If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.
Remark made by von Neumann as keynote speaker at the first national meeting of the Association for Computing Machinery in 1947, as mentioned by Franz L. Alt at the end of "Archaeology of computers: Reminiscences, 1945--1947", Communications of the ACM, volume 15, issue 7, July 1972, special issue: Twenty-fifth anniversary of the Association for Computing Machinery, p. 694.
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.John Von Neumann
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.John Von Neumann
When we talk mathematics, we may be discussing a secondary language built on the primary language of the nervous system.John Von Neumann
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
Young man, in mathematics you don't understand things. You just get used to them.John Von Neumann
The goys have proven the following theorem…John Von Neumann
You wake me up early in the morning to tell me that I'm right? Please wait until I'm wrong.John Von Neumann
If one has really technically penetrated a subject, things that previously seemed in complete contrast, might be purely mathematical transformations of each other.John Von Neumann
There probably is a God. Many things are easier to explain if there is than if there isn't.John Von Neumann