Natura non facis Saltus.

In this sense, an object is of the highest degree of complexity if it can do very difficult and involved things.

In any conceivable method ever invented by man, an automaton which produces an object by copying a pattern, will go first from the pattern to a description to the object. It first abstracts what the thing is like, and then carries it out. It’s therefore simpler not to extract from a real object its definition, but to start from the definition.

An element which stimulates itself will hold a stimulus indefinitely.

A large part of mathematics which becomes useful developed with absolutely no desire to be useful, and in a situation where nobody could possibly know in what area it would become useful; and there were no general indications that it ever would be so.

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.

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.

You don’t have to be responsible for the world that you’re in.

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.