The pendulum of mathematics swings back and forth towards abstraction and away from it with a timing that remains to be estimated.

Combinatorics is an honest subject. No adèles, no sigma-algebras. You count balls in a box, and you either have the right number or you haven't. You get the feeling that the result you have discovered is forever, because it's concrete. Other branches of mathematics are not so clear-cut. Functional analysis of infinite-dimensional spaces is never fully convincing; you don't get a feeling of having done an honest day's work. Don't get the wrong idea - combinatorics is not just putting balls into boxes. Counting finite sets can be a highbrow undertaking, with sophisticated techniques.

Making mathematics accessible to the educated layman, while keeping high scientific standards, has always been considered a treacherous navigation between the Scylla of professional contempt and the Charybdis of public misunderstanding.

The pendulum of mathematics swings back and forth towards abstraction and away from it with a timing that remains to be estimated.

Stan Ulam was lazy, ... He talked too much ... He was self-centered ... . He had an overpowering personality.

Mathematics is the study of analogies between analogies. All science is. Scientists want to show that things that don't look alike are really the same. That is one of their innermost Freudian motivations. In fact, that is what we mean by understanding.

It is a common public relations gimmick to give the entire credit for the solution of famous problems to the one mathematician who is responsible for the last step.