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All human knowledge thus begins with intuitions, proceeds thence to concepts, and ends with ideas. Quoted in Hilbert’s Foundations of Geometry.
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Allen, Woody Standard mathematics has recently been rendered obsolete by the discovery that for years we have been writing the numeral five backward. This has led to reevaluation of counting as a method of getting from one to ten. Students are taught advanced concepts of Boolean algebra, and formerly unsolvable equations are dealt with by threats of reprisals. In Howard Eves’ Return to Mathematical Circles, Boston: Prindle, Weber, and Schmidt, 1988.
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An educated mind is, as it were, composed of all the minds of preceding ages.- Fontenelle
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Anglin, W.S. Mathematics is not a careful march down a well-cleared highway, but a journey into a strange wilderness, where the explorers often get lost. Rigour should be a signal to the historian that the maps have been made, and the real explorers have gone elsewhere. ‘Mathematics and History’, Mathematical Intelligencer, v. 4, no. 4.
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Anonymous Defendit numerus: There is safety in numbers. In J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956, p. 1452.
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Anonymous If thou art able, O stranger, to find out all these things and gather them together in your mind, giving all the relations, thou shalt depart crowned with glory and knowing that thou hast been adjudged perfect in this species of wisdom. In Ivor Thomas ‘Greek Mathematics’ in J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956.
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Anonymous Like the crest of a peacock so is mathematics at the head of all knowledge. [An old Indian saying. Also, ‘Like the Crest of a Peacock’ is the title of a book by G.G. Joseph]
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Anonymous Referee’s report: This paper contains much that is new and much that is true. Unfortunately, that which is true is not new and that which is new is not true. In H.Eves Return to Mathematical Circles, Boston: Prindle, Weber, and Schmidt, 1988.
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Aristophanes (ca 444 – 380 BC) Meton: With the straight ruler I set to work To make the circle four-cornered [First(?) allusion to the problem of squaring the circle]
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Aristotle (ca 330 BC) Now that practical skills have developed enough to provide adequately for material needs, one of these sciences which are not devoted to utilitarian ends [mathematics] has been able to arise in Egypt, the priestly caste there having the leisure necessary for disinterested research. Metaphysica, 1-981b
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Aristotle (ca 330 BC) The whole is more than the sum of its parts. Metaphysica 10f-1045a
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Aristotle It is not once nor twice but times without number that the same ideas make their appearance in the world. ‘On The Heavens’, in T. L. Heath Manual of Greek Mathematics, Oxford: Oxford University Press, 1931.
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Aristotle The mathematical sciences particularly exhibit order, symmetry, and limitation; and these are the greatest forms of the beautiful. Metaphysica, 3-1078b.
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Aristotle The so-called Pythagoreans, who were the first to take up mathematics, not only advanced this subject, but saturated with it, they fancied that the principles of mathematics were the principles of all things. Metaphysica 1-5
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Aristotle To Thales the primary question was not what do we know, but how do we know it. Mathematical Intelligencer v. 6, no. 3, 1984.
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Ascham, Roger (1515-1568) Mark all mathematical heads which be wholly and only bent on these sciences, how solitary they be themselves, how unfit to live with others, how unapt to serve the world. In E G R Taylor, Mathematical Practitioners of Tudor and Stuart England, Cambridge: Cambridge University Press, 1954.
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Aubrey, John (1626-1697) [About Thomas Hobbes:] He was 40 years old before he looked on geometry; which happened accidentally. Being in a gentleman’s library, Euclid’s Elements lay open, and ’twas the 47 El. libri I’ [Pythagoras’ Theorem]. He read the proposition ‘By God’, sayd he, ‘this is impossible:’ So he reads the demonstration of it, which referred him back to such a proposition; which proposition he read. That referred him back to another, which he also read. Et sic deinceps, that at last he was demonstratively convinced of that trueth. This made him in love with geometry. In O. L. Dick (ed.) Brief Lives, Oxford: Oxford University Press, 1960, p. 604.
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Auden, W. H. (1907-1973) Thou shalt not answer questionnaires Or quizzes upon world affairs, Nor with compliance Take any test. Thou shalt not sit with statisticians nor commit A social science. ‘Under which lyre’ in Collected Poems of W H Auden, London: Faber and Faber.
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Augarten, Stan Computers are composed of nothing more than logic gates stretched out to the horizon in a vast numerical irrigation system. State of the Art: A Photographic History of the Integrated Circuit. New York: Ticknor and Fields.
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Babbage, Charles (1792-1871) On two occasions I have been asked [by members of Parliament], ‘Pray, Mr. Babbage, if you put into the machine wrong figures, will the right answers come out?’ I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question.
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