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.
There probably is a God. Many things are easier to explain if there is than if there isn’t.
There’s no sense in being precise when you don’t even know what you’re talking about.
Young man, in mathematics you don’t understand things. You just get used to them.
I would like to make a confession which may seem immoral: I do not believe in Hilbert space anymore.
When we talk mathematics, we may be discussing a secondary language built on the primary language of the nervous system.
Anyone who attempts to generate random numbers by deterministic means is, of course, living in a state of sin.
All stable processes we shall predict. All unstable processes we shall control.
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.
Truth is much too complicated to allow anything but approximations.
You don’t have to be responsible for the world that you’re in.
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.
I am thinking about something much more important than bombs. I am thinking about computers.
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.
With four parameters I can fit an elephant, and with five I can make him wiggle his trunk.
You wake me up early in the morning to tell me I am right? Please wait until I am wrong.
If one has really technically penetrated a subject, things that previously seemed in complete contrast, might be purely mathematical transformations of each other.
Technological possibilities are irresistible to man. If man can go to the moon, he will. If he can control the climate, he will.
Life is a process which may be abstracted from other media.
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.