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

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

Our faith in Mathematics is not likely to wane if we openly acknowledge that the personalities of even the greatest mathematicians may be as flawed as those of anyone else.

The progress of mathematics can be viewed as progress from the infinite to the finite.

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

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).

The apex of mathematical achievement occurs when two or more fields which were thought to be entirely unrelated turn out to be closely intertwined. Mathematicians have never decided whether they should feel excited or upset by such events.