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Home > Dictionary of Science Quotations > Scientist Names Index G > Carl Friedrich Gauss Quotes

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Carl Friedrich Gauss
(30 Apr 1777 - 23 Feb 1855)

German mathematician who transformed nearly all areas of mathematics, and contributed much to other areas of science.


Science Quotes by Carl Friedrich Gauss (44 quotes)

...durch planmässiges Tattonieren.
(... through systematic, palpable experimentation.)
Response, when asked how he came upon his theorems.
— Carl Friedrich Gauss
Quoted in A.L. Mackay, Dictionary of Scientific Quotations (1994).
Science quotes on:  |  Experiment (369)  |  Theorem (34)

..und Juwele wδgt man nicht mit der Krδmerwaage
... and jewels are not weighed on a grocery scale.
Comment on Dirichlet's publication as being not prolific, but profound.
— Carl Friedrich Gauss
Letter to Alexander von Humbolt (9 Jul 1845). In Jagdish Mehra and Helmut Rechenberg, The Historical Development of Quantum Theory, 267. By
Science quotes on:  |  Achievement (73)

Pauca sed matura.
(Few, but ripe.)
His motto. He would limit his publications to work he regarded as complete and perfect.
— Carl Friedrich Gauss
Science quotes on:  |  Motto (13)

Thou, nature, art my goddess; to thy laws my services are bound...
His second motto (from King Lear by Shakespeare).
— Carl Friedrich Gauss
Science quotes on:  |  Motto (13)

A great part of its [higher arithmetic] theories derives an additional charm from the peculiarity that important propositions, with the impress of simplicity on them, are often easily discovered by induction, and yet are of so profound a character that we cannot find the demonstrations till after many vain attempts; and even then, when we do succeed, it is often by some tedious and artificial process, while the simple methods may long remain concealed.
— Carl Friedrich Gauss
Quoted in H. Eves, Mathematical Circles (1977) .
Science quotes on:  |  Induction (22)  |  Mathematics (367)  |  Success (114)

As is well known the principle of virtual velocities transforms all statics into a mathematical assignment, and by D'Alembert's principle for dynamics, the latter is again reduced to statics. Although it is is very much in order that in gradual training of science and in the instruction of the individual the easier precedes the more difficult, the simple precedes the more complicated, the special precedes the general, yet the min, once it has arrived at the higher standpoint, demands the reverse process whereby all statics appears only as a very special case of mechanics.
— Carl Friedrich Gauss
Collected Works (1877), Vol. 5, 25-26. Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 412.
Science quotes on:  |  Jean le Rond D'Alembert (3)  |  Mechanics (27)  |  Statics (2)  |  Theory (353)

Ask her to wait a moment. I am almost done.
When told, while working, that his wife was dying.
— Carl Friedrich Gauss
Quoted in E.T. Bell, Men of Mathematics, (1937).
Science quotes on:  |  Biography (199)

By explanation the scientist understands nothing except the reduction to the least and simplest basic laws possible, beyond which he cannot go, but must plainly demand them; from them however he deduces the phenomena absolutely completely as necessary.
— Carl Friedrich Gauss
From his memoir 'Erdmagnetismus und Magnetometer' in Collected Works (1877), Vol. 5, 315-316. Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 411.
Science quotes on:  |  Law (273)  |  Scientific Method (101)

Finally, two days ago, I succeeded - not on account of my hard efforts, but by the grace of the Lord. Like a sudden flash of lightning, the riddle was solved. I am unable to say what was the conducting thread that connected what I previously knew with what made my success possible.
— Carl Friedrich Gauss
Quoted in H. Eves, Mathematical Circles Squared, (1972).
Science quotes on:  |  Success (114)

For three days now this angel, almost too heavenly for earth has been my fiancée … Life stands before me like an eternal spring with new and brilliant colours. Upon his engagement to Johanne Osthof of Brunswick; they married 9 Oct 1805.
— Carl Friedrich Gauss
Letter to Farkas Wolfgang Bolyai (1804). Quoted in Stephen Hawking, God Created the Integers: The Mathematical Breakthroughs (2005), 567.
Science quotes on:  |  Biography (199)  |  Marriage (19)

God does arithmetic.
— Carl Friedrich Gauss
Attributed. Quoted in A.L. Mackay, A Dictionary of Scientific Quotations (1991), 100.
Science quotes on:  |  Arithmetic (38)  |  God (234)

I am coming more and more to the conviction that the necessity of our geometry cannot be demonstrated, at least neither by, nor for, the human intellect...geometry should be ranked, not with arithmetic, which is purely aprioristic, but with mechanics.
— Carl Friedrich Gauss
Quoted in J Koenderink, Solid Shape (1990).
Science quotes on:  |  Arithmetic (38)  |  Geometry (68)  |  Mechanics (27)

I am giving this winter two courses of lectures to three students, of which one is only moderately prepared, the other less than moderately, and the third lacks both preparation and ability. Such are the onera of a mathematical profession.
— Carl Friedrich Gauss
Letter to Friedrich Bessel (4 Dec 1808). In Gauss-Bessel Briefwechsel (1880), 107. In Robert Ιdouard Moritz, Memorabilia Mathematica; Or, The Philomath's Quotation-book (1914), 158.
Science quotes on:  |  Education (177)

I confess that Fermat's Theorem as an isolated proposition has very little interest for me, for a multitude of such theorems can wasily be set up, which one could neither prove nor disprove. But I have been stimulated by it to bring our again several old ideas for a great extension of the theory of numbers. Of course, this theory belongs to the things where one cannot predict to what extent one will succeed in reaching obscurely hovering distant goals. A happy star must also rule, and my situation and so manifold distracting affairs of course do not permit me to pursue such meditations as in the happy years 1796-1798 when I created the pricipal topics of my Disquisitiones arithmeticae. But I am convinced that if good fortune should do more than I expect, and make me successful in some advances in that theory, even the Fermat theorem will appear in it only as one of the least interesting corollaries.
In reply to Olbers' attempt in 1816 to entice him to work on Fermat's Theorem. The hope Gauss expressed for his success was never realised.
— Carl Friedrich Gauss
Letter to Heinrich Olbers (21 Mar 1816). Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 413.
Science quotes on:  |  Pierre de Fermat (8)  |  Theorem (34)

I have a true aversion to teaching. The perennial business of a professor of mathematics is only to teach the ABC of his science; most of the few pupils who go a step further, and usually to keep the metaphor, remain in the process of gathering information, become only Halbwisser [one who has superficial knowledge of the subject], for the rarer talents do not want to have themselves educated by lecture courses, but train themselves. And with this thankless work the professor loses his precious time.
— Carl Friedrich Gauss
Letter to Heinrich Olbers (26 Oct 1802). Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 414.
Science quotes on:  |  Education (177)

I have had my results for a long time: but I do not yet know how I am to arrive at them.
— Carl Friedrich Gauss
Quoted in A. Arber, The Mind and the Eye (1954).
Science quotes on:  |  Proof (136)

I have the vagary of taking a lively interest in mathematical subjects only where I may anticipate ingenious association of ideas and results recommending themselves by elegance or generality.
— Carl Friedrich Gauss
Letter to Heinrich Schumacher (17 Sep 1808). Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 416.
Science quotes on:  |  Biography (199)

I mean the word proof not in the sense of the lawyers, who set two half proofs equal to a whole one, but in the sense of a mathematician, where half proof = 0, and it is demanded for proof that every doubt becomes impossible.
— Carl Friedrich Gauss
Quoted in G. Simmons, Calculus Gems (1992).
Science quotes on:  |  Lawyer (12)  |  Proof (136)

If others would but reflect on mathematical truths as deeply and continuously as I have, they would make my discoveries.
— Carl Friedrich Gauss
Quoted in J. R. Newman (ed.), The World of Mathematics (1956).
Science quotes on:  |  Discovery (360)  |  Mathematics (367)  |  Truth (450)

In general I would be cautious against … plays of fancy and would not make way for their reception into scientific astronomy, which must have quite a different character. Laplace's cosmogenic hypotheses belong in that class. Indeed, I do not deny that I sometimes amuse myself in a similar manner, only I would never publish the stuff. My thoughts about the inhabitants of celestial bodies, for example, belong in that category. For my part, I am (contrary to the usual opinion) convinced ... that the larger the cosmic body, the smaller are the inhabitants and other products. For example, on the sun trees, which in the same ratio would be larger than ours, as the sun exceeds the earth in magnitude, would not be able to exist, for on account of the much greater weight on the surface of the sun, all branches would break themselves off, in so far as the materials are not of a sort entirely heterogeneous with those on earth.
— Carl Friedrich Gauss
Letter to Heinrich Schumacher (7 Nov 1847). Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 411.
Science quotes on:  |  Cosmology (11)  |  Gravity (59)  |  Pierre-Simon Laplace (45)

In mathematics there are no true controversies. (1811)
— Carl Friedrich Gauss
This quote is usually seen without any specific source citation. The sense of it is given, not in quotation marks, as “In 1811 Gauss stated that there are no true controversies in mathematics,” in G. Waldo Dunnington, Jeremy Gray and Fritz-Egbert Dohse, Carl Friedrich Gauss: Titan of Science (2003), 418. If you know the primary source, please contact Webmaster.
Science quotes on:  |  Controversy (13)  |  Mathematics (367)  |  True (29)

In my opinion instruction is very purposeless for such individuals who do no want merely to collect a mass of knowledge, but are mainly interested in exercising (training) their own powers. One doesn't need to grasp such a one by the hand and lead him to the goal, but only from time to time give him suggestions, in order that he may reach it himself in the shortest way.
— Carl Friedrich Gauss
Letter to Heinrich Schumacher (2 Oct 1808). Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 416.
Science quotes on:  |  Achievement (73)  |  Education (177)

In the last two months I have been very busy with my own mathematical speculations, which have cost me much time, without my having reached my original goal. Again and again I was enticed by the frequently interesting prospects from one direction to the other, sometimes even by will-o'-the-wisps, as is not rare in mathematic speculations.
— Carl Friedrich Gauss
Letter to Ernst Weber (21 May 1843). Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 416.
Science quotes on:  |  Mathematics (367)  |  Speculation (44)

It is always noteworthy that all those who seriously study this science [the theory of numbers] conceive a sort of passion for it.
— Carl Friedrich Gauss
Letter to Jonos Boyai (2 Sep 1808). Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 413.
Science quotes on:  |  Mathematics (367)

It is not knowledge, but the act of learning, not possession but the act of getting there, which grants the greatest enjoyment. When I have clarified and exhausted a subject, then I turn away from it, in order to go into darkness again; the never-satisfied man is so strange if he has completed a structure, then it is not in order to dwell in it peacefully,but in order to begin another. I imagine the world conqueror must feel thus, who, after one kingdom is scarcely conquered, stretches out his arms for others.
— Carl Friedrich Gauss
Letter to Farkas Wolfgang Bolyai (2 Sep 1808). Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 416.
Science quotes on:  |  Biography (199)  |  Knowledge (679)  |  Learning (130)

It may be true that people who are merely mathematicians have certain specific shortcomings; however that is not the fault of mathematics, but is true of every exclusive occupation. Likewise a mere linguist, a mere jurist, a mere soldier, a mere merchant, and so forth. One could add such idle chatter that when a certain exclusive occupation is often connected with certain specific shortcomings, it is on the other hand always free of certain other shortcomings.
— Carl Friedrich Gauss
Letter to Heinrich Schumacher (1-5 Jan 1845). Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 414.
Science quotes on:  |  Mathematician (110)  |  Occupation (28)

Mathematical discoveries, like springtime violets in the woods, have their season which no human can hasten or retard.
— Carl Friedrich Gauss
Quoted in E.T. Bell, The Development of Mathematics (1945).
Science quotes on:  |  Discovery (360)  |  Mathematics (367)

Mathematics is concerned only with the enumeration and comparison of relations.
— Carl Friedrich Gauss
Quoted in E. T. Bell, The Development of Mathematics (1945).
Science quotes on:  |  Mathematics (367)

Mathematics is the queen of the sciences and arithmetic [number theory] is the queen of mathematics. She often condescends to render service to astronomy and other natural sciences, but in all relations, she is entitled to first rank.
— Carl Friedrich Gauss
I>Sartorius von Waltershausen: Gauss zum Gedδchtniss (1856), 79. Quoted in Robert Edouard Moritz, Memorabilia Mathematica (1914), 271.
Science quotes on:  |  Arithmetic (38)  |  Mathematics (367)

My young friend, I wish that science would intoxicate you as much as our good Göttingen beer! Upon seeing a student staggering down a street.
— Carl Friedrich Gauss
Attributed. Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 416.
Science quotes on:  |  Achievement (73)  |  Science (875)

Referring to the decimal system of numeration or its equivalent (with some base other than 10): To what heights would science now be raised if Archimedes had made that discovery!
Gauss regarded this oversight as the greatest calamity in the history of science.
— Carl Friedrich Gauss
Quoted in James Roy Newman, The World of Mathematics, 328.
Science quotes on:  |  Archimedes (13)  |  Decimal (8)  |  Number (90)

Sophie Germain proved to the world that even a woman can accomplish something in the most rigorous and abstract of sciences and for that reason would well have deserved an honorary degree.
— Carl Friedrich Gauss
Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 68.
Science quotes on:  |  Sophie Germain (3)  |  Woman (36)

That this subject [of imaginary magnitudes] has hitherto been considered from the wrong point of view and surrounded by a mysterious obscurity, is to be attributed largely to an ill-adapted notation. If, for example, +1, -1, and the square root of -1 had been called direct, inverse and lateral units, instead of positive, negative and imaginary (or even impossible), such an obscurity would have been out of the question.
— Carl Friedrich Gauss
Theoria Residiorum Biquadraticorum, Commentario secunda', Werke (1863), Vol. 2. Quoted in Robert Edouard Moritz, Memorabilia Mathematica (1914), 282.
Science quotes on:  |  Number (90)

The enchanting charms of this sublime science reveal only to those who have the courage to go deeply into it. But when a woman, who because of her sex and our prejudices encounters infinitely more obstacles that an man in familiarizing herself with complicated problems, succeeds nevertheless in surmounting these obstacles and penetrating the most obscure parts of them, without doubt she must have the noblest courage, quite extraordinary talents and superior genius.
— Carl Friedrich Gauss
in a letter to Sophie Germain (c.April 1807)
Science quotes on:  |  Sophie Germain (3)  |  Women Scientists (13)

The problem of distinguishing prime numbers from composite numbers and of resolving the latter into their prime factors is known to be one of the most important and useful in arithmetic. It has engaged the industry and wisdom of ancient and modern geometers to such an extent that it would be superfluous to discuss the problem at length... Further, the dignity of the science itself seems to require that every possible means be explored for the solution of a problem so elegant and so celebrated.
— Carl Friedrich Gauss
Disquisitiones Arithmeticae (1801), Article 329
Science quotes on:  |  Number (90)

Theory attracts practice as the magnet attracts iron.
— Carl Friedrich Gauss
Attributed. Quoted in Speaking of Science: Notable Quotes on Science, Engineering, and the Environment (2000), 53.
Science quotes on:  |  Theory (353)

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.
— Carl Friedrich Gauss
Quoted in J.R. Newman, The World of Mathematics (1956), 314.
Science quotes on:  |  Problem (180)  |  Solution (109)

There have been only three epoch-making mathematicians, Archimedes, Newton, and Eisenstein.
— Carl Friedrich Gauss
Attributed
Science quotes on:  |  Archimedes (13)  |  Mathematician (110)  |  Sir Isaac Newton (176)

To the distracting occupations belong especially my lecture courses which I am holding this winter for the first time, and which now cost much more of my time than I like. Meanwhile I hope that the second time this expenditure of time will be much less, otherwise I would never be able to reconcile myself to it, even practical (astronomical) work must give far more satisfaction than if one brings up to B a couple more mediocre heads which otherwise would have stopped at A.
— Carl Friedrich Gauss
Letter to Friedrich Bessel (4 Dec 1808). Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 415.
Science quotes on:  |  Education (177)  |  Occupation (28)

We must admit with humility that, while number is purely a product of our minds, space has a reality outside our minds, so that we cannot completely prescribe its properties a priori.
— Carl Friedrich Gauss
Letter to Friedrich Bessel (1830).
Science quotes on:  |  Number (90)

When a philosopher says something that is true then it is trivial. When he says something that is not trivial then it is false.
— Carl Friedrich Gauss
Science quotes on:  |  Truth (450)

With a thousand joys I would accept a nonacademic job for which industriousness, accuracy, loyalty, and such are sufficient without specialized knowledge, and which would give a comfortable living and sufficient leisure, in order to sacrifice to my gods [mathematical research]. For example, I hope to get the editting of the census, the birth and death lists in local districts, not as a job, but for my pleasure and satisfaction...
— Carl Friedrich Gauss
Letter to Heinrich Olbers (26 Oct 1802). Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 415.
Science quotes on:  |  Biography (199)  |  Pleasure (52)

You know that I write slowly. This is chiefly because I am never satisfied until I have said as much as possible in a few words, and writing briefly takes far more time than writing at length.
— Carl Friedrich Gauss
Quoted in G. Simmons, Calculus Gems (1992).
Science quotes on:  |  Publication (75)

…as our friend Zach has often noted, in our days those who do the best for astronomy are not the salaried university professors, but so-called dillettanti, physicians, jurists, and so forth.Lamenting the fragmentary time left to a professor has remaining after fulfilling his teaching duties.
— Carl Friedrich Gauss
Letter to Heinrich Olbers (26 Oct 1802). Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 415.
Science quotes on:  |  Astronomy (105)  |  Education (177)



Quotes by others about Carl Friedrich Gauss (9)

The importance of C.F. Gauss for the development of modern physical theory and especially for the mathematical fundament of the theory of relativity is overwhelming indeed; also his achievement of the system of absolute measurement in the field of electromagnetism. In my opinion it is impossible to achieve a coherent objective picture of the world on the basis of concepts which are taken more or less from inner psychological experience.
Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 350.
Science quotes on:  |  Electromagnetism (14)  |  Relativity (33)

The best that Gauss has given us was likewise an exclusive production. If he had not created his geometry of surfaces, which served Riemann as a basis, it is scarcely conceivable that anyone else would have discovered it. I do not hesitate to confess that to a certain extent a similar pleasure may be found by absorbing ourselves in questions of pure geometry.
Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 350.
Science quotes on:  |  Geometry (68)  |  Pleasure (52)

In describing the honourable mission I charged him with, M. Pernety informed me that he made my name known to you. This leads me to confess that I am not as completely unknown to you as you might believe, but that fearing the ridicule attached to a female scientist, I have previously taken the name of M. LeBlanc in communicating to you those notes that, no doubt, do not deserve the indulgence with which you have responded.
Explaining her use of a male psuedonym.
Letter to Carl Friedrich Gauss (1807)
Science quotes on:  |  Biography (199)

[About Gauss' mathematical writing style] He is like the fox, who effaces his tracks in the sand with his tail.
In G. F. Simmons, Calculus Gems (1992), 177.
Science quotes on:  |  Biography (199)

For other great mathematicians or philosophers, he [Gauss] used the epithets magnus, or clarus, or clarissimus; for Newton alone he kept the prefix summus.
History of Mathematics (3rd Ed., 1901), 362.
Science quotes on:  |  Anecdote (15)  |  Mathematician (110)  |  Sir Isaac Newton (176)  |  Philosopher (67)

[Gauss calculated the elements of the planet Ceres] and his analysis proved him to be the first of theoretical astronomers no less than the greatest of 'arithmeticians.'
History of Mathematics (3rd Ed., 1901), 458.
Science quotes on:  |  Analysis (82)  |  Anecdote (15)  |  Astronomer (28)  |  Calculate (3)  |  Planet (84)  |  Theory (353)

The great masters of modern analysis are Lagrange, Laplace, and Gauss, who were contemporaries. It is interesting to note the marked contrast in their styles. Lagrange is perfect both in form and matter, he is careful to explain his procedure, and though his arguments are general they are easy to follow. Laplace on the other hand explains nothing, is indifferent to style, and, if satisfied that his results are correct, is content to leave them either with no proof or with a faulty one. Gauss is as exact and elegant as Lagrange, but even more difficult to follow than Laplace, for he removes every trace of the analysis by which he reached his results, and studies to give a proof which while rigorous shall be as concise and synthetical as possible.
History of Mathematics (3rd Ed., 1901), 468.
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The mathematical giant [Gauss], who from his lofty heights embraces in one view the stars and the abysses …
Kurzer Grundriss eines Versuchs (1851), 44. In Robert Ιdouard Moritz, Memorabilia Mathematica; Or, The Philomath's Quotation-book (1914), 158.
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The analytical geometry of Descartes and the calculus of Newton and Leibniz have expanded into the marvelous mathematical method—more daring than anything that the history of philosophy records—of Lobachevsky and Riemann, Gauss and Sylvester. Indeed, mathematics, the indispensable tool of the sciences, defying the senses to follow its splendid flights, is demonstrating today, as it never has been demonstrated before, the supremacy of the pure reason.
'What Knowledge is of Most Worth?', Presidential address to the National Education Association, Denver, Colorado (9 Jul 1895). In Educational Review (Sep 1895), 10, 109.
Science quotes on:  |  Analysis (82)  |  Calculus (14)  |  Renι Descartes (32)  |  Geometry (68)  |  Gottfried Wilhelm Leibniz (24)  |  Nikolay Ivanovich Lobachevsky (2)  |  Sir Isaac Newton (176)  |  Reason (173)  |  Sense (104)  |  James Joseph Sylvester (3)  |  Tool (30)


See also:
  • todayinsci icon 30 Apr - short biography, births, deaths and events on date of Gauss's birth.
  • book icon Carl Friedrich Gauss: Titan of Science, by G. Waldo Dunnington. - book suggestion.

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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Sophie Germain
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Carl Gauss
Paul Feyerabend
- 90 -
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- 80 -
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- 70 -
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Robert Fulton
Pierre Laplace
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Lord Kelvin
Theodore Roosevelt
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- 60 -
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Rene Descartes
Francis Crick
Hippocrates
Michael Faraday
Srinivasa Ramanujan
Francis Bacon
Galileo Galilei
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Aristotle
John Watson
Rosalind Franklin
Michio Kaku
Isaac Asimov
Charles Darwin
Sigmund Freud
Albert Einstein
Florence Nightingale
Isaac Newton