P and NP problem p problem p is the first letter of polynomial time. The time t used by deterministic (non-probabilistic) algorithm to calculate a problem is a polynomial function t=P(n) of the problem scale n, so we call it "polynomial time determination method". The problem that this algorithm can solve is the P problem. On the contrary, it is called "non-polynomial time deterministic algorithm", and this kind of problem is "NP problem", which is short for non-deterministic polynomial time. By definition, P problem is a part of NP problem. But is there anything in NP that doesn't belong to P? Or will the NP problem eventually become a P problem? This is the quite famous PNP problem. It is generally believed that there is something in NP problem that does not belong to the level of P problem.

Riemann assumes that all nontrivial zeros of zeta function zeta (s) (s belongs to c) are on the straight line Re(z)= 1/2 of the complex plane.

Yang-Mill Theory In the theory put forward by Yang Zhenning and Mills, there will be particles that transmit force, and the difficulty they encounter is the quality of this particle. As a result of their mathematical deduction, this particle has a charge and no mass. However, the difficulty is that if this charged particle has no mass, why is there no experimental evidence? If the particle is assumed to have mass, the gauge symmetry will be destroyed. Most physicists believe in quality, so how to fill this loophole is a very challenging mathematical problem.

Pochi and Swinerton- Dai Ya conjecture the rational number solution of y 2 = x 3+ax+b, and this kind of curve will be encountered when calculating the arc length of an ellipse. Since 1950s, mathematicians have found that elliptic curves are closely related to number theory, geometry and cryptography. For example, one of the key steps for wiles to prove Fermat's Last Theorem is to use the relationship between elliptic curve and module form, that is, the Gushan-Zhicun conjecture. The typical mathematical method is the concept of congruence, from which the congruence class, that is, the remainder after dividing a number, is obtained. Mathematicians naturally choose prime numbers, so this problem is related to the Zeta function of Riemann conjecture. After a long period of calculation and data collection, Pochi and others observed some laws and patterns and put forward this conjecture. According to the results of computer calculation, they assert that an elliptic curve will have infinite rational points if and only if it is attached to the curve.

The zeta function zeta (s) takes the value of 0 when s= 1, that is, zeta (1) = 0.

Hodge conjecture: Any harmonic differential form on nonsingular projective algebraic curve is one of algebraic circles.

Rational combination of cohomology classes.

There seems to be an unconfirmed list of number theory in Wikipedia.

Take your time. . . . . . . . . . .