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.

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

Very little mathematics has direct applications - though fortunately most of it has plenty of indirect ones.

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.

Every field has its taboos. In algebraic geometry the taboos are (1) writing a draft that can be followed by anyone but two or three of one's closest friends, (2) claiming that a result has applications, (3) mentioning the word 'combinatorial,' and (4) claiming that algebraic geometry existed before Grothendieck (only some handwaving references to 'the Italians' are allowed provided they are not supported by specific references).

God created infinity, and man, unable to understand infinity, had to invent finite sets.

We often hear that mathematics consists mainly of "proving theorems." Is a writer's job mainly that of "writing sentences?"