1. Riemann conjecture: On the distribution of prime numbers. Riemann conjecture holds that the distribution of prime numbers follows certain laws, but so far no method has been found to prove or refute this conjecture.

2. Poincare conjecture: the problem of closed borderless shape in three-dimensional space. Poincare conjecture holds that the closed borderless shape in three-dimensional space must be composed of massless and uncharged substances, but so far no method has been found to prove or refute this conjecture.

3.PvsNP problem: the problem of computational complexity. The PvsNP problem is to ask whether there is an algorithm that can quickly verify whether the solution of a problem is correct or not, and whether the problem itself belongs to a P-type problem (which can be solved in polynomial time). At present, no solution to this problem has been found.

4. The existence of 4.Young-Mills and the problem of mass gap: the problem of quantum field theory. The existence and mass gap of Young-Mills is to ask whether there is a particle with a gap between mass and charge, and the existence of this particle can be described by quantum field theory. At present, no solution to this problem has been found.

5. Hodge conjecture: a question about algebraic geometry. Hodge conjecture is about the relationship between harmonic forms and their integrals on complex algebraic curves. At present, no solution to this problem has been found.