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Proceed Quotes (41 quotes)

As long as algebra and geometry proceeded along separate paths, their advance was slow and their applications limited. But when these sciences joined company, they drew from each other fresh vitality and thenceforward marched on at a rapid pace toward perfection.
In Leçons Élémentaires sur la Mathematiques, Leçon cinquième. As quoted and cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 81.
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But I believe that there is no philosophical high-road in science, with epistemological signposts. No, we are in a jungle and find our way by trial and error, building our road behind us as we proceed. We do not find signposts at cross-roads, but our own scouts erect them, to help the rest.
Max Born
In Experiment and Theory in Physics (1943), 44.
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Doubtless the reasoning faculty, the mind, is the leading and characteristic attribute of the human race. By the exercise of this, man arrives at the properties of the natural bodies. This is science, properly and emphatically so called. It is the science of pure mathematics; and in the high branches of this science lies the truly sublime of human acquisition. If any attainment deserves that epithet, it is the knowledge, which, from the mensuration of the minutest dust of the balance, proceeds on the rising scale of material bodies, everywhere weighing, everywhere measuring, everywhere detecting and explaining the laws of force and motion, penetrating into the secret principles which hold the universe of God together, and balancing worlds against worlds, and system against system. When we seek to accompany those who pursue studies at once so high, so vast, and so exact; when we arrive at the discoveries of Newton, which pour in day on the works of God, as if a second fiat had gone forth from his own mouth; when, further, we attempt to follow those who set out where Newton paused, making his goal their starting-place, and, proceeding with demonstration upon demonstration, and discovery upon discovery, bring new worlds and new systems of worlds within the limits of the known universe, failing to learn all only because all is infinite; however we may say of man, in admiration of his physical structure, that “in form and moving he is express and admirable,” it is here, and here without irreverence, we may exclaim, “In apprehension how like a god!” The study of the pure mathematics will of course not be extensively pursued in an institution, which, like this [Boston Mechanics’ Institute], has a direct practical tendency and aim. But it is still to be remembered, that pure mathematics lie at the foundation of mechanical philosophy, and that it is ignorance only which can speak or think of that sublime science as useless research or barren speculation.
In Works (1872), Vol. 1, 180.
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Earthworms, though in appearance a small and despicable link in the chain of nature, yet, if lost, would make a lamentable chasm … worms seem to be the great promoters of vegetation, which would proceed but lamely without them.
[Showing an early awareness in ecology.]
Letter XXXV, to Daines Barrington, (20 May 1777) in The Natural History of Selborne (1789), 216 and (1899), 174.
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Few will deny that even in the first scientific instruction in mathematics the most rigorous method is to be given preference over all others. Especially will every teacher prefer a consistent proof to one which is based on fallacies or proceeds in a vicious circle, indeed it will be morally impossible for the teacher to present a proof of the latter kind consciously and thus in a sense deceive his pupils. Notwithstanding these objectionable so-called proofs, so far as the foundation and the development of the system is concerned, predominate in our textbooks to the present time. Perhaps it will be answered, that rigorous proof is found too difficult for the pupil’s power of comprehension. Should this be anywhere the case,—which would only indicate some defect in the plan or treatment of the whole,—the only remedy would be to merely state the theorem in a historic way, and forego a proof with the frank confession that no proof has been found which could be comprehended by the pupil; a remedy which is ever doubtful and should only be applied in the case of extreme necessity. But this remedy is to be preferred to a proof which is no proof, and is therefore either wholly unintelligible to the pupil, or deceives him with an appearance of knowledge which opens the door to all superficiality and lack of scientific method.
In 'Stücke aus dem Lehrbuche der Arithmetik', Werke, Bd. 2 (1904), 296.
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For man being the minister and interpreter of nature, acts and understands so far as he has observed of the order, the works and mind of nature, and can proceed no further; for no power is able to loose or break the chain of causes, nor is nature to be conquered but by submission: whence those twin intentions, human knowledge and human power, are really coincident; and the greatest hindrance to works is the ignorance of causes.
In The Great lnstauration.
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He that would learn by experiments, ought to proceed from particulars to generals; but the method of instructing academically, proceeds from generals to particulars
As quoted in Thomas Steele Hall, A Source Book in Animal Biology (1951), 486.
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I find out what the world needs, then I proceed to invent. My main purpose in life is to make money so that I can afford to go on creating more inventions.
…...
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I have decided today that the United States should proceed at once with the development of an entirely new type of space transportation system designed to help transform the space frontier of the 1970s into familiar territory, easily accessible for human endeavor in the 1980s and ’90s. This system will center on a space vehicle that can shuttle repeatedly from Earth to orbit and back. It will revolutionize transportation into near space, by routinizing it. It will take the astronomical costs out of astronautics. In short, it will go a long way toward delivering the rich benefits of practical space utilization and the valuable spin-offs from space efforts into the daily lives of Americans and all people.
Statement by President Nixon (5 Jan 1972).
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I think equation guessing might be the best method to proceed to obtain the laws for the part of physics which is presently unknown.
In his Nobel Prize Lecture (11 Dec 1965), 'The Development of the Space-Time View of Quantum Electrodynamics'. Collected in Stig Lundqvist, Nobel Lectures: Physics, 1963-1970 (1998), 177.
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I wanted certainty in the kind of way in which people want religious faith. I thought that certainty is more likely to be found in mathematics than elsewhere. But I discovered that many mathematical demonstrations, which my teachers expected me to accept, were full of fallacies, and that, if certainty were indeed discoverable in mathematics, it would be in a new field of mathematics, with more solid foundations than those that had hitherto been thought secure. But as the work proceeded, I was continually reminded of the fable about the elephant and the tortoise. Having constructed an elephant upon which the mathematical world could rest, I found the elephant tottering, and proceeded to construct a tortoise to keep the elephant from falling. But the tortoise was no more secure than the elephant, and after some twenty years of very arduous toil, I came to the conclusion that there was nothing more that I could do in the way of making mathematical knowledge indubitable.
In 'Reflections on my Eightieth Birthday', Portraits from Memory (1956), 54.
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If a mathematician of the past, an Archimedes or even a Descartes, could view the field of geometry in its present condition, the first feature to impress him would be its lack of concreteness. There are whole classes of geometric theories which proceed not only without models and diagrams, but without the slightest (apparent) use of spatial intuition. In the main this is due, to the power of the analytic instruments of investigations as compared with the purely geometric.
In 'The Present Problems in Geometry', Bulletin American Mathematical Society (1906), 286.
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If he [Thomas Edison] had a needle to find in a haystack, he would not stop to reason where it was most likely to be, but would proceed at once with the feverish diligence of a bee, to examine straw after straw until he found the object of his search. … [J]ust a little theory and calculation would have saved him ninety percent of his labor.
As quoted in 'Tesla Says Edison Was an Empiricist', The New York Times (19 Oct 1931), 25. In 1884, Tesla had moved to America to assist Edison in the designing of motors and generators.
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It is by no means hopeless to expect to make a machine for really very difficult mathematical problems. But you would have to proceed step-by-step. I think electricity would be the best thing to rely on.
In Charles Sanders Peirce, Max Harold Fisch, Christian J. W. Kloesel Writings of Charles S. Peirce: 1884-1886 (1993), 422.
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My belief (is) that one should take a minimum of care and preparation over first experiments. If they are unsuccessful one is not then discouraged since many possible reasons for failure can be thought of, and improvements can be made. Much can often be learned by the repetition under different conditions, even if the desired result is not obtained. If every conceivable precaution is taken at first, one is often too discouraged to proceed at all.
Nobel Lectures in Chemistry (1999), Vol. 3, 364.
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Owing to this struggle for life, any variation, however slight and from whatever cause proceeding, if it be in any degree profitable to an individual of any species, in its infinitely complex relationship to other organic beings and to external nature, will tend to the preservation of that individual, and will generally be inherited by its offspring.
…...
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Science gives us the grounds of premises from which religious truths are to be inferred; but it does not set about inferring them, much less does it reach the inference; that is not its province. It brings before us phenomena, and it leaves us, if we will, to call them works of design, wisdom, or benevolence; and further still, if we will, to proceed to confess an Intelligent Creator. We have to take its facts, and to give them a meaning, and to draw our own conclusions from them. First comes Knowledge, then a view, then reasoning, then belief. This is why Science has so little of a religious tendency; deductions have no power of persuasion. The heart is commonly reached, not through the reason, but through the imagination, by means of direct impressions, by the testimony of facts and events, by history, by description. Persons influence us, voices melt us, looks subdue us, deeds inflame us. Many a man will live and die upon a dogma; no man will be a martyr for a conclusion.
Letter collected in Tamworth Reading Room: Letters on an Address Delivered by Sir Robert Peel, Bart., M.P. on the Establishment of a Reading Room at Tamworth (1841), 32. Excerpted in John Henry Newman, An Essay in Aid of a Grammar of Assent (1870), 89 & 94 footnote.
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Science proceeds by successive answers to questions more and more subtle, coming nearer and nearer to the very essence of phenomena.
From Études sur la bière, Chap 6, Sec. vi. As translated by René J. Dubos, quoted and cited in Maurice B. Strauss, Familiar Medical Quotations (1968), 526.
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Science too proceeds by lantern-flashes; it explores nature’s inexhaustible mosaic piece by piece. Too often the wick lacks oil; the glass panes of the lantern may not be clean. No matter: his work is not in vain who first recognizes and shows to others one speck of the vast unknown.
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Step by step we cross great eras in the development of thought: there is no sudden gigantic stride; a theory proceeds by slow evolution until it dominates or is destroyed.
In 'Theory of Phlogiston', The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science (Jan 1868), 35, 28-29.
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The actual evolution of mathematical theories proceeds by a process of induction strictly analogous to the method of induction employed in building up the physical sciences; observation, comparison, classification, trial, and generalisation are essential in both cases. Not only are special results, obtained independently of one another, frequently seen to be really included in some generalisation, but branches of the subject which have been developed quite independently of one another are sometimes found to have connections which enable them to be synthesised in one single body of doctrine. The essential nature of mathematical thought manifests itself in the discernment of fundamental identity in the mathematical aspects of what are superficially very different domains. A striking example of this species of immanent identity of mathematical form was exhibited by the discovery of that distinguished mathematician … Major MacMahon, that all possible Latin squares are capable of enumeration by the consideration of certain differential operators. Here we have a case in which an enumeration, which appears to be not amenable to direct treatment, can actually be carried out in a simple manner when the underlying identity of the operation is recognised with that involved in certain operations due to differential operators, the calculus of which belongs superficially to a wholly different region of thought from that relating to Latin squares.
In Presidential Address to British Association for the Advancement of Science (1910), Nature, 84, 290.
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The advance of technology, like the growth of population and industry, has also been proceeding exponentially.
Foreign Affairs (Summer 1972).
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The axis cylinders of all nerve fibers (motor, secretory, sensitive and sensory, conducting centrifugally or centripetally) have been proved to proceed directly from the cells. A connection with a fiber network, or an origin from such a network, does not take place.
In 'Uber einige neuere Forschungen im Gebiete der Anatomie des Centralnervensystems', Deutsche Medizirusche Wochenschrlft (1891), 7, 1352. Trans. Edwin Clarke and L. S. Jacyna, Nineteenth Century Origins of Neuroscientific Concepts (1987), 99.
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The best and safest way of philosophising seems to be, first to enquire diligently into the properties of things, and to establish those properties by experiences [experiments] and then to proceed slowly to hypotheses for the explanation of them. For hypotheses should be employed only in explaining the properties of things, but not assumed in determining them; unless so far as they may furnish experiments.
Letter to the French Jesuit, Gaston Pardies. Translation from the original Latin, as in Richard S. Westfall, Never at Rest: a Biography of Isaac Newton (1983), 242.
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The Big Idea that had been developed in the seventeenth century ... is now known as the scientific method. It says that the way to proceed when investigating how the world works is to first carry out experiments and/or make observations of the natural world. Then, develop hypotheses to explain these observations, and (crucially) use the hypothesis to make predictions about the future outcome of future experiments and/or observations. After comparing the results of those new observations with the predictions of the hypotheses, discard those hypotheses which make false predictions, and retain (at least, for the time being) any hypothesis that makes accurate predictions, elevating it to the status of a theory. Note that a theory can never be proved right. The best that can be said is that it has passed all the tests applied so far.
In The Fellowship: the Story of a Revolution (2005), 275.
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The errors of definitions multiply themselves according as the reckoning proceeds; and lead men into absurdities, which at last they see but cannot avoid, without reckoning anew from the beginning.
In Thomas Hobbes and William Molesworth (ed.) Leviathan: Or the Matter, Form and Power of a Commonwealth Ecclesiastical and Civil (1839), Vol. 3, 24.
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The existence of a first cause of the universe is a necessity of thought ... Amid the mysteries which become more mysterious the more they are thought about, there will remain the one absolute certainty that we are over in the presence of an Infinite, Eternal Energy from which all things proceed.
As quoted in John Murdoch, India's Needs: Material, Political, Social, Moral, and Religious (1886), 126.
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The farther a mathematical theory is developed, the more harmoniously and uniformly does its construction proceed, and unsuspected relations are disclosed between hitherto separated branches of the science.
In 'Mathematical Problems', Lecture at the International Congress of Mathematics, Paris, (8 Aug 1900). Translated by Dr. Maby Winton Newson in Bulletin of the American Mathematical Society (1902), 8, 479.
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The laws of conscience, which we pretend to be derived from nature, proceed from custom
…...
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The problem is not to find the best or most efficient method to proceed to a discovery, but to find any method at all.
In his Nobel Prize Lecture (11 Dec 1965), 'The Development of the Space-Time View of Quantum Electrodynamics'. Collected in Stig Lundqvist, Nobel Lectures: Physics, 1963-1970 (1998), 177.
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The Simiadae then branched off into two great stems, the New World and Old World monkeys; and from the latter at a remote period, Man, the wonder and the glory of the universe, proceeded.
In The Descent of Man, and Selection in Relation to Sex (1871), 213.
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The stars are laboratories in which the evolution of matter proceeds in the direction of large molecules.
In Teilhard de Chardin and Bernard Wall (trans.), The Phenomenon of Man (1959, 2008), 50. Originally published in French as Le Phénomene Humain (1955).
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There are … two fields for human thought and action—the actual and the possible, the realized and the real. In the actual, the tangible, the realized, the vast proportion of mankind abide. The great, region of the possible, whence all discovery, invention, creation proceed, and which is to the actual as a universe to a planet, is the chosen region of genius. As almost every thing which is now actual was once only possible, as our present facts and axioms were originally inventions or discoveries, it is, under God, to genius that we owe our present blessings. In the past, it created the present; in the present, it is creating the future.
In 'Genius', Wellman’s Miscellany (Dec 1871), 4, No. 6, 202.
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This most beautiful system of the sun, planets, and comets could only proceed from the counsel and dominion of an intelligent and powerful Being.
In The Mathematical Principles of Natural Philosophy (1729), Vol. 2, 388.
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We, however, maintain … that all animals whatsoever, even the viviparous, and man himself not excepted, are produced from ova; that the first conception, from which the foetus proceeds in all, is an ovum of one description or another, as well as the seeds of all kinds of plants.
As translated by Robert Willis in The Works of William Harvey (1847), Vol. 7, 170. Harvey’s doctrine, given herein, has been summarized in later literature as: omne vivum ex ovo omnia, (all life from an egg). Also see the quote “Ex ova omnia,” elsewhere on this webpage.
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When Cayley had reached his most advanced generalizations he proceeded to establish them directly by some method or other, though he seldom gave the clue by which they had first been obtained: a proceeding which does not tend to make his papers easy reading. …
His literary style is direct, simple and clear. His legal training had an influence, not merely upon his mode of arrangement but also upon his expression; the result is that his papers are severe and present a curious contrast to the luxuriant enthusiasm which pervades so many of Sylvester’s papers. He used to prepare his work for publication as soon as he carried his investigations in any subject far enough for his immediate purpose. … A paper once written out was promptly sent for publication; this practice he maintained throughout life. … The consequence is that he has left few arrears of unfinished or unpublished papers; his work has been given by himself to the world.
In Proceedings of London Royal Society (1895), 58, 23-24.
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While seeing any number of black crows does not prove all the crows are black, seeing one white crow disproves it. Thus science proceeds not by proving models correct but by discarding false ones or improving incomplete ones.
In 'On the Nature of Science', Physics in Canada (Jan/Feb 2007), 63, No. 1, 7.
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[In mathematics] we behold the conscious logical activity of the human mind in its purest and most perfect form. Here we learn to realize the laborious nature of the process, the great care with which it must proceed, the accuracy which is necessary to determine the exact extent of the general propositions arrived at, the difficulty of forming and comprehending abstract concepts; but here we learn also to place confidence in the certainty, scope and fruitfulness of such intellectual activity.
In Ueber das Verhältniss der Naturwissenschaften zur Gesammlheit der Wissenschaft, Vortrage und Reden (1896), Bd. 1, 176.
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[The famous attack of Sir William Hamilton on the tendency of mathematical studies] affords the most express evidence of those fatal lacunae in the circle of his knowledge, which unfitted him for taking a comprehensive or even an accurate view of the processes of the human mind in the establishment of truth. If there is any pre-requisite which all must see to be indispensable in one who attempts to give laws to the human intellect, it is a thorough acquaintance with the modes by which human intellect has proceeded, in the case where, by universal acknowledgment, grounded on subsequent direct verification, it has succeeded in ascertaining the greatest number of important and recondite truths. This requisite Sir W. Hamilton had not, in any tolerable degree, fulfilled. Even of pure mathematics he apparently knew little but the rudiments. Of mathematics as applied to investigating the laws of physical nature; of the mode in which the properties of number, extension, and figure, are made instrumental to the ascertainment of truths other than arithmetical or geometrical—it is too much to say that he had even a superficial knowledge: there is not a line in his works which shows him to have had any knowledge at all.
In Examination of Sir William Hamilton's Philosophy (1878), 607.
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…so slow is moral progress. True, we have the bicycle, the motor-car, the dirigible airship and other marvellous means of breaking our bones; but our morality is not one rung the higher for it all. One would even say that, the farther we proceed in our conquest of matter, the more our morality recedes. The most advanced of our inventions consists in bringing men down with grapeshot and explosives with the swiftness of the reaper mowing the corn.
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“Scientific people,” proceeded the Time Traveler, after the pause required for the proper assimilation of this, “know very well that Time is only a kind of Space.”
In The Time Machine (1898), 6.
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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
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Bible
Thomas Huxley
Alessandro Volta
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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



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