John von Neumann Quotes

24 Sourced Quotes

I think that it is a relatively good approximation to truth — which is much too complicated to allow anything but approximations — that mathematical ideas originate in empirics. But, once they are conceived, the subject begins to live a peculiar life of its own and is … governed by almost entirely aesthetical motivations. In other words, at a great distance from its empirical source, or after much "abstract" inbreeding, a mathematical subject is in danger of degeneration. Whenever this stage is reached the only remedy seems to me to be the rejuvenating return to the source: the reinjection of more or less directly empirical ideas.

John von Neumann
In mathematics you don't understand things. You just get used to them.

John von Neumann
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
Mathematics is not an empirical science, or at least that it is practiced in a manner which differs in several decisive respects from the techniques of the empirical sciences.

John von Neumann
Much of the best mathematical inspiration comes from experience and that it is hardly possible to believe in the existence of an absolute, immutable concept of mathematical rigor, dissociated from all human experience.

John von Neumann
We must regard classical mathematics as a combinatorial game played with symbols.

John von Neumann
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
There are two ways to teach mathematics. One is to take real pains toward creating understanding visual aids, that sort of thing. The other is the old British system of teaching until you're blue in the face.

John von Neumann
Mathematics is nourished by dreamers — as it nourishes them...

John von Neumann
I would like to make a confession which may seem immoral: I do not believe in Hilbert space anymore.

John von Neumann
It must be emphasized that it is not a question of accepting the correct theory and rejecting the false one. It is a matter of accepting that theory which shows greater formal adaptability for a correct extension. This is a formalistic esthetic criterion, with a highly opportunistic flavor.

John von Neumann
You don't have to be responsible for the world that you're in.

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
You should call it entropy, for two reasons. In the first place your uncertainty function has been used in statistical mechanics under that name, so it already has a name. In the second place, and more important, no one really knows what entropy really is, so in a debate you will always have the advantage.

John von Neumann
If you say why not bomb them tomorrow, I say why not today? If you say today at five o' clock, I say why not one o' clock?

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
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
Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin.

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

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

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
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