I think that it is a relatively good approximation to truth — which is much too complicated to allow anything but approximations.
John von Neumann (1903-1957) Hungarian-American mathematician, physicist, inventor, polymath [János "Johann" Lajos Neumann]
“The Mathematician” (1947)
(Source)
Quotations by:
Von Neumann, John
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. 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 thirty to a hundred 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 (1903-1957) Hungarian-American mathematician, physicist, inventor, polymath [János "Johann" Lajos Neumann]
“The Role of Mathematics in the Sciences and in Society,” Speech, Princeton (1954)
(Source)
In mathematics, you don’t understand things, you just get used to them.
John von Neumann (1903-1957) Hungarian-American mathematician, physicist, inventor, polymath [János "Johann" Lajos Neumann]
(Attributed)
The primary source for this comes from Gary Zukav, The Dancing Wu Li Masters: An Overview of the New Physics (1979), in a footnote on p. 208, related to von Neumann's time working on the H-bomb.
Dr. Felix Smith, Head of Molecular Physics, Stanford Research Institute, once related to me the true story of a physicist friend who worked at Los Alamos after World War II. Seeking help on a difficult problem, he went to the great Hungarian mathematician, John von Neumann, who was at Los Alamos as a consultant.
"Simple," said von Neumann. "The can be solved by using the method of characteristics."
After the explanation, the physicist said, "I'm afraid I don't understand the method of characteristics."
"Young man," said von Neumann, "in mathematics you don't understand things, you just get used to them."
David Wells offers a variant in The Penguin Book of Curious and Interesting Mathematics (1997):
Van Neumann had just about ended his lecture when a student stood up and in a vaguely abashed tone said he hadn't understood the final argument. Von Neumann answered: "Young man, in mathematics you don't understand things. You just get used to them.
Variant: "Don't worry, young man: in mathematics, none of us really understands any idea -- we just get used to them."
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.
John von Neumann (1903-1957) Hungarian-American mathematician, physicist, inventor, polymath [János "Johann" Lajos Neumann]
(Attributed)
(Source)
More in Eugene Wigner, "John von Neumann (1903-1957)," Yearbook of the American Philosophical Society (1958); later collected in Wigner's Symmetries and Reflections.
There probably is a God. Many things are easier to explain if there is than if there isn’t.
John von Neumann (1903-1957) Hungarian-American mathematician, physicist, inventor, polymath [János "Johann" Lajos Neumann]
(Attributed)
(Source)
As quoted in Norman Macrae, John Von Neumann: The Scientific Genius Who Pioneered the Modern Computer, Game Theory, Nuclear Deterrence and Much More (1992).
If you look at automata which have been built by men or which exist in nature you will very frequently notice that their structure is controlled to a much larger extent by the manner in which they might fail and by the (more or less effective) precautionary measures which have been taken against their failure. And to say that they are precautions against failure is to overstate the case, to use an optimistic terminology which is completely alien to the subject. Rather than precautions against failure, they are arrangements by which it is attempted to achieve a state where at least a majority of all failures will not be lethal. There can be no question of eliminating failures or of completely paralyzing the effects of failures. All we can try to do is to arrange an automaton so that in the vast majority of failures it can continue to operate. These arrangements give palliatives of failures, not cures. Most of the arrangements of artificial and natural automata and the principles involved therein are of this sort.
John von Neumann (1903-1957) Hungarian-American mathematician, physicist, inventor, polymath [János "Johann" Lajos Neumann]
Theory of Self-Reproducing Automata, Lecture 3 “Statistical Theories of Information”
(Source)
If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.
John von Neumann (1903-1957) Hungarian-American mathematician, physicist, inventor, polymath [János "Johann" Lajos Neumann]
Speech, Association for Computing Machinery inaugural conference, Columbia University, New York (15 Sep 1947)
(Source)
Von Neumann insisted that ENIAC's command language could encompass all mathematics, given how only a thousand words could handle most needs of life, and mathematics was, he insisted, simpler than life. When the audience laughed, he replied with this comment. Quoted in Franz L. Alt, "Archaeology of computers: Reminiscences, 1945-1947," Communications of the ACM, Vol 15, #7 (Jul 1972).