One of the seven math problems has been solved. The seven "world puzzles" are NP-complete problem, Hodge conjecture, Poincare conjecture, Riemann hypothesis, existence and poor quality of Young-Mills, Naville-Stoke equation and BSD conjecture. The main problems in mathematics usually don't always attract outside interest like the secrets in other scientific fields. "Many people are still confused about the appearance or significance of mathematical research," said Wei Huo, a mathematician at the University of Michigan. Although people often misunderstand the nature of her work, it is not difficult to explain why. "The topic I chat at parties is always about elliptic curves," she added. He often asks people attending parties, "Do you still remember the parabola and circle you learned in middle school? Once you start to create cubic equations, things will become very difficult ... there are still many unresolved questions about them. "

A well-known unsolved puzzle named Birchands Winnerton-Dyer conjecture involves the properties of solutions of elliptic curve equations, and it is one of the seven Millennium Prize-winning puzzles selected by ClayMathematicsInstitute (CMI). These selected problems are described by the institute as "the most difficult problems that mathematicians try to solve at the turn of the millennium".

On May 24th, 2000, in a special event held in Paris, the Institute announced that it would provide the first person to prove or overturn any difficult problem with a prize of $6,543,800+.

The revised rule of 20 18 stipulates that the results must be "generally accepted by the global mathematics community".

The announcement in 2000 provided people with a "reason" worth $7 million to solve these seven problems: Riemann conjecture, Behr and Svineton-Dale conjecture, P/NP problem, existence and poor quality of Yang-Mills, Poincare conjecture, existence and smoothness of Naville-Stokes, and Hodge conjecture. Despite the huge momentum and rich economic returns, it took 2 1 year to prove Poincare's conjecture.

Millennium prize issue

1, NP complete problem

Some calculation problems are deterministic, such as addition, subtraction, multiplication and division. As long as you follow the formula step by step, you can get the result. But some problems can't be worked out directly step by step. For example, the answer to the question of finding a big prime number cannot be calculated directly, and the result can only be obtained through indirect "guessing". It is found that all complete polynomial uncertainty problems can be transformed into a kind of logical operation problems called satisfaction problems. Because all possible answers to such questions can be calculated in polynomial time, people want to know whether there is a deterministic algorithm for such questions, and they can directly calculate or search for the correct answers in polynomial time. This is the famous NP=P? Guess.

2. Hodge conjecture

Hodge conjecture is an important unsolved problem in algebraic geometry. It is a conjecture about the association between the algebraic topology of nonsingular complex algebraic clusters and their geometry represented by polynomial equations defining subgroups. In layman's terms, it means "no matter how good and complex the palace is, it can also be made of a pile of building blocks." In the words of literati, any geometric figure, no matter how complicated, can be composed of a bunch of simple geometric figures. In practical work, we can't draw complex multidimensional graphics on two-dimensional paper. Hodge's conjecture is to break the complex topology diagram into components, and as long as they are installed according to the rules, we can understand the designer's ideas.

3. Poincare conjecture

Poincare conjecture is a conjecture put forward by French mathematician Poincare, that is, "any simply connected and closed three-dimensional manifold must be homeomorphic to a three-dimensional sphere." Simply put, a closed three-dimensional manifold is a three-dimensional space with boundaries; Simple connectivity means that every closed curve in this space can shrink to a point continuously, or in a closed three-dimensional space, if every closed curve can shrink to a point, then this space must be a three-dimensional sphere. Poincare conjecture is a proposition of fundamental significance in topology, which will help people to better study three-dimensional space, and the result will deepen people's understanding of manifold properties.

4. Riemann hypothesis

Riemann conjecture is a conjecture about the zero distribution of Riemann zeta function zeta (s), which was put forward by the mathematician Riemann in 1859. Some numbers have special properties and cannot be expressed by the product of two smaller integers, such as 2, 3, 5, 7 and so on. 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. The famous Riemann hypothesis asserts that all meaningful solutions of the equation ζ(s)=0 are on a straight line z= 1/2+ib, where b is a real number, and this straight line is usually called the critical line. This has been verified in the first batch of 150000000 solutions. Proving that it applies to every meaningful solution will uncover many mysteries surrounding the distribution of prime numbers.

5. The existence and quality gap of Poplar Mill.

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. 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. The progress on this issue needs to introduce basic new concepts into physics and mathematics.

6. 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. Although these equations were written in19th century, we still know little about them. The challenge is to make substantial progress in mathematical theory, so that we can solve the mystery hidden in Naville-Stokes equation.

7.BSD conjecture

BSD conjecture, the full name of Behr and Swinaton-Dale conjecture, describes the relationship between the arithmetic properties and analytical properties of Abelian clusters. 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.