John von Neumann (1903-1957) was an influential mathematician best known his contributions to game theory and working on the Manhattan Project during World War II. Von Neumann also made contributions to statistics and quantum mechanics. His daughter Marina von Neumann Whitman said,

...throughout much of his career, he led a double life: as an intellectual leader in the ivory tower of pure mathematics and as a man of action, in constant demand as an advisor, consultant and decision-maker to what is sometimes called the military-industrial complex of the United States... He had the scientist's passion for learning and discovery for its own sake and the genius's ego-driven concern for the significance and durability of his own contributions.This post is a list of quotes from von Neumann talking about mathematics._{}^{}

## Philosophy of mathematics

"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, 1954)

"When we talk mathematics, we may be discussing a secondary language built on the primary language of the nervous system." (Quoted in John von Neumann, 1903-1957 by Oxtoby and Pettis)

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"The calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than anything else the inception of modern mathematics; and the system of mathematical analysis, which is its logical development, still constitutes the greatest technical advance in exact thinking." (Quoted in Bigeometric Calculus by James Stewart)

## Philosophy of science

"Truth.. is much too complicated to allow anything but approximations." (Quoted in The Works of the Mind by R. B. Heywood)

"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." (Quoted in The World of Mathematics by James Roy Newman)

"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." (Method in the Physical Sciences, 1955)

"If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is." (Quoted in Archaeology of computers)

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