Which 1900 mathematical address set an agenda that occupied the next century?

Hilbert's, at the International Congress in Paris - a list of 23 unsolved problems, chosen to point the field where he thought it should go. He was 38, and the talk was a bet that mathematics had no limits: his phrase was that in mathematics there is no ignorabimus, no we shall not know.

Several of the answers were no. The second problem, asking for a proof that arithmetic is consistent, was answered by Gödel showing that no such proof can be given from within the system; the tenth, asking for an algorithm to decide whether a polynomial equation has whole-number solutions, was answered by proving no algorithm exists. Hilbert's programme was refuted by the work it provoked, which is a peculiar kind of success.

Others are still open. The eighth includes the Riemann hypothesis, about where the zeros of a particular function lie, which controls how the prime numbers are distributed and is now the most famous unsolved problem in mathematics. It is one of the seven Millennium Prize problems, each carrying a million dollars; only one of those has been solved, the Poincaré conjecture, and Perelman refused the money.