On May 24th, 2000, the Clay Institute of Mathematics announced that it would award one million dollars to each of the seven "Millennium Mathematical Problems". Here is a brief introduction to these seven difficult problems.
1. poincare conjecture, any closed three-dimensional space must be a three-dimensional sphere as long as all closed curves can be shrunk to one point.
Six centuries of problems remain to be solved.
Two. non deterministic polynomial complete problems
If someone tells you that the number 137 1742 1 can be written as the product of two smaller numbers, you may not know whether to believe him or not, but if he tells you that this number can be decomposed into 3607 times 3803, you can use a pocket calculator to verify whether this number is correct. It is considered to be one of the most prominent problems in logic and computer science to quickly verify an answer with internal structure or spend a lot of time solving it. Is that Steven? It was stated by StephenCook in 197 1.
Third, Hodge conjecture.
Hodge conjecture asserts that for the so-called projective algebraic family, a component called Hodge closed chain is actually a (rational linear) combination of geometric components called algebraic closed chain.
Fourthly, Riemann hypothesis.
The famous Riemann hypothesis asserts that all meaningful solutions of the equation z(s)=0 are on a straight 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.
Fifth, Yang-Mills theory.
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. However, they describe heavy particles and mathematically strict equations have no known solutions. The hypothesis of "quality gap" has never been proved satisfactorily in mathematics.
The intransitive verb Naville-Stokes 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.
Seven, Bell (Birch) and Swanton-Dyer (Swinnerton-Dyer) conjecture.
When the solution is a point of the Abelian cluster, Behe and Swenorton-Dale suspect that the size of the rational point group is related to the behavior of the related Zeta function z(s) near the point s= 1. In particular, this interesting conjecture holds that if z( 1) is equal to 0, there are infinite rational points (solutions); On the other hand, if z( 1) is not equal to 0, there are only a limited number of such points.