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Toutes les fois que dans une équation finale on trouve deux quantités inconnues, on a un lieu, l'extrémité de l'une d’elles décrivant une ligne droite ou courbe. La ligne droite est simple et unique dans son genre; les espèces des courbes sont en nombre indéfini, cercle, parabole, hyperbole, ellipse, etc.
Whenever two unknown magnitudes appear in a final equation, we have a locus, the extremity of one of the unknown magnitudes describing a straight line or a curve. The straight line is simple and unique; the classes of curves are indefinitely many,—circle, parabola, hyperbola, ellipse, etc.
Introduction aux Lieux Plans et Solides (1679) collected in OEuvres de Fermat (1896), Vol. 3, 85. Introduction to Plane and Solid Loci, as translated by Joseph Seidlin in David E. Smith(ed.)A Source Book in Mathematics (1959), 389. Alternate translation using Google Translate: “Whenever in a final equation there are two unknown quantities, there is a locus, the end of one of them describing a straight line or curve. The line is simple and unique in its kind, species curves are indefinite in number,—circle, parabola, hyperbola, ellipse, etc.”
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A process which led from the amoeba to man appeared to the philosophers to be obviously a progress—though whether the amoeba would agree with this opinion is not known.
From 'Current Tendencies', delivered as the first of a series of Lowell Lectures in Boston (Mar 1914). Collected in Our Knowledge of the External World (1914), 12.
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A star is drawing on some vast reservoir of energy by means unknown to us. This reservoir can scarcely be other than the subatomic energy which, it is known exists abundantly in all matter; we sometimes dream that man will one day learn how to release it and use it for his service. The store is well nigh inexhaustible, if only it could be tapped. There is sufficient in the Sun to maintain its output of heat for 15 billion years.
Address to the British Association in Cardiff, (24 Aug 1920), in Observatory (1920), 43 353. Reprinted in Foreward to Arthur S. Eddington, The Internal Constitution of the Stars (1926, 1988), x.
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All Nature is but Art, unknown to thee;
All Chance, Direction, which thou canst not see;
All Discord, Harmony, not understood;
All partial Evil, universal Good:
And, spite of Pride, in erring Reason's spite,
One truth is clear, 'Whatever IS, is RIGHT.'
'An Essay on Man' (1733-4), Epistle I. In John Butt (ed.), The Poems of Alexander Pope (1965), 515.
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Astronomers have built telescopes which can show myriads of stars unseen before; but when a man looks through a tear in his own eye, that is a lens which opens reaches into the unknown, and reveals orbs which no telescope, however skilfully constructed, could do.
Life Thoughts (1858), 20.
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But I think that in the repeated and almost entire changes of organic types in the successive formations of the earth—in the absence of mammalia in the older, and their very rare appearance (and then in forms entirely. unknown to us) in the newer secondary groups—in the diffusion of warm-blooded quadrupeds (frequently of unknown genera) through the older tertiary systems—in their great abundance (and frequently of known genera) in the upper portions of the same series—and, lastly, in the recent appearance of man on the surface of the earth (now universally admitted—in one word, from all these facts combined, we have a series of proofs the most emphatic and convincing,—that the existing order of nature is not the last of an uninterrupted succession of mere physical events derived from laws now in daily operation: but on the contrary, that the approach to the present system of things has been gradual, and that there has been a progressive development of organic structure subservient to the purposes of life.
'Address to the Geological Society, delivered on the Evening of the 18th of February 1831', Proceedings of the Geological Society (1834), 1, 305-6.
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For myself, I like a universe that, includes much that is unknown and, at the same time, much that is knowable. A universe in which everything is known would be static and dull, as boring as the heaven of some weak-minded theologians. A universe that is unknowable is no fit place for a thinking being. The ideal universe for us is one very much like the universe we inhabit. And I would guess that this is not really much of a coincidence.
'Can We know the Universe?' in M. Gardner (ed.), The Sacred Beetle and Other Great Essays in Science (1985), 109.
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Forces of nature act in a mysterious manner. We can but solve the mystery by deducing the unknown result from the known results of similar events.
In The Words of Gandhi (2001), 87.
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If a given scientist had not made a given discovery, someone else would have done so a little later. Johann Mendel dies unknown after having discovered the laws of heredity: thirty-five years later, three men rediscover them. But the book that is not written will never be written. The premature death of a great scientist delays humanity; that of a great writer deprives it.
Pensées d'un Biologiste (1939). Translated in The Substance of Man (1962), 89.
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If I go out into nature, into the unknown, to the fringes of knowledge, everything seems mixed up and contradictory, illogical, and incoherent. This is what research does; it smooths out contradictions and makes things simple, logical, and coherent.
In 'Dionysians and Apollonians', Science (2 Jun 1972), 176, 966. Reprinted in Mary Ritchie Key, The Relationship of Verbal and Nonverbal Communication (1980), 318.
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If Louis Pasteur were to come out of his grave because he heard that the cure for cancer still had not been found, NIH would tell him, “Of course we'll give you assistance. Now write up exactly what you will be doing during the three years of your grant.” Pasteur would say, “Thank you very much,” and would go back to his grave. Why? Because research means going into the unknown. If you know what you are going to do in science, then you are stupid! This is like telling Michelangelo or Renoir that he must tell you in advance how many reds and how many blues he will buy, and exactly how he will put those colors together.
Interview for Saturday Evening Post (Jan/Feb 1981), 30.
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In the vast cosmical changes, the universal life comes and goes in unknown quantities ... sowing an animalcule here, crumbling a star there, oscillating and winding, ... entangling, from the highest to the lowest, all activities in the obscurity of a dizzying mechanism, hanging the flight of an insect upon the movement of the earth... Enormous gearing, whose first motor is the gnat, and whose last wheel is the zodiac.
Victor Hugo and Charles E. Wilbour (trans.), Les Misérables (1862), 41.
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It is imperative in the design process to have a full and complete understanding of how failure is being obviated in order to achieve success. Without fully appreciating how close to failing a new design is, its own designer may not fully understand how and why a design works. A new design may prove to be successful because it has a sufficiently large factor of safety (which, of course, has often rightly been called a “factor of ignorance”), but a design's true factor of safety can never be known if the ultimate failure mode is unknown. Thus the design that succeeds (ie, does not fail) can actually provide less reliable information about how or how not to extrapolate from that design than one that fails. It is this observation that has long motivated reflective designers to study failures even more assiduously than successes.
In Design Paradigms: Case Histories of Error and Judgment in Engineering (1994), 31. books.google.comHenry Petroski - 1994
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It may be observed of mathematicians that they only meddle with such things as are certain, passing by those that are doubtful and unknown. They profess not to know all things, neither do they affect to speak of all things. What they know to be true, and can make good by invincible arguments, that they publish and insert among their theorems. Of other things they are silent and pass no judgment at all, chusing [choosing] rather to acknowledge their ignorance, than affirm anything rashly. They affirm nothing among their arguments or assertions which is not most manifestly known and examined with utmost rigour, rejecting all probable conjectures and little witticisms. They submit nothing to authority, indulge no affection, detest subterfuges of words, and declare their sentiments, as in a Court of Judicature [Justice], without passion, without apology; knowing that their reasons, as Seneca testifies of them, are not brought to persuade, but to compel.
Mathematical Lectures (1734), 64.
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Mankind is drawn to the heavens for the same reason we were once drawn into unknown lands and across the open sea. We choose to explore space because doing so improves our lives, and lifts our national spirit. So let us continue the journey.
Conclusion of speech, NASA Headquarters (14 Jan 2004). In Office of the Federal Register (U.S.) Staff (eds.), Public Papers of the Presidents of the United States, George W. Bush (2007), 59.
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Modern science has been a voyage into the unknown, with a lesson in humility waiting at every stop. Many passengers would rather have stayed home.
Pale Blue Dot: A Vision of the Human Future in Space (1994), 23.
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Necessity is not the mother of invention. Knowledge and experiment are its parents. It sometimes happens that successful search is made for unknown materials to fill well-recognized and predetermined requirements. It more often happens that the acquirement of knowledge of the previously unknown properties of a material suggests its trial for some new use. These facts strongly indicate the value of knowledge of properties of materials and indicate a way for research.
Quoted in Guy Suits, 'Willis Rodney Whitney', National Academy of Sciences, Biographical Memoirs (1960), 357.
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Nomenclature, the other foundation of botany, should provide the names as soon as the classification is made... If the names are unknown knowledge of the things also perishes... For a single genus, a single name.
Philosophia Botanica (1751), aphorism 210. Trans. Frans A. Stafleu, Linnaeus and the Linnaeans: The Spreading of their Ideas in Systematic Botany, 1735-1789 (1971), 80.
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Now when you cut a forest, an ancient forest in particular, you are not just removing a lot of big trees and a few birds fluttering around in the canopy. You are drastically imperiling a vast array of species within a few square miles of you. The number of these species may go to tens of thousands. ... Many of them are still unknown to science, and science has not yet discovered the key role undoubtedly played in the maintenance of that ecosystem, as in the case of fungi, microorganisms, and many of the insects.
On Human Nature (2000). In John H. Morgan, Naturally Good (2005), 252.
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Reports that say that something hasn't happened are always interesting to me, because as we know, there are known knowns, there are things we know we know.
We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns—the ones we don't know we don't know. ... And each year, we discover a few more of those unknown unknowns.
Answering a question concerning Iraq, on the facts about weapons of mass destruction, at a Press Conference, NATO Headquarters, Brussels, Belgium (6 June 2002). From transcript on U.S. Department of Defense website.
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Science has thus, most unexpectedly, placed in our hands a new power of great but unknown energy. It does not wake the winds from their caverns; nor give wings to water by the urgency of heat; nor drive to exhaustion the muscular power of animals; nor operate by complicated mechanism; nor summon any other form of gravitating force, but, by the simplest means—the mere contact of metallic surfaces of small extent, with feeble chemical agents, a power everywhere diffused through nature, but generally concealed from our senses, is mysteriously evolved, and by circulation in insulated wires, it is still more mysteriously augmented, a thousand and a thousand fold, until it breaks forth with incredible energy.
Comment upon 'The Notice of the Electro-Magnetic Machine of Mr. Thomas Davenport, of Brandon, near Rutland, Vermont, U.S.', The Annals of Electricity, Magnetism, & Chemistry; and Guardian of Experimental Science (1838), 2, 263.
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Something unknown is doing we don't know what—that is what our theory amounts to.
[Expressing the quantum theory description of an electron has no familiar conception of a real form.]
The Nature Of The Physical World (1928), 291.
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The contents of this section will furnish a very striking illustration of the truth of a remark, which I have more than once made in my philosophical writings, and which can hardly be too often repeated, as it tends greatly to encourage philosophical investigations viz. That more is owing to what we call chance, that is, philosophically speaking, to the observation of events arising from unknown causes, than to any proper design, or pre-conceived theory in this business. This does not appear in the works of those who write synthetically upon these subjects; but would, I doubt not, appear very strikingly in those who are the most celebrated for their philosophical acumen, did they write analytically and ingenuously.
'On Dephlogisticated Air, and the Constitution of the Atmosphere', in The Discovery of Oxygen, Part I, Experiments by Joseph Priestley 1775 (Alembic Club Reprint, 1894), 5.
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The history of this paper suggests that highly speculative investigations, especially by an unknown author, are best brought before the world through some other channel than a scientific society, which naturally hesitates to admit into its printed records matters of uncertain value. Perhaps one may go further and say that a young author who believes himself capable of great things would usually do well to secure the favourable recognition of the scientific world by work whose scope is limited and whose value is easily judged, before embarking upon higher flights.
'On the Physics of Media that are Composed of Free and Perfectly Elastic Molecules in a State of Motion', Philosophical Transactions (1892), 183, 560.
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The known is finite, the unknown infinite; spiritually we find ourselves on a tiny island in the middle of a boundless ocean of the inexplicable. It is our task, from generation to generation, to drain a small amount of additional land.
As given in Herbert and W. Roesky and Klaud Möckel, translated from the original German by T.N. Mitchell and W.E. Russey, Chemical Curiosities: Spectacular Experiments and Inspired Quotes (1996), 212. It is a restatement of an original quote from concluding remarks to a chapter by Thomas Huxley, 'On the Reception of the ‘Origin of Species’', the last chapter in Charles Darwin and Francis Darwin (ed.), The Life and Letters of Charles Darwin (1887), Vol. 1, 557. Webmaster suggests, the original Huxley quote was translated for the original German text, and when that was translated for the English edition, the quote morphed into into the form above.
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The man in the street will, therefore, twist the statement that the scientist has come to the end of meaning into the statement that the scientist has penetrated as far as he can with the tools at his command, and that there is something beyond the ken of the scientist. This imagined beyond, which the scientist has proved he cannot penetrate, will become the playground of the imagination of every mystic and dreamer. The existence of such a domain will be made the basis of an orgy of rationalizing. It will be made the substance of the soul; the spirits of the dead will populate it; God will lurk in its shadows; the principle of vital processes will have its seat here; and it will be the medium of telepathic communication. One group will find in the failure of the physical law of cause and effect the solution of the age-long problem of the freedom of the will; and on the other hand the atheist will find the justification of his contention that chance rules the universe.
Reflections of a Physicist (1950),102-3.
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The only level of the hierarchy [of biological communities] that is both necessary and sufficient to meet all objectives is the ecosystem or some higher-level approach. The strategy selected should not only ensure the conservation of spotted owls, but all the intricate linkages that are associated with natural populations of spotted owls in naturally functioning ecosystems. Many of these are as yet unknown.
In The Fragmented Forest: Island Biogeography Theory and the Preservation of Biotic Diversity (1984), 107.
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The presentation of mathematics where you start with definitions, for example, is simply wrong. Definitions aren't the places where things start. Mathematics starts with ideas and general concepts, and then definitions are isolated from concepts. Definitions occur somewhere in the middle of a progression or the development of a mathematical concept. The same thing applies to theorems and other icons of mathematical progress. They occur in the middle of a progression of how we explore the unknown.
Interview for website of the Mathematical Association of America.
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The process of discovery is very simple. An unwearied and systematic application of known laws to nature, causes the unknown to reveal themselves. Almost any mode of observation will be successful at last, for what is most wanted is method.
A Week on the Concord and Merrimack Rivers (1873), 384.
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The regularity with which we conclude that further advances in a particular field are impossible seems equaled only by the regularity with which events prove that we are of too limited vision. And it always seems to be those who have the fullest opportunity to know who are the most limited in view. What, then, is the trouble? I think that one answer should be: we do not realize sufficiently that the unknown is absolutely infinite, and that new knowledge is always being produced.
Quoted in Guy Suits, 'Willis Rodney Whitney', National Academy of Sciences, Biographical Memoirs (1960), 357.
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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 theory of probability is the only mathematical tool available to help map the unknown and the uncontrollable. It is fortunate that this tool, while tricky, is extraordinarily powerful and convenient.
The Fractal Geometry of Nature (1977), 201.
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The value the world sets upon motives is often grossly unjust and inaccurate. Consider, for example, two of them: mere insatiable curiosity and the desire to do good. The latter is put high above the former, and yet it is the former that moves some of the greatest men the human race has yet produced: the scientific investigators. What animates a great pathologist? Is it the desire to cure disease, to save life? Surely not, save perhaps as an afterthought. He is too intelligent, deep down in his soul, to see anything praiseworthy in such a desire. He knows by life-long observation that his discoveries will do quite as much harm as good, that a thousand scoundrels will profit to every honest man, that the folks who most deserve to be saved will probably be the last to be saved. No man of self-respect could devote himself to pathology on such terms. What actually moves him is his unquenchable curiosity–his boundless, almost pathological thirst to penetrate the unknown, to uncover the secret, to find out what has not been found out before. His prototype is not the liberator releasing slaves, the good Samaritan lifting up the fallen, but the dog sniffing tremendously at an infinite series of rat-holes.
Prejudices (1923), 269-70.
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To what part of electrical science are we not indebted to Faraday? He has increased our knowledge of the hidden and unknown to such an extent, that all subsequent writers are compelled so frequently to mention his name and quote his papers, that the very repetition becomes monotonous. [How] humiliating it may be to acknowledge so great a share of successful investigation to one man...
In the Second Edition ofElements of Electro-Metallurgy: or The Art of Working in Metals by the Galvanic Fluid (143), 128.
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We have found that where science has progressed the farthest, the mind has but regained from nature that which the mind has put into nature.
We have found a strange foot-print on the shores of the unknown. We have devised profound theories, one after another, to account for its origin. At last, we have succeeded in reconstructing the creature that made the foot-print. And Lo! it is our own.
Concluding sentences in Space, Time and Gravitation: An Outline ofthe General Relativity Theory (1921), 200-201
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What animates a great pathologist? Is it the desire to cure disease, to save life? Surely not, save perhaps as an afterthought. He is too intelligent, deep in his soul, to see anything praiseworthy in such a desire. He knows from life-long observation that his discoveries will do quite as much harm as good, that a thousand scoundrels will profit to every honest man, that the folks who most deserve to be saved will probably be the last to be saved. ... What actually moves him is his unquenchable curiosity—his boundless, almost pathological thirst to penetrate the unknown, to uncover the secret, to find out what has not been found out before. ... [like] the dog sniffing tremendously at an infinite series of rat-holes. ... And yet he stands in the very front rank of the race
In 'The Scientist', Prejudices: third series (1922), 269-70.
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What struck me most in England was the perception that only those works which have a practical tendency awake attention and command respect, while the purely scientific, which possess far greater merit are almost unknown. And yet the latter are the proper source from which the others flow. Practice alone can never lead to the discovery of a truth or a principle. In Germany it is quite the contrary. Here in the eyes of scientific men no value, or at least but a trifling one, is placed upon the practical results. The enrichment of science is alone considered worthy attention.
Letter to Michael Faraday (19 Dec 1844). In Bence Jones (ed.), The life and letters of Faraday (1870), Vol. 2, 188-189.
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Whereas, to borrow an illustration from mathematics, life was formerly an equation of, say, 100 unknown quantities, it is now one of 99 only, inasmuch as memory and heredity have been shown to be one and the same thing.
Samuel Butler, Henry Festing Jones (ed.), The Note-Books of Samuel Butler (1917), 57.
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[No one will be able to] deter the scientific mind from probing into the unknown any more than Canute could command the tides.
Comment upon the U.S. Supreme Court's 1980 decision permitting the patenting of life forms.
'Shaping Life in the Lab'. In Time (9 Mar 1981).
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[Urbain Jean Joseph] Le Verrier—without leaving his study, without even looking at the sky—had found the unknown planet [Neptune] solely by mathematical calculation, and, as it were, touched it with the tip of his pen!
In Camille Flammarion, Astronomy (1914), 171.
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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
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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
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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