John von Neumann Quotes About Mathematics

Quotes about: Mathematics

• If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.

  John von Neumann

  Believe, Math, Simple

  John von Neumann's remarks as keynote speaker at the first national meeting of the Association for Computing Machinery (1947) as quoted in "Archaeology of computers: Reminiscences, 1945-1947" by Franz L. Alt, Communications of the ACM, Volume 15, Issue 7, special issue: Twenty-fifth anniversary of the Association for Computing Machinery (p. 694), July 1972.

• Young man, in mathematics you don't understand things. You just get used to them.

  John von Neumann

  Math, Science, Men

  Quoted in Gary Zukav, The DancingWu Li Masters (1979)

• 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-that is, correctly to describe phenomena from a reasonably wide area.

  John von Neumann

  Science, Trying, Mathematics

  John Von Neumann, F. Bródy, Tibor Vámos (1995). “The Neumann Compendium”, p.628, World Scientific

• 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.

  John von Neumann

  Teaching, Math, Thinking

  John Von Neumann, F. Bródy, Tibor Vámos (1995). “The Neumann Compendium”, p.620, World Scientific

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

  John von Neumann

  May, Language, Nervous

  "John Von Neumann, 1903-1957". Book edited by John C. Oxtoby, Billy J. Pettis and G. B. Price, 1958.

• 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.

  John von Neumann

  Running, Effort, Understanding

  John Von Neumann, F. Bródy, Tibor Vámos (1995). “The Neumann Compendium”, p.618, World Scientific

• The total subject of mathematics is clearly too broad for any of us. I do not think that any mathematician since Gauss has covered it uniformly and fully; even Hilbert did not and all of us are of considerably lesser width quite apart from the question of depth than Hilbert.

  John von Neumann

  Thinking, Depth, Mathematics

• I would like to make a confession which may seem immoral: I do not believe absolutely in Hilbert space any more.

  John von Neumann

  Believe, Space, May

  "John Von Neumann: Selected Letters".

• The emphasis on mathematical methods seems to be shifted more towards combinatorics and set theory - and away from the algorithm of differential equations which dominates mathematical physics.

  John von Neumann

  Algorithms, Physics, Mathematics

  John Von Neumann, F. Bródy, Tibor Vámos (1995). “The Neumann Compendium”, p.453, World Scientific

• Neumann, to a physicist seeking help with a difficult problem: Simple. This can be solved by using the method of characteristics. Physicist: I'm afraid I don't understand the method of characteristics. Neumann: In mathematics you don't understand things. You just get used to them.

  John von Neumann

  Science, Simple, Understanding

  Quoted in Gary Zukav, The DancingWu Li Masters (1979)

• The most vitally characteristic fact about mathematics is, in my opinion, its quite peculiar relationship to the natural sciences, or more generally, to any science which interprets experience on a higher than purely descriptive level.

  John von Neumann

  Levels, Facts, Peculiar

  John Von Neumann, F. Bródy, Tibor Vámos (1995). “The Neumann Compendium”, p.618, World Scientific

• 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.

  John von Neumann

  Years, Discovery, Desire

  "The Role of Mathematics in the Sciences and in Society". John von Neumann's address to Princeton alumni (1954) as quoted in "John von Neumann: Collected Works" edited by A. H. Taub, 1963.

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