“The number of syllables in the English names of finite integers tends to increase as the integers grow larger, and must gradually increase indefinitely, since only a finite number of names can be made with a given finite number of syllables. Hence the names of some integers must consist of at least nineteen syllables, and among these there must be a least. Hence "the least integer not nameable in fewer than nineteen syllables" must denote a definite integer; in fact, it denotes 111, 777. But "the least integer not nameable in fewer than nineteen syllables" is itself a name consisting of eighteen syllables; hence the least integer not nameable in fewer than nineteen syllables can be named in eighteen syllables, which is a contradiction. This contradiction was suggested to us by Mr. G. G. Berry of the Bodleian Library.”
Principia Mathematica, written with Alfred North Whitehead, (1910), vol. I, Introduction, ch. II: The Theory of Logical Types. This is a statement of the Berry paradox.
1910s
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Bertrand Russell562
logician, one of the first analytic philosophers and politi… 1872–1970Related quotes
“God made the integers, all the rest is the work of man.”
Leopold Kronecker (1823–1891) German mathematician who worked on number theory and algebra (1823–1891)
Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk.
Quoted in "Philosophies of Mathematics" - Page 13 - by Alexander George, Daniel J. Velleman - Philosophy - 2002
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Source: Group Theory in the Bedroom (2008), Chapter 11, Identity Crisis, p. 206 (See also: George Cantor)
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Roger Cooke in: The history of mathematics: a brief course http://books.google.co.in/books?id=z-ruAAAAMAAJ, Wiley, 7 October 1997, p. 207.
“Is a woman a thinking unit at all, or a fraction always wanting its integer?”
Thomas Hardy (1840–1928) English novelist and poet
Henry Burchard Fine (1858–1928) American academic
Source: The Number-System of Algebra, (1890), p. 86; Reported in Moritz (1914, 282)
John Edensor Littlewood (1885–1977) English Mathematician
(about Ramanujan) p. lvii of [Hardy, G. H., G. H. Hardy, Obituary Notices: Srinivasa Ramanujan, Proceedings of the London Mathematical Society, 19, xl-lviii, 1921, http://www.numbertheory.org/obituaries/LMS/ramanujan/index.html, 2008-05-26]
Georg Cantor (1845–1918) mathematician, inventor of set theory
Letter to Gustac Enestrom, as quoted in Georg Cantor : His Mathematics and Philosophy of the Infinite (1990) by Joseph Warren Dauben ~ ISBN 0691024472
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Source: An Introduction to English Poetry (2002), Ch. 18: Syllabics (p. 99)