1.NP complete problem

2. Hodge conjecture

3. Poincare conjecture

4. Riemann hypothesis

5. The existence and quality gap of poplar paper mill

6. Existence and smoothness of 6.Navier-Stoke equation

The undulating waves follow our ship across the lake, and the turbulent airflow follows the flight of our modern jet plane. Mathematicians and physicists are convinced that both breeze and turbulence can be explained and predicted by understanding the solution of Naville-Stokes equation. Although these equations were written in19th century, we still know little about them. The challenge is to make substantial progress in mathematical theory, so that we can solve the mystery hidden in Naville-Stokes equation.

7.BSD conjecture

Mathematicians are always fascinated by the characterization of all integer solutions of algebraic equations such as BSD conjecture. Euclid once gave a complete solution to this equation, but for more complex equations, it became extremely difficult. In fact, as Matthias Sevic pointed out, Hilbert's tenth problem has no solution, that is, there is no universal method to determine whether such an equation has an integer solution. When the solution is a point of the Abelian cluster, Behe and Swenorton-Dale suspect that the size of the rational point group is related to the behavior of the related Zeta function z(s) near the point s= 1. In particular, this interesting conjecture holds that if z( 1) equals 0, there are infinite rational points (solutions). On the other hand, if z( 1) is not equal to 0. Then there are only a few such points.