NP-complete problem (NP-C problem) is one of the seven major mathematical problems in the world. The English full name of NP is the problem of nondeterministic polynomials, that is, the uncertainty of polynomial complexity. The simple writing is NP=P? The question is whether NP is equal to p or NP is not equal to p.
2. Hodge conjecture
Hodge conjecture is an important unsolved problem in algebraic geometry. Proposed by william vallance douglas hodge, it is a conjecture about the correlation between the algebraic topology of nonsingular complex algebraic clusters and the geometry represented by polynomial equations defining subgroups, which belongs to one of the seven major mathematical problems in the world.
3. Poincare conjecture
Poincare conjecture is a conjecture put forward by French mathematician Poincare, and its three-dimensional situation was proved by Russian mathematician grigory perelman around 2003. In 2006, the mathematical community finally confirmed that perelman's proof solved Poincare's conjecture. Later, this conjecture was extended to more than three dimensions, and it was called the high-dimensional Poincare conjecture. After putting forward this conjecture, Poincare once thought that he had proved it.
4. Overview of Riemann Hypothesis
Some numbers have special properties, and they cannot be expressed as the product of two smaller numbers, such as 2, 3, 5, 7, etc. Such numbers are called prime numbers and play an important role in the fields of pure mathematics and applied mathematics. The distribution of prime numbers in all natural numbers does not follow any laws. However, German mathematician Riemann (1826- 1866) observed that the frequency of prime numbers is closely related to a complex function.
5. The existence and quality gap of young mills.
The existence and poor quality of Young Mills is one of the seven major mathematical problems in the world, which originated from Young Mills theory in physics. The formal expression of this problem is to prove that for any compact and simple gauge group, Young Mills equation in four-dimensional Euclidean space has a solution to predict the existence of mass gap. The solution of this problem will clarify the basic aspects of nature that physicists have not fully understood.
6. Naville-Stokes equation
The relationship between the change rate (acceleration) of fluid particle momentum and the change of pressure acting inside the liquid, the dissipation of viscous force (similar to friction force) and gravity is established. These viscous forces come from the interaction between molecules and can tell us how viscous the liquid is. In this way, Naville-Stokes equation describes the dynamic balance of forces acting on any given area of liquid, which is of great significance in fluid mechanics.
7.BSD conjecture
BSD conjecture, named Birchand Swinnerton-Dyer conjecture, belongs to one of the seven mathematical problems in the world. Given an Abelian cluster in a global domain, it is assumed that the rank of its module group is equal to the zero order of its L function at 1, and the first term coefficient of Taylor expansion of its L function at 1 has an exact equality relationship with the finite part size, free part volume, periods of all prime positions and sand groups of the module group.
8. Goldbach conjecture
Goldbach put forward the following conjecture in his letter 1742 to Euler: any even number greater than 2 can be written as the sum of two prime numbers. But Goldbach himself could not prove it, so he wrote to the famous mathematician Euler and asked him to help him prove it, but until his death, Euler could not prove it.
9. Four-color theorem
Four-color theorem, also known as four-color conjecture and four-color problem, is one of the three major mathematical conjectures in the world. The essence of the four-color theorem is the inherent property of a two-dimensional plane, that is, two straight lines in the plane that cannot intersect and have no common points. The content of the four-color problem is that any map with only four colors can make countries with the same border have different colors. In other words, a map only needs four colors to mark it, which will not cause confusion.
10, Fermat's last theorem
Fermat's Last Theorem, also known as Fermat's Last Theorem, was put forward by French mathematician Pierre de Fermat in the 7th century. The theorem asserts that when the integer n > 2, the equation x n+y n = z n about x, y and z has no positive integer solution. After Fermat's last theorem was put forward, it experienced many people's conjectures and dialectics. After more than 300 years of history, it was finally proved by the British mathematician andrew wiles in 1995.