Millenium Problems

The Millennium Problems are seven mathematical challenges established by the Clay Mathematics Institute in 2000, each with a prize of one million dollars for a correct solution. These problems represent some of the most persistent and critical unsolved issues in mathematics, spanning areas such as number theory, geometry, analysis, and fluid dynamics. Only one of the problems, the Poincaré Conjecture, has been solved so far. Unresolved - as of AE53 - ones are:

Birch and Swinnerton-Dyer Conjecture

Hodge Conjecture

Navier–Stokes Existence and Smoothness

P vs NP Problem

Riemann Hypothesis

Yang–Mills Existence and Mass Gap