John von Neumann

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1903

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1947

in 1947

" I think that it is a relatively good approximation to truth — which is much too complicated to allow anything but approximations — that mathematical ideas originate in empirics."

"The Mathematician", in The Works of the Mind (1947) edited by R. B. Heywood, University of Chicago Press, Chicago

in 1947

" But, once they are conceived, the subject begins to live a peculiar life of its own and is … governed by almost entirely aesthetical motivations. In other words, at a great distance from its empirical source, or after much "abstract" inbreeding, a mathematical subject is in danger of degeneration. Whenever this stage is reached the only remedy seems to me to be the rejuvenating return to the source: the reinjection of more or less directly empirical ideas."

"The Mathematician", in The Works of the Mind (1947) edited by R. B. Heywood, University of Chicago Press, Chicago

1949

1950

1951

in 1951

" Any one who considers arithmetical methods of producing random digits is, of course, in a state of sin. For, as has been pointed out several times, there is no such thing as a random number — there are only methods to produce random numbers, and a strict arithmetic procedure of course is not such a method."

in Monte Carlo Method (1951) edited by A.S. Householder, G.E. Forsythe, and H.H. Germond

1952

1953

1954

in 1954

" A large part of mathematics which becomes useful developed with absolutely no desire to be useful, and in a situation where nobody could possibly know in what area it would become useful; and there were no general indications that it ever would be so."

"The Role of Mathematics in the Sciences and in Society" an address to Princeton alumni

(

39.283,-76.616

) in 1954

" By and large it is uniformly true in mathematics that there is a time lapse between a mathematical discovery and the moment when it is useful; and that this lapse of time can be anything from 30 to 100 years, in some cases even more; and that the whole system seems to function without any direction, without any reference to usefulness, and without any desire to do things which are useful."

"The Role of Mathematics in the Sciences and in Society" (1954) an address to Princeton alumni

1955

in 1955

" The sciences do not try to explain, they hardly even try to interpret, they mainly make models. By a model is meant a mathematical construct which, with the addition of certain verbal interpretations, describes observed phenomena. The justification of such a mathematical construct is solely and precisely that it is expected to work."

"Method in the Physical Sciences", in The Unity of Knowledge (1955), ed. L. G. Leary (Doubleday & Co., New York), p. 157

in 1955

" When we talk mathematics, we may be discussing a secondary language built on the primary language of the nervous system."

As quoted in John von Neumann

in 1955

" It is just as foolish to complain that people are selfish and treacherous as it is to complain that the magnetic field does not increase unless the electric field has a curl. Both are laws of nature."

1956

in 1956

" It is exceptional that one should be able to acquire the understanding of a process without having previously acquired a deep familiarity with running it, with using it, before one has assimilated it in an instinctive and empirical way… Thus any discussion of the nature of intellectual effort in any field is difficult, unless it presupposes an easy, routine familiarity with that field. In mathematics this limitation becomes very severe."

As quoted in "The Mathematician" in The World of Mathematics

1957

in 1957

" If you say why not bomb them tomorrow, I say why not today? If you say today at five o' clock, I say why not one o' clock?"

As quoted in "The Passing of a Great Mind" by Clay Blair, Jr., in LIFE Magazine

Other Events

"Anyone who attempts to generate random numbers by deterministic means is of course living in a state of sin."

"It would appear that we have reached the limits of what it is possible to achieve with computer technology although one should be careful with such statements as they tend to sound pretty silly in 5 years."