to remember rather than problems to solve. This is a mistake.
In 'Observing the Brain Through a Cat's Eyes', Saturday Review World (1974), 2, 132.
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Problems are the price of progress. Don't bring me anything but trouble. Good news weakens me.
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Research has deserted the individual and entered the group. The individual worker find the problem too large, not too difficult. He must learn to work with others.
Letter to Dr. E. B. Krumhaar (11 Oct 1933), in Journal of Bacteriology (Jan 1934), 27, No. 1, 20.
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Richard Feynman was fond of giving the following advice on how to be a genius. You have to keep a dozen of your favorite problems constantly present in your mind, although by and large they will lay in a dormant state. Every time you hear or read a new trick or a new result, test it against each of your twelve problems to see whether it helps. Every once in a while there will be a hit, and people will say, “How did he do it? He must be a genius!”
In 'Ten Lessons I Wish I Had Been Taught', Indiscrete Thoughts (2008), 202.
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Science fiction writers foresee the inevitable, and although problems and catastrophes may be inevitable, solutions are not.
'How Easy to See the Future'. In Asimov on Science Fiction (1981), 86.
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Science is a game—but a game with reality, a game with sharpened knives … If a man cuts a picture carefully into 1000 pieces, you solve the puzzle when you reassemble the pieces into a picture; in the success or failure, both your intelligences compete. In the presentation of a scientific problem, the other player is the good Lord. He has not only set the problem but also has devised the rules of the game—but they are not completely known, half of them are left for you to discover or to deduce. The experiment is the tempered blade which you wield with success against the spirits of darkness—or which defeats you shamefully. The uncertainty is how many of the rules God himself has permanently ordained, and how many apparently are caused by your own mental inertia, while the solution generally becomes possible only through freedom from its limitations.
Quoted in Walter Moore, Schrödinger: Life and Thought (1989), 348.
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Science is measurement. If I cannot make measurements, I cannot study a problem scientifically.
In 'Musical Acoustics Today', New Scientist (1 Nov 1962), 16 No. 311, 257.
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Science itself, therefore, may be regarded as a minimal problem, consisting of the completest possible presentment of facts with the least possible expenditure of thought.
Ernst Mach and Thomas Joseph McCormick (trans.), The Science of Mechanics: a Critical and Historical Account of its Development (1919), 490.
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Scientists come in two varieties, hedgehogs and foxes. I borrow this terminology from Isaiah Berlin (1953), who borrowed it from the ancient Greek poet Archilochus. Archilochus told us that foxes know many tricks, hedgehogs only one. Foxes are broad, hedgehogs are deep. Foxes are interested in everything and move easily from one problem to another. Hedgehogs are only interested in a few problems that they consider fundamental, and stick with the same problems for years or decades. Most of the great discoveries are made by hedgehogs, most of the little discoveries by foxes. Science needs both hedgehogs and foxes for its healthy growth, hedgehogs to dig deep into the nature of things, foxes to explore the complicated details of our marvelous universe. Albert Einstein and Edwin Hubble were hedgehogs. Charley Townes, who invented the laser, and Enrico Fermi, who built the first nuclear reactor in Chicago, were foxes.
In 'The Future of Biotechnology', A Many-Colored Glass: Reflections on the Place of Life in the Universe (2007), 1.
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Scientists like ripping problems apart, collecting as much data as possible and then assembling the parts back together to make a decision. [Reflecting on being president of Princeton University.]
As quoted by Diane Cole in 'Shirley Tilghman, Educator: From Lab Table to President's Chair', U.S. News & World Reports (12 Nov 2007)
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Scientists often have a naive faith that if only they could discover enough facts about a problem, these facts would somehow arrange themselves in a compelling and true solution.
In Mankind Evolving: The Evolution of the Human Species, 128. As cited in Ted Woods & Alan Grant, Reason in Revolt - Dialectical Philosophy and Modern Science (2003), Vol. 2, 183.
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Since my first discussions of ecological problems with Professor John Day around 1950 and since reading Konrad Lorenz's “King Solomon's Ring,” I have become increasingly interested in the study of animals for what they might teach us about man, and the study of man as an animal. I have become increasingly disenchanted with what the thinkers of the so-called Age of Enlightenment tell us about the nature of man, and with what the formal religions and doctrinaire political theorists tell us about the same subject.
'Autobiography of Allan M. Cormack,' Les Prix Nobel/Nobel Lectures 1979, editted by Wilhelm Odelberg.
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Since the seventeenth century, physical intuition has served as a vital source for mathematical porblems and methods. Recent trends and fashions have, however, weakened the connection between mathematics and physics; mathematicians, turning away from their roots of mathematics in intuition, have concentrated on refinement and emphasized the postulated side of mathematics, and at other times have overlooked the unity of their science with physics and other fields. In many cases, physicists have ceased to appreciate the attitudes of mathematicians. This rift is unquestionably a serious threat to science as a whole; the broad stream of scientific development may split into smaller and smaller rivulets and dry out. It seems therefore important to direct our efforts towards reuniting divergent trends by classifying the common features and interconnections of many distinct and diverse scientific facts.
In R. Courant and David Hilbert, Methods of Mathematical Physics (1937, 1989), Preface, v.
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Some mathematics problems look simple, and you try them for a year or so, and then you try them for a hundred years, and it turns out that they're extremely hard to solve. There's no reason why these problems shouldn't be easy, and yet they turn out to be extremely intricate. [Fermat's] Last Theorem is the most beautiful example of this.
From interview for PBS website on the NOVA program, 'The Proof'.
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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.”
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.
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The advances of biology during the past 20 years have been breathtaking, particularly in cracking the mystery of heredity. Nevertheless, the greatest and most difficult problems still lie ahead. The discoveries of the 1970‘s about the chemical roots of memory in nerve cells or the basis of learning, about the complex behavior of man and animals, the nature of growth, development, disease and aging will be at least as fundamental and spectacular as those of the recent past.
As quoted in 'H. Bentley Glass', New York Times (12 Jan 1970), 96.
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The American Businessman has a problem: if he comes up with something new, the Russians invent it six months later and the Japanese make it cheaper.
Anonymous
In E.C. McKenzie, 14,000 Quips and Quotes for Speakers, Writers, Editors, Preachers, and Teachers (1990), 58.
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The answers are always inside the problem, not outside.
(Attributed ??) This quote is often seen, but without a citation, even on the official Marshall McLuhan website. If you known a primary print source, please contact Webmaster.
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The art of research [is] the art of making difficult problems soluble by devising means of getting at them.
Pluto's Republic (1982), 2.
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The central problem of biological evolution is the nature of mutation, but hitherto the occurrence of this has been wholly refractory and impossible to influence by artificial means, although a control of it might obviously place the process of evolution in our hands.
'The Recent Findings in Heredity' (unpublished lecture, 1916, Lilly Library), 3. Quoted in Elof Axel Carlson, Genes, Radiation, and Society: The Life and Work of H. J. Muller (1981), 104.
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The certainties of one age are the problems of the next.
Religion and the Rise of Capitalism (1926, 2008), 282.
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The definition of a good mathematical problem is the mathematics it generates rather than the problem itself.
From interview for PBS website on the NOVA program, 'The Proof'.
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The dropping of the Atomic Bomb is a very deep problem... Instead of commemorating Hiroshima we should celebrate... man's triumph over the problem [of transmutation], and not its first misuse by politicians and military authorities.
Address to New Europe Group meeting on the third anniversary of the Hiroshima bomb. Quoted in New Europe Group, In Commemoration of Professor Frederick Soddy (1956), 6-7.
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The equation of animal and vegetable life is too complicated a problem for human intelligence to solve, and we can never know how wide a circle of disturbance we produce in the harmonies of nature when we throw the smallest pebble into the ocean of organic life.
Man and Nature, (1864), 103.
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The fact remains that, if the supply of energy failed, modern civilization would come to an end as abruptly as does the music of an organ deprived of wind.
Matter and Energy (1911), 251.
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The fact that death from cancer is on the increase is not only a problem of medicine, but its at the same time testifies to the wonderful efficiency of medical science... [as it] enables more persons top live long enough to develop some kind of cancer in old and less resistant tissues.
Charles H. Mayo and William A. Hendricks, 'Carcinoma of the Right Segment of the Colon', presented to Southern Surgical Assoc. (15 Dec 1925). In Annals of Surgery (Mar 1926), 83, 357.
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The formulation of a problem is often more essential than its solution, which may be merely a matter of mathematical or experimental skill. To raise new questions, new possibilities, to regard old problems from a new angle requires creative imagination and marks real advances in science.
In Albert Einstein and Léopold Infeld, The Evolution of Physics: The Growth of Ideas from Early Concepts to Relativity and Quanta (1938, 1966), 92.
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The fundamental problem in the origin of species is not the origin of differences in appearance, since these arise at the level of the geographical race, but the origin of genetic segregation. The test of species-formation is whether, when two forms meet, they interbreed and merge, or whether they keep distinct.
Darwin's Finches (1947), 129.
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The future mathematician ... should solve problems, choose the problems which are in his line, meditate upon their solution, and invent new problems. By this means, and by all other means, he should endeavor to make his first important discovery: he should discover his likes and dislikes, his taste, his own line.
How to Solve it: A New Aspect of Mathematical Method (1957), 206.
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The Golden Gate Bridge is a giant moving math problem.
Quoted on web site for PBS American Experience episode for 'Golden Gate Bridge.'
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The great problem of today is, how to subject all physical phenomena to dynamical laws. With all the experimental devices, and all the mathematical appliances of this generation, the human mind has been baffled in its attempts to construct a universal science of physics.
'President's Address', Proceedings of the American Association for the Advancement of Science (1874), 23, 34-5.
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The ideal engineer is a composite. … He is not a scientist, he is not a mathematician, he is not a sociologist or a writer. But he may use the knowledge and techniques of any or all of these disciplines in solving problems.
Student, Teacher, and Engineer: Selected Speeches and Articles of Nathan W Dougherty (1972), 33.
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The inherent unpredictability of future scientific developments—the fact that no secure inference can be drawn from one state of science to another—has important implications for the issue of the limits of science. It means that present-day science cannot speak for future science: it is in principle impossible to make any secure inferences from the substance of science at one time about its substance at a significantly different time. The prospect of future scientific revolutions can never be precluded. We cannot say with unblinking confidence what sorts of resources and conceptions the science of the future will or will not use. Given that it is effectively impossible to predict the details of what future science will accomplish, it is no less impossible to predict in detail what future science will not accomplish. We can never confidently put this or that range of issues outside 'the limits of science', because we cannot discern the shape and substance of future science with sufficient clarity to be able to say with any assurance what it can and cannot do. Any attempt to set 'limits' to science—any advance specification of what science can and cannot do by way of handling problems and solving questions—is destined to come to grief.
The Limits of Science (1984), 102-3.
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The intellect has little to do on the road to discovery. There comes a leap in consciousness, call it intuition or what you will, and the solution comes to you and you don’t know why or how.
Quoted in Forbes (15 Sep 1974). In Larry Chang, Wisdom for the Soul (2006), 179.
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The investigation of causal relations between economic phenomena presents many problems of peculiar difficulty, and offers many opportunities for fallacious conclusions. Since the statistician can seldom or never make experiments for himself, he has to accept the data of daily experience, and discuss as best he can the relations of a whole group of changes; he cannot, like the physicist, narrow down the issue to the effect of one variation at a time. The problems of statistics are in this sense far more complex than the problems of physics.
Udny Yule
In 'On the Theory of Correlation', Journal of the Royal Statistical Society (Dec 1897), 60, 812, as cited in Stephen M. Stigler, The History of Statistics: The Measurement of Uncertainty Before 1900 (1986), 348.
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The life and soul of science is its practical application, and just as the great advances in mathematics have been made through the desire of discovering the solution of problems which were of a highly practical kind in mathematical science, so in physical science many of the greatest advances that have been made from the beginning of the world to the present time have been made in the earnest desire to turn the knowledge of the properties of matter to some purpose useful to mankind.
From 'Electrical Units of Measurement', a lecture delivered at the Institution of Civil Engineers, London (3 May 1883), Popular Lectures and Addresses Vol. 1 (1891), 86-87.
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The major credit I think Jim and I deserve ... is for selecting the right problem and sticking to it. It's true that by blundering about we stumbled on gold, but the fact remains that we were looking for gold. Both of us had decided, quite independently of each other, that the central problem in molecular biology was the chemical structure of the gene. ... We could not see what the answer was, but we considered it so important that we were determined to think about it long and hard, from any relevant point of view.
What Mad Pursuit (1990), 74-75.
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The meaning of time has become terribly problematic in contemporary physics. The situation is so uncomfortable that by far the best thing to do is declare oneself an agnostic.
Quoted by Tim Folger in 'Newsflash: Time May Not Exist', Discover Magazine (Jun 2007).
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The most important and urgent problems of the technology of today are no longer the satisfactions of the primary needs or of archetypal wishes, but the reparation of the evils and damages by technology of yesterday.
Innovations: Scientific Technological and Social (1970), 9.
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The mystery of life is certainly the most persistent problem ever placed before the thought of man. There is no doubt that from the time humanity began to think it has occupied itself with the problem of its origin and its future which undoubtedly is the problem of life. The inability of science to solve it is absolute. This would be truly frightening were it not for faith.
Address (10 Sep 1934) to the International Congress of Electro-Radio Biology, Venice. In Associated Press, 'Life a Closed Book, Declares Marconi', New York Times (11 Sep 1934), 15.
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The next decade will perhaps raise us a step above despair to a cleaner, clearer wisdom and biology cannot fail to help in this. As we become increasingly aware of the ethical problems raised by science and technology, the frontiers between the biological and social sciences are clearly of critical importance—in population density and problems of hunger, psychological stress, pollution of the air and water and exhaustion of irreplaceable resources.
As quoted in 'H. Bentley Glass', New York Times (12 Jan 1970), 96.
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The only difference between a problem and a solution is that people understand the solution.
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The open secret of real success is to throw your whole personality into your problem.
How to Solve it: A New Aspect of Mathematical Method (1957), 207.
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The prediction of nuclear winter is drawn not, of course, from any direct experience with the consequences of global nuclear war, but rather from an investigation of the governing physics. (The problem does not lend itself to full experimental verification—at least not more than once.)[co-author with American atmospheric chemist Richard P. Turco (1943- )]
A Path Where No Man Thought: Nuclear Winter and the End of the Arms Race (1990), 26.
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The present rate of progress [in X-ray crystallography] is determined, not so much by the lack of problems to investigate or the limited power of X-ray analysis, as by the restricted number of investigators who have had a training in the technique of the new science, and by the time it naturally takes for its scientific and technical importance to become widely appreciated.
Concluding remark in Lecture (1936) on 'Forty Years of Crystal Physics', collected in Needham and Pagel (eds.) in Background to Modern Science: Ten Lectures at Cambridge Arranged by the History of Science Committee, (1938), 89.
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The real achievement in discoveries … is seeing an analogy where no one saw one before. .. The essence of discovery is that unlikely marriage of … previously unrelated forms of reference or universes of discourse, whose union will solve the previously insoluble problem.
Arthur Koestler, Act of Creation (1964), 201.
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The real value of science is in the getting, and those who have tasted the pleasure of discovery alone know what science is. A problem solved is dead. A world without problems to be solved would be devoid of science.
In Matter and Energy (1912), 18.
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The same society which receives the rewards of technology must, as a cooperating whole, take responsibility for control. To deal with these new problems will require a new conservation. We must not only protect the countryside and save it from destruction, we must restore what has been destroyed and salvage the beauty and charm of our cities. Our conservation must be not just the classic conservation of protection and development, but a creative conservation of restoration and innovation. Its concern is not with nature alone, but with the total relation between man and the world around him. Its object is not just man's welfare, but the dignity of man's spirit.
In his 'Message to Congress on Conservation and Restoration of Natural Beauty' written to Congress (8 Feb 1965). It was a broad initiative aimed at beautifying America, guaranteeing water and air quality, and preserving natural areas. In Lyndon B. Johnson: Containing the Public Messages, Speeches, and Statements of the President (1965), Vol.1, 156. United States. President (1963-1969 : Johnson), Lyndon Baines Johnson, United States. Office of the Federal Register - 1970
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The scientific method of examining facts is not peculiar to one class of phenomena and to one class of workers; it is applicable to social as well as to physical problems, and we must carefully guard ourselves against supposing that the scientific frame of mind is a peculiarity of the professional scientist.
The Grammar of Science (1900), 6.
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The scientist, by the very nature of his commitment, creates more and more questions, never fewer. Indeed the measure of our intellectual maturity, one philosopher suggests, is our capacity to feel less and less satisfied with our answers to better problems.
Becoming: Basic Considerations for a Psychology of Personality (1955), 67.
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The secret of science is to ask the right question, and it is the choice of problem more than anything else that marks the man of genius in the scientific world.
As quoted in the Inaugural Sir Henry Tizard Memorial Lecture at Westminster School (21 Feb 1963) by Sir George Thomson 'Research in Theory and Practice'. As cited Ray Corrigan, Digital Decision Making: Back to the Future (2007), 142.
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The situation with regard to insulin is particularly clear. In many parts of the world diabetic children still die from lack of this hormone. ... [T]hose of us who search for new biological facts and for new and better therapeutic weapons should appreciate that one of the central problems of the world is the more equitable distribution and use of the medical and nutritional advances which have already been established. The observations which I have recently made in parts of Africa and South America have brought this fact very forcible to my attention.
'Studies on Diabetes and Cirrhosis', Proceedings, American Philosophical Society (1952) 96, No. 1, 29.
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The skeptic does not mean him who doubts, but him who investigates or researches, as opposed to him who asserts and thinks that he has found. The one is the man who studies the problem and the other is the man who gives us a formula, correct or incorrect, as the solution of it.
'My Religion', Essays and Soliloquies, translated by John Ernest Crawford Flitch (1925), 56. In Robert Andrews, The Columbia Dictionary of Quotations (1993), 844:9.
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The suppression of crime is not entirely a legal question. It is a problem for the physician, the economist and the lawyer. We, as physicians, should encourage the criminologist by lending to him the surgeon, the internist and all of the rest of the resources of medicine, just as we have done in the case of the flea man, the fly man, the mosquito man, the bed-bug man and all the other ologists.
From paper read at the Section on State Medicine and Public Hygiene of the State Medical Association of Texas at El Paso (11 May 1922), 'The Use Of Scopolamine In Criminology', published in Texas State Journal of Medicine (Sep 1922). Reprinted in The American Journal of Police Science (Jul-Aug 1931), 2, No. 4, 328.
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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 from various sides.
In How to Solve It: A New Aspect of Mathematical Method (2004), 77
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The transition from a paradigm in crisis to a new one from which a new tradition of normal science can emerge is far from a cumulative process, one achieved by an articulation or extension of the old paradigm. Rather it is a reconstruction of the field from new fundamentals, a reconstruction that changes some of the field's most elementary theoretical generalizations as well as many of its paradigm methods and applications. During the transition period there will be a large but never complete overlap between the problems that can be solved by the old and by the new paradigm. But there will also be a decisive difference in the modes of solution. When the transition is complete, the profession will have changed its view of the field, its methods, and its goals.
The Structure of Scientific Revolutions (1962), 84-5.
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The Unexpected stalks a farm in big boots like a vagrant bent on havoc. Not every farmer is an inventor, but the good ones have the seeds of invention within them. Economy and efficiency move their relentless tinkering and yet the real motive often seems to be aesthetic. The mind that first designed a cutter bar is not far different from a mind that can take the intractable steel of an outsized sickle blade and make it hum in the end. The question is how to reduce the simplicity that constitutes a problem (“It's simple; it's broke.”) to the greater simplicity that constitutes a solution.
In Making Hay (2003), 33-34.
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There are problems to whose solution I would attach an infinitely greater importance than to those of mathematics, for example touching ethics, or our relation to God, or concerning our destiny and our future; but their solution lies wholly beyond us and completely outside the province of science.
Quoted in J.R. Newman, The World of Mathematics (1956), 314.
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There are still psychologists who, in a basic misunderstanding, think that gestalt theory tends to underestimate the role of past experience. Gestalt theory tries to differentiate between and-summative aggregates, on the one hand, and gestalten, structures, on the other, both in sub-wholes and in the total field, and to develop appropriate scientific tools for investigating the latter. It opposes the dogmatic application to all cases of what is adequate only for piecemeal aggregates. The question is whether an approach in piecemeal terms, through blind connections, is or is not adequate to interpret actual thought processes and the role of the past experience as well. Past experience has to be considered thoroughly, but it is ambiguous in itself; so long as it is taken in piecemeal, blind terms it is not the magic key to solve all problems.
In Productive Thinking (1959), 65.
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There are, at present, fundamental problems in theoretical physics … the solution of which … will presumably require a more drastic revision of our fundmental concepts than any that have gone before. Quite likely, these changes will be so great that it will be beyond the power of human intelligence to get the necessary new ideas by direct attempts to formulate the experimental data in mathematical terms. The theoretical worker in the future will, therefore, have to proceed in a more direct way. The most powerful method of advance that can be suggested at present is to employ all the resources of pure mathematics in attempts to perfect and generalize the mathematical formalism that forms the existing basis of theoretical physics, and after each success in this direction, to try to interpret the new mathematical features in terms of physical entities.
At age 28.
Proceedings of the Royal Society (1931), A133, 60. In A. Pais, 'Playing With Equations, the Dirac Way'. Behram N. Kursunoglu (Ed.) and Eugene Paul Wigner (Ed.), Paul Adrien Maurice Dirac: Reminiscences about a Great Physicist (1990), 109.
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There is no counting the unsolved problems of Natural History.
In Riddles of Science (1932), 102.
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There was yet another disadvantage attaching to the whole of Newton’s physical inquiries, ... the want of an appropriate notation for expressing the conditions of a dynamical problem, and the general principles by which its solution must be obtained. By the labours of LaGrange, the motions of a disturbed planet are reduced with all their complication and variety to a purely mathematical question. It then ceases to be a physical problem; the disturbed and disturbing planet are alike vanished: the ideas of time and force are at an end; the very elements of the orbit have disappeared, or only exist as arbitrary characters in a mathematical formula
Address to the Mechanics Institute, 'An Address on the Genius and Discoveries of Sir Isaac Newton' (1835), excerpted in paper by Luis M. Laita, Luis de Ledesma, Eugenio Roanes-Lozano and Alberto Brunori, 'George Boole, a Forerunner of Symbolic Computation', collected in John A. Campbell and Eugenio Roanes-Lozano (eds.), Artificial Intelligence and Symbolic Computation: International Conference AISC 2000 (2001), 3.
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They think that differential equations are not reality. Hearing some colleagues speak, it's as though theoretical physics was just playing house with plastic building blocks. This absurd idea has gained currency, and now people seem to feel that theoretical physicists are little more than dreamers locked away ivory towers. They think our games, our little houses, bear no relation to their everyday worries, their interests, their problems, or their welfare. But I'm going to tell you something, and I want you to take it as a ground rule for this course. From now on I will be filling this board with equations. ... And when I'm done, I want you to do the following: look at those numbers, all those little numbers and Greek letters on the board, and repeat to yourselves, “This is reality,” repeat it over and over.
Zig Zag, trans. Lisa Dillman (2008), 63.
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Think of a single problem confronting the world today. Disease, poverty, global warming… If the problem is going to be solved, it is science that is going to solve it. Scientists tend to be unappreciated in the world at large, but you can hardly overstate the importance of the work they do. If anyone ever cures cancer, it will be a guy with a science degree. Or a woman with a science degree.
Quoted in Max Davidson, 'Bill Bryson: Have faith, science can solve our problems', Daily Telegraph (26 Sep 2010)
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This integrative action in virtue of which the nervous system unifies from separate organs an animal possessing solidarity, an individual, is the problem before us.
The Integrative Action of the Nervous System (1906), 2.
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Through the discovery of Buchner, Biology was relieved of another fragment of mysticism. The splitting up of sugar into CO2 and alcohol is no more the effect of a 'vital principle' than the splitting up of cane sugar by invertase. The history of this problem is instructive, as it warns us against considering problems as beyond our reach because they have not yet found their solution.
The Dynamics of Living Matter (1906), 22.
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To solve a problem is to create new problems, new knowledge immediately reveals new areas of ignorance, and the need for new experiments. At least, in the field of fast reactions, the experiments do not take very long to perform.
'Flash Photolysis and Some of its Applications', Nobel Lecture (11 Dec 1967). In Nobel Lectures: Chemistry 1963-1970 (1972), 261.
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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.
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True rigor is productive, being distinguished in this from another rigor which is purely formal and tiresome, casting a shadow over the problems it touches.
From address to the section of Algebra and Analysis, International Congress of Arts and Sciences, St. Louis (22 Sep 1904), 'On the Development of Mathematical Analysis and its Relation to Certain Other Sciences,' as translated by M.W. Haskell in Bulletin of the American Mathematical Society (May 1905), 11, 417.
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Truth and falsity, indeed understanding, is not necessarily something purely intellectual, remote from feelings and attitudes. ... It is in the total conduct of men rather than in their statements that truth or falsehood lives, more in what a man does, in his real reaction to other men and to things, in his will to do them justice, to live at one with them. Here lies the inner connection between truth and justice. In the realm of behavior and action, the problem recurs as to the difference between piece and part.
From 'On Truth', collected in Mary Henle (ed.), Documents of Gestalt Psychology (1961), 28.
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Typical of the fundamental scientific problems whose solution should lead to important industrial consequences are, for example, the release of atomic energy, which experiment has shown to exist in quantities millions of times greater than is liberated by combustion.
An early speculation on using the amount of energy that could be released from uranium atoms. In a letter to Henry Ford (18 May 1931). He recorded earlier thoughts on the subject in his Research Notebook, entry for 23 Jul 1930, in Arthur H. Compton Notebooks, Washington University, St. Louis, and AIP. Cited by Stanley Coben, in 'The Scientific Establishment and the Transmission of Quantum Mechanics to the United States, 1919-32', The American Historical Review (Apr 1971), 76, No. 2, 466.
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We academic scientists move within a certain sphere, we can go on being useless up to a point, in the confidence that sooner or later some use will be found for our studies. The mathematician, of course, prides himself on being totally useless, but usually turns out to be the most useful of the lot. He finds the solution but he is not interested in what the problem is: sooner or later, someone will find the problem to which his solution is the answer.
'Concluding Remarks', Proceedings of the Royal Society of London, Series A, A Discussion of New Materials, 1964, 282, 152-3.
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We call the one side [of humanity] religion, and we call the other science. Religion is always right. ... Science is always wrong; it is the very artifice of men. Science can never solve one problem without raising ten more problems.
Speech at the Einstein Dinner, Savoy Hotel, London (28 Oct 1930). Reproduced in George Bernard Shaw and Warren Sylvester Smith (ed.), The Religious Speeches of George Bernard Shaw (1963), 83.
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We called the new [fourth] quark the “charmed quark” because we were pleased, and fascinated by the symmetry it brought to the subnuclear world. “Charm” also means a “a magical device to avert evil,” and in 1970 it was realized that the old three quark theory ran into very serious problems. ... As if by magic the existence of the charmed quark would [solve those problems].
From asppearance in the BBC-TV program written by Nigel Calder, 'The Key to the Universe,' (27 Jan 1977). As cited in Arthur Lewis Caso, 'The Production of New Scientific Terms', American Speech (Summer 1980), 55, No. 2, 102.
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What is important is the gradual development of a theory, based on a careful analysis of the ... facts. ... Its first applications are necessarily to elementary problems where the result has never been in doubt and no theory is actually required. At this early stage the application serves to corroborate the theory. The next stage develops when the theory is applied to somewhat more complicated situations in which it may already lead to a certain extent beyond the obvious and familiar. Here theory and application corroborate each other mutually. Beyond lies the field of real success: genuine prediction by theory. It is well known that all mathematized sciences have gone through these successive stages of evolution.
'Formulation of the Economic Problem' in Theory of Games and Economic Behavior (1964), 8. Reprinted in John Von Neumann, F. Bródy (ed.) and Tibor Vámos (ed.), The Neumann Compendium (2000), 416.
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When I am working on a problem, I never think about beauty … but when I have finished, if the solution is not beautiful, I know it is wrong.
Quoted in David J. Darling, The Universal Book of Mathematics (2004). 34.
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When the difficulty of a problem lies only in finding out what follows from certain fixed premises, mathematical methods furnish invaluable wings for flying over intermediate obstructions.
From The Economic Theory of the Location of Railways (1887, 1914), viii.
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Whenever the essential nature of things is analysed by the intellect, it must seem absurd or paradoxical. This has always been recognized by the mystics, but has become a problem in science only very recently.
In The Tao of Physics (1975), 50.
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Where should I start? Start from the statement of the problem. ... What can I do? Visualize the problem as a whole as clearly and as vividly as you can. ... What can I gain by doing so? You should understand the problem, familiarize yourself with it, impress its purpose on your mind.
How to Solve It: a New Aspect of Mathematical Method (1957), 33.
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While knowledge can create problems, it is not through ignorance that we can solve them.
In Asimov's New Guide to Science (1984), 15.
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Why does man behave like perfect idiot? This is the problem I wish to deal with.
The Crazy Ape (1970), 11.
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Why is it so easy to acquire the solutions of past problems and so difficult to solve current ones
(Attributed ??) This quote is often seen, but without a citation, even on the official Marshall McLuhan website. If you known a primary print source, please contact Webmaster.
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Will it be possible to solve these problems? It is certain that nobody has thus far observed the transformation of dead into living matter, and for this reason we cannot form a definite plan for the solution of this problem of transformation. But we see that plants and animals during their growth continually transform dead into living matter, and that the chemical processes in living matter do not differ in principle from those in dead matter. There is, therefore, no reason to predict that abiogenesis is impossible, and I believe that it can only help science if the younger investigators realize that experimental abiogenesis is the goal of biology.
The Dynamics of Living Matter (1906), 223.
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Willis Rodney Whitney ... once compared scientific research to a bridge being constructed by a builder who was fascinated by the construction problems involved. Basic research, he suggested, is such a bridge built wherever it strikes the builder's fancy—wherever the construction problems seem to him to be most challenging. Applied research, on the other hand, is a bridge built where people are waiting to get across the river. The challenge to the builder's ingenuity and skill, Whitney pointed out, can be as great in one case as the other.
'Willis Rodney Whitney', National Academy of Sciences, Biographical Memoirs (1960), 351.
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Without a commitment to science and rationality in its proper domain, there can be no solution to the problems that engulf us. Still, the Yahoos never rest.
Ever Since Darwin (1980),146.
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You can't really discover the most interesting conflicts and problems in a subject until you've tried to write about them. At that point, one discovers discontinuities in the data, perhaps, or in one's own thinking; then the act of writing forces you to work harder to resolve these contradictions.
From Robert S. Grumet, 'An Interview with Anthony F. C. Wallace', Ethnohistory (Winter 1998), 45, No. 1, 109.
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You propound a complicated arithmetical problem: say cubing a number containing four digits. Give me a slate and half an hour's time, and I can produce a wrong answer.
Cashel Byron's Profession (1886, 1901), xxiii.
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[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.
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[It] is not the nature of things for any one man to make a sudden, violent discovery; science goes step by step and every man depends on the work of his predecessors. When you hear of a sudden unexpected discovery—a bolt from the blue—you can always be sure that it has grown up by the influence of one man or another, and it is the mutual influence which makes the enormous possibility of scientific advance. Scientists are not dependent on the ideas of a single man, but on the combined wisdom of thousands of men, all thinking of the same problem and each doing his little bit to add to the great structure of knowledge which is gradually being erected.
Concluding remark in Lecture ii (1936) on 'Forty Years of Physics', revised and prepared for publication by J.A. Ratcliffe, collected in Needham and Pagel (eds.), Background to Modern Science: Ten Lectures at Cambridge Arranged by the History of Science Committee, (1938), 73-74. Note that the words as prepared for publication may not be verbatim as spoken in the original lecture by the then late Lord Rutherford.
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[My father] advised me to sit every few months in my reading chair for an entire evening, close my eyes and try to think of new problems to solve. I took his advice very seriously and have been glad ever since that he did.
Alvarez: Adventures of a Physicist (1987), 58.
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[The purpose of flight research] is to separate the real from the imagined problems and to make known the overlooked and the unexpected.
Description of the purpose of the X-15 program given in a meeting at the Langley Research Center (Oct 1956). Quoted in Michael H. Gorn, Expanding the Envelope (2001), 3.
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… our “Physick” and “Anatomy” have embraced such infinite varieties of being, have laid open such new worlds in time and space, have grappled, not unsuccessfully, with such complex problems, that the eyes of Vesalius and of Harvey might be dazzled by the sight of the tree that has grown out of their grain of mustard seed.
A Lay Sermon, delivered at St. Martin's Hall (7 Jan 1866), 'On the Advisableness of Improving Natural Knowledge', published in The Fortnightly Review (1866), Vol. 3, 629.
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Carl Sagan Thumbnail 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) -- Carl Sagan
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- 100 -
Sophie Germain
Gertrude Elion
Ernest Rutherford
James Chadwick
Marcel Proust
William Harvey
Johann Goethe
John Keynes
Carl Gauss
Paul Feyerabend
- 90 -
Antoine Lavoisier
Lise Meitner
Charles Babbage
Ibn Khaldun
Euclid
Ralph Emerson
Robert Bunsen
Frederick Banting
Andre Ampere
Winston Churchill
- 80 -
John Locke
Bronislaw Malinowski
Bible
Thomas Huxley
Alessandro Volta
Erwin Schrodinger
Wilhelm Roentgen
Louis Pasteur
Bertrand Russell
Jean Lamarck
- 70 -
Samuel Morse
John Wheeler
Nicolaus Copernicus
Robert Fulton
Pierre Laplace
Humphry Davy
Thomas Edison
Lord Kelvin
Theodore Roosevelt
Carolus Linnaeus
- 60 -
Francis Galton
Linus Pauling
Immanuel Kant
Martin Fischer
Robert Boyle
Karl Popper
Paul Dirac
Avicenna
James Watson
William Shakespeare
- 50 -
Stephen Hawking
Niels Bohr
Nikola Tesla
Rachel Carson
Max Planck
Henry Adams
Richard Dawkins
Werner Heisenberg
Alfred Wegener
John Dalton
- 40 -
Pierre Fermat
Edward Wilson
Johannes Kepler
Gustave Eiffel
Giordano Bruno
JJ Thomson
Thomas Kuhn
Leonardo DaVinci
Archimedes
David Hume
- 30 -
Andreas Vesalius
Rudolf Virchow
Richard Feynman
James Hutton
Alexander Fleming
Emile Durkheim
Benjamin Franklin
Robert Oppenheimer
Robert Hooke
Charles Kettering
- 20 -
Carl Sagan
James Maxwell
Marie Curie
Rene Descartes
Francis Crick
Hippocrates
Michael Faraday
Srinivasa Ramanujan
Francis Bacon
Galileo Galilei
- 10 -
Aristotle
John Watson
Rosalind Franklin
Michio Kaku
Isaac Asimov
Charles Darwin
Sigmund Freud
Albert Einstein
Florence Nightingale
Isaac Newton