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.

Twenty years have passed, and six of the seven difficult problems in Millennium mathematics have not been solved.

In May, 2000, Clay Institute of Mathematics, funded by the American rich, carefully selected seven unsolved mathematical problems. Anyone who solves one of them, whether a mathematician or a tramp, can take away $654.38+00,000. The United States hopes to solve the problem efficiently by offering a reward, which is undoubtedly an opportunity for mathematicians to make a name for themselves. These seven problems are also called "seven difficult problems of Millennium mathematics".

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. ”。