1.NP complete problem. On a Saturday night, you attended a grand party. It's embarrassing. You want to know if there is anyone you already know in this hall. The host of the party hinted to you that you must know Ms. Ross sitting in the corner near the dessert plate. You don't need a second to glance over there and find that the host of the party is right. However, if there is no such hint, you must look around the whole hall and look at everyone one by one to see if there is anyone you know.
2. Hodge conjecture. Mathematicians in the twentieth century found an effective method to study the shapes of complex objects. The basic idea is to ask to what extent we can shape a given object by bonding simple geometric building blocks with added dimensions. This technology has become so useful that it can be popularized in many different ways; Finally, some powerful tools were used to make mathematicians make great progress in classifying various objects they encountered in their research.
3. Poincare conjecture. If we stretch the rubber band on the surface of the apple, we can move it slowly and shrink it into a point without breaking it or letting it leave the surface. On the other hand, if we imagine that the same rubber belt is stretched in a proper direction on the tire tread, there is no way to shrink it to a point without destroying the rubber belt or tire tread.
4. Riemann hypothesis. Some numbers have special properties and cannot be expressed by the product of two smaller numbers, such as 2, 3, 5, 7, etc. Such numbers are called prime numbers; They play an important role in pure mathematics and its application. In all natural numbers, the distribution of such prime numbers does not follow any laws.
However, German mathematician Riemann (1826 ~ 1866) observed that the frequency of prime numbers is closely related to the behavior of a well-constructed so-called Riemann zeta function zeta (s). The famous Riemann hypothesis asserts that all meaningful solutions of the equation ζ (s) = 0 are on a straight line.
5. The existence and quality gap of 5.Young-Mills. The laws of quantum physics are established for the elementary particle world, just as Newton's classical laws of mechanics are established for the macroscopic world. About half a century ago, Yang Zhenning and Mills discovered that quantum physics revealed the amazing relationship between elementary particle physics and geometric object mathematics.
6. Existence and smoothness of Naville-Stoke equation. The undulating waves follow our ship across the lake, and the turbulent airflow follows the flight of our modern jet plane. Mathematicians and physicists are convinced that both breeze and turbulence can be explained and predicted by understanding the solution of Naville-Stokes equation.
7.BSD conjecture. Mathematicians are always fascinated by the characteristics of all integer solutions of such algebraic equations. Euclid once gave a complete solution to this equation, but for more complex equations, it became extremely difficult.
Baidu Encyclopedia-Seven Mathematical Problems in the World