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Harish-Chandra I have often pondered over the roles of knowledge or experience, on the one hand, and imagination or intuition, on the other, in the process of discovery. I believe that there is a certain fundamental conflict between the two, and knowledge, by advocating caution, tends to inhibit the flight of imagination. Therefore, a certain naivete, unburdened by conventional wisdom, can sometimes be a positive asset. R. Langlands, ‘Harish-Chandra,’ Biographical Memoirs of Fellows of the Royal Society 31 (1985) 197 – 225.
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Harris, Sydney J. The real danger is not that computers will begin to think like men, but that men will begin to think like computers. In H. Eves Return to Mathematical Circles, Boston: Prindle, Weber and Schmidt, 1988.
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Hawking, Stephen Williams (1942- ) God not only plays dice. He also sometimes throws the dice where they cannot be seen. [See related quotation from Albert Einstein.] Nature 1975 257.
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Heath, Sir Thomas [The works of Archimedes] are without exception, monuments of mathematical exposition; the gradual revelation of the plan of attack, the masterly ordering of the propositions, the stern elimination of everything not immediately relevant to the purpose, the finish of the whole, are so impressive in their perfection as to create a feeling akin to awe in the mind of the reader. A History of Greek Mathematics. 1921.
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Heaviside, Oliver (1850-1925) [Criticized for using formal mathematical manipulations, without understanding how they worked:] Should I refuse a good dinner simply because I do not understand the process of digestion?
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Heinlein, Robert A. Anyone who cannot cope with mathematics is not fully human. At best he is a tolerable subhuman who has learned to wear shoes, bathe, and not make messes in the house. Time Enough for Love.
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Heisenberg, Werner (1901-1976) An expert is someone who knows some of the worst mistakes that can be made in his subject, and how to avoid them. Physics and Beyond. 1971.
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Hempel, Carl G. …to characterize the import of pure geometry, we might use the standard form of a movie-disclaimer: No portrayal of the characteristics of geometrical figures or of the spatial properties of relationships of actual bodies is intended, and any similarities between the primitive concepts and their customary geometrical connotations are purely coincidental. ‘Geometry and Empirical Science’ in J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956.
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Hempel, Carl G. The most distinctive characteristic which differentiates mathematics from the various branches of empirical science, and which accounts for its fame as the queen of the sciences, is no doubt the peculiar certainty and necessity of its results. ‘Geometry and Empirical Science’ in J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956.
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Hempel, Carl G. The propositions of mathematics have, therefore, the same unquestionable certainty which is typical of such propositions as ‘All bachelors are unmarried,’ but they also share the complete lack of empirical content which is associated with that certainty: The propositions of mathematics are devoid of all factual content; they convey no information whatever on any empirical subject matter. ‘On the Nature of Mathematical Truth’ in J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956.
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Henkin, Leon One of the big misapprehensions about mathematics that we perpetrate in our classrooms is that the teacher always seems to know the answer to any problem that is discussed. This gives students the idea that there is a book somewhere with all the right answers to all of the interesting questions, and that teachers know those answers. And if one could get hold of the book, one would have everything settled. That’s so unlike the true nature of mathematics. L.A. Steen and D.J. Albers (eds.), Teaching Teachers, Teaching Students, Boston: Birkh’ser, 1981, p89.
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Hermite, Charles (1822 – 1901) There exists, if I am not mistaken, an entire world which is the totality of mathematical truths, to which we have access only with our mind, just as a world of physical reality exists, the one like the other independent of ourselves, both of divine creation. In The Mathematical Intelligencer, v. 5, no. 4.
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Hermite, Charles (1822-1901) We are servants rather than masters in mathematics. In H. Eves Mathematical Circles Squared, Boston: Prindle, Weber and Schmidt, 1972.
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Hertz, Heinrich One cannot escape the feeling that these mathematical formulas have an independent existence and an intelligence of their own, that they are wiser that we are, wiser even than their discoverers, that we get more out of them than was originally put into them. Quoted by ET Bell in Men of Mathematics, New York, 937.
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Hesse, Hermann (1877-1962) You treat world history as a mathematician does mathematics, in which nothing but laws and formulae exist, no reality, no good and evil, no time, no yesterday, no tomorrow, nothing but an eternal, shallow, mathematical present. The Glass Bead Game, 1943.
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Hilbert, David (1862-1943) Wir mssen wissen. Wir werden wissen. [Engraved on his tombstone in Gttingen.]
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Hirst, Thomas Archer 10th August 1851: On Tuesday evening at Museum, at a ball in the gardens. The night was chill, I dropped too suddenly from Differential Calculus into ladies’ society, and could not give myself freely to the change. After an hour’s attempt so to do, I returned, cursing the mode of life I was pursuing; next morning I had already shaken hands, however, with Diff. Calculus, and forgot the ladies…. J. Helen Gardner and Robin J. Wilson, ‘Thomas Archer Hirst – Mathematician Xtravagant II – Student Days in Germany’, The American Mathematical Monthly , v. 6, no. 100.
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Hobbes, Thomas Geometry, which is the only science that it hath pleased God hitherto to bestow on mankind. In J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956.
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Hobbes, Thomas 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 J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956.
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Hobbes, Thomas There is more in Mersenne than in all the universities together. In G. Simmons Calculus Gems, New York: McGraw Hill Inc., 1992.
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