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

Categorized in : Thinking Depth 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

simple math believe

You insist that there is something a machine cannot do. If you tell me precisely what it is a machine cannot do, then I can always make a machine which will do just that.

John von Neumann

machines ifs justice

Computers are like humans - they do everything except think.

John von Neumann

computer humans thinking

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

John von Neumann

math men science

Science, as well as technology, will in the near and in the farther future increasingly turn from problems of intensity, substance, and energy, to problems of structure, organization, information, and control.

John von Neumann

technology organization energy

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

mathematics trying science

There's no sense in being precise when you don't even know what you're talking about.

John von Neumann

programming knows talking

Truth is much too complicated to allow anything but approximations.

John von Neumann

truth-is complicated religion

If you tell me precisely what it is a machine cannot do, then I can always make a machine which will do just that.

John von Neumann

machines i-can ifs

Anyone who attempts to generate random numbers by deterministic means is, of course, living in a state of sin.

John von Neumann

numbers science mean

All stable processes we shall predict. All unstable processes we shall control.

John von Neumann

meteorology unstable process

With four parameters I can fit an elephant, and with five I can make him wiggle his trunk.

John von Neumann

fit four elephants

There probably is a God. Many things are easier to explain if there is than if there isn't.

John von Neumann

easier ifs god

Technological possibilities are irresistible to man. If man can go to the moon, he will. If he can control the climate, he will.

John von Neumann

climate moon men

I am thinking about something much more important than bombs. I am thinking about computers.

John von Neumann

bombs important thinking

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

John von Neumann

nervous language may

Problems are often stated in vague terms... because it is quite uncertain what the problems really are.

John von Neumann

uncertain term problem

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

John von Neumann

space may believe

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

selfish law people

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