Millennium Prize Problems

The problems divided, very roughly, into two algebraic problems, two topological problems, two problems in mathematical physics, and one problem in the theory of computation.

— Millennium Prize Problems

Posed in 1904 by Henri Poincaré, the leading mathematician of his era and among the most gifted of all time, the Poincaré conjecture is a bold guess about nothing less than the potential shape of our own universe.

— Millennium Prize Problems

The P versus NP problem was first mentioned in a 1956 letter from Kurt Gödel to John von Neumann, two of the greatest mathematical minds of the twentieth century.

— Millennium Prize Problems

The Hodge conjecture postulates a deep and powerful connection between three of the pillars of modern mathematics: algebra, topology, and analysis.

— Millennium Prize Problems

At the beginning of the new millennium the most famous unsolved problem in Analytic number theory and complex analysis, if not in all of mathematics, is to determine whether the Riemann Hypothesis holds.

— Millennium Prize Problems

The BSD Conjecture has its natural context within the larger scope of modern algebraic geometry and number theory.

— Millennium Prize Problems