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

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.

By and large it is uniformly true that in mathematics there is a time lapse between a mathematical discovery and the moment it becomes useful; and that this lapse can be anything from 30 to 100 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.

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

There is an infinite setAthat is not too big.

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

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.

It would appear that we have reached the limits of what it is possible to achieve with computer technology, although one should be careful with such statements, as they tend to sound pretty silly in 5 years.

(Said in 1949)

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

If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.