2/kloc-0 At the beginning of the 20th century, the Clay Institute of Mathematics (CMI) in Cambridge, Massachusetts, USA consulted David Hilbert, a German mathematician, more than 0/00 years ago, and publicly collected the answers to seven mathematical questions at the Millennium Annual Meeting held in France on May 24th, 2000. These seven questions were carefully selected by the Scientific Advisory Committee of Clay Institute of Mathematics, and the board of directors of Clay Institute of Mathematics provided a prize of one million dollars for the solution of each question. These questions are (in alphabetical order) [description of 7 questions]
1.Birch and Swinerton-Dyer conjecture: for any elliptic curve in rational number domain, the zero order of its l function in 1 is equal to the rank of Abel group formed by rational points on the curve.
2.Hodge conjecture: On nonsingular complex projective algebras, any Hodge class is a rational linear combination of algebraic closed-chain classes.
3. Naville-Stokes equation: Prove or deny the existence and smoothness of the solution of three-dimensional Naville-Stokes equation (under reasonable boundary and initial conditions).
4.P VS NP problem: Is the problem class P with deterministic polynomial time algorithm equal to the problem class NP with uncertain polynomial time algorithm?
5. Poincare conjecture: Any closed and simply connected 3- stream homeomorphism in 3- sphere.
6. Riemann hypothesis: The real parts of nontrivial zeros of Riemann zeta function are all 1/2.
7. Yang-Mills Theory: A Proof of Quantum Yang? Mills field exists and there is a mass gap.
Poincaré conjecture
Poincare conjecture: Poincare proposed in a set of papers published in 1904 that any simply connected and closed three-dimensional manifold is homeomorphic to a three-dimensional sphere.
For example, if we stretch the rubber band around the surface of an 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. We say that the apple surface is "single connected", but the tire tread is not. About a hundred years ago, Poincare knew that the two-dimensional sphere could be characterized by simple connectivity in essence, and he put forward the corresponding problem of the three-dimensional sphere (all points in the four-dimensional space at a unit distance from the origin). This problem became extremely difficult at once, and mathematicians have been fighting for it ever since.
history
Poincare conjecture was put forward by French mathematician Henri Poincare in 1904. No one can solve it in a hundred years. Shortly after Poincare conjecture was put forward, it was extended to the case of n≥4 dimensions, which is called generalized Poincare conjecture. 196 1 year, the American mathematician S.Smale used a very clever method to bypass the difficult situation of giving three or four, and proved the Poincare conjecture with more than five dimensions. 198 1 year, another American mathematician, M.Freedman, proved the four-dimensional conjecture, so far the generalized Poincare conjecture has been proved. But today, Poincare's conjecture remains the same. In 2002, a paper by Russian mathematician grigory perelman proved this conjecture.
On June 3rd, 2006, Qiu Chengtong, a professor of Harvard University, a famous mathematician and a winner of Fields Prize, announced at Morningside Mathematics Research Center of China Academy of Sciences that on the basis of the work of American and Russian scientists, Professor Zhu Xiping of Sun Yat-sen University and Cao Huaidong, a mathematician living in the United States and an adjunct professor in Tsinghua University, have completely proved the Poincare conjecture.