P pair NP problem, Hodge conjecture, Riemann hypothesis, existence and poor quality of Young-Mills theory, existence and smoothness of Navier-Stokes equation, BSD conjecture.

In May, 2000, Clay Institute of Mathematics (CMI), founded by American tycoons, carefully selected seven unsolved mathematical problems. Anyone who solves these problems can get a bonus of up to one million dollars. These seven problems are also called "seven difficult problems of Millennium mathematics".

Only one of the seven Millennium problems has been solved:

But now 20 years later, six of the seven problems remain unsolved. The only thing that has been broken is the "Poincare conjecture" that has plagued mankind for nearly a hundred years.

A language that can be popularly understood can be defined as: in a three-dimensional space, if every closed curve can be contracted to a point, then this space must be a three-dimensional sphere. 1904, the French scientist Poincare, known as the last encyclopedia, put forward this conjecture. Poincare conjecture "is the basic problem of topology." If this problem is solved, human understanding of the universe and space will be further deepened. ”。

This problem was solved by the talented Russian mathematician Gregory perelman. He is tied with German peter schulz as the top young mathematician in the world, and both of them have won the top Fields Prize in mathematics.