1, p and NP problems: a problem is called p if it can be solved by an algorithm that runs polynomial times (that is, the running time is at most a polynomial function with an input size). If the proposed solution can be tested by polynomial algorithm, then the problem becomes NP problem.

2. Riemann hypothesis/Riemann conjecture: Every nontrivial zero of Riemann zeta function has a real part equal to 1/2.

3. Poincare conjecture: Any simply connected three-dimensional closed flow is an embryo in a three-dimensional sphere.

4.Hodge conjecture: Any Hodge class about nonsingular complex projective algebraic family is a rational linear combination of some algebraic closed-chain classes.

5.Birch and Swinnerton-Dyer conjecture: For every elliptic curve based on rational number field, the order where its L function becomes zero is equal to the rank of Abel group of rational points on the curve.

6. Naville-Stoke equation: Prove or deny the existence of smooth solution of three-dimensional Naville-Stoke equation (under appropriate boundary and initial conditions).

7. Young-Mills theory: It is proved that the quantum Young-Mills field exists and there is a mass gap.