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Copernicus, Nicholaus (1473-1543) Mathematics is written for mathematicians. De Revolutionibus.
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Crick, Francis Harry Compton (1916 – ) In my experience most mathematicians are intellectually lazy and especially dislike reading experimental papers. He (Ren’Thom) seemed to have very strong biological intuitions but unfortunately of negative sign. What Mad Pursuit. London: Weidenfeld and Nicolson, 1988.
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Crowe, Michael Revolutions never occur in mathematics. Historia Mathematica. 1975.
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da Vinci, Leonardo (1452-1519) Whoever despises the high wisdom of mathematics nourishes himself on delusion and will never still the sophistic sciences whose only product is an eternal uproar. In N. Rose Mathematical Maxims and Minims, Raleigh NC:Rome Press Inc., 1988.
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D’Alembert, Jean Le Rond (1717-17830 Thus metaphysics and mathematics are, among all the sciences that belong to reason, those in which imagination has the greatest role. I beg pardon of those delicate spirits who are detractors of mathematics for saying this …. The imagination in a mathematician who creates makes no less difference than in a poet who invents…. Of all the great men of antiquity, Archimedes may be the one who most deserves to be placed beside Homer. Discours Preliminaire de L’Encyclopedie, Tome 1, 1967. pp 47 – 48.
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Dantzig Neither in the subjective nor in the objective world can we find a criterion for the reality of the number concept, because the first contains no such concept, and the second contains nothing that is free from the concept. How then can we arrive at a criterion? Not by evidence, for the dice of evidence are loaded. Not by logic, for logic has no existence independent of mathematics: it is only one phase of this multiplied necessity that we call mathematics. How then shall mathematical concepts be judged? They shall not be judged. Mathematics is the supreme arbiter. From its decisions there is no appeal. We cannot change the rules of the game, we cannot ascertain whether the game is fair. We can only study the player at his game; not, however, with the detached attitude of a bystander, for we are watching our own minds at play.
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Dantzig The mathematician may be compared to a designer of garments, who is utterly oblivious of the creatures whom his garments may fit. To be sure, his art originated in the necessity for clothing such creatures, but this was long ago; to this day a shape will occasionally appear which will fit into the garment as if the garment had been made for it. Then there is no end of surprise and delight.
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Darwin, Charles Every new body of discovery is mathematical in form, because there is no other guidance we can have. In N. Rose (ed.) Mathematical Maxims and Minims, Raleigh NC: Rome Press Inc., 1988.
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Darwin, Charles Mathematics seems to endow one with something like a new sense. In N. Rose (ed.) Mathematical Maxims and Minims, Raleigh NC: Rome Press Inc., 1988.
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Davis, Philip J. and Hersh, Reuben One began to hear it said that World War I was the chemists’ war, World War II was the physicists’ war, World War III (may it never come) will be the mathematicians’ war. The Mathematical Experience, Boston: Birkh’ser, 1981.
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Davis, Philip J. One of the endlessly alluring aspects of mathematics is that its thorniest paradoxes have a way of blooming into beautiful theories. Number, Scientific American, 211, (Sept. 1964), 51 – 59.
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Davis, Philip J. The numbers are a catalyst that can help turn raving madmen into polite humans. In N. Rose (ed.) Mathematical Maxims and Minims, Raleigh NC: Rome Press Inc., 1988.
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de Fermat, Pierre (1601?-1665) And perhaps, posterity will thank me for having shown it that the ancients did not know everything. In D. M. Burton, Elementary Number Theory, Boston: Allyn and Bacon, Inc., 1976.
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de Laplace, Pierre-Simon (1749 – 1827) Napoleon: You have written this huge book on the system of the world without once mentioning the author of the universe. Laplace: Sire, I had no need of that hypothesis. Later when told by Napoleon about the incident, Lagrange commented: Ah, but that is a fine hypothesis. It explains so many things. DeMorgan’s Budget of Paradoxes.
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De Morgan, Augustus (1806-1871) Every science that has thriven has thriven upon its own symbols: logic, the only science which is admitted to have made no improvements in century after century, is the only one which has grown no symbols. Transactions Cambridge Philosophical Society, vol. X, 1864, p. 184.
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De Sua, F. (1956) Suppose we loosely define a religion as any discipline whose foundations rest on an element of faith, irrespective of any element of reason which may be present. Quantum mechanics for example would be a religion under this definition. But mathematics would hold the unique position of being the only branch of theology possessing a rigorous demonstration of the fact that it should be so classified. In H. Eves In Mathematical Circles, Boston: Prindle, Weber and Schmidt, 1969.
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Dehn, Max Mathematics is the only instructional material that can be presented in an entirely undogmatic way. In The Mathematical Intelligencer, v. 5, no. 2, 1983.
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Descartes, Ren'(1596-1650) When writing about transcendental issues, be transcendentally clear. In G. Simmons Calculus Gems. New York: McGraw Hill Inc., 1992.
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Diophantus [His epitaph.] This tomb hold Diophantus Ah, what a marvel! And the tomb tells scientifically the measure of his life. God vouchsafed that he should be a boy for the sixth part of his life; when a twelfth was added, his cheeks acquired a beard; He kindled for him the light of marriage after a seventh, and in the fifth year after his marriage He granted him a son. Alas! late-begotten and miserable child, when he had reached the measure of half his father’s life, the chill grave took him. After consoling his grief by this science of numbers for four years, he reached the end of his life. In Ivor Thomas Greek Mathematics, in J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956.
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Dirac, Paul Adrien Maurice (1902- ) I think that there is a moral to this story, namely that it is more important to have beauty in one’s equations that to have them fit experiment. If Schroedinger had been more confident of his work, he could have published it some months earlier, and he could have published a more accurate equation. It seems that if one is working from the point of view of getting beauty in one’s equations, and if one has really a sound insight, one is on a sure line of progress. If there is not complete agreement between the results of one’s work and experiment, one should not allow oneself to be too discouraged, because the discrepancy may well be due to minor features that are not properly taken into account and that will get cleared up with further development of the theory. Scientific American, May 1963.
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