9. Young-Mills Existence and Mass Gap: Young-Mills Theory is the basis of modern gauge field theory and an important physical breakthrough in the second half of the 20th century, aiming at describing the behavior of elementary particles with non-Abelian Lie groups. It was first proposed by physicists Yang Zhenning and Mills in 1954. This theory, which was not valued by the physics community at that time, developed into the standard model today through the concepts of spontaneous symmetry breaking and asymptotic freedom introduced by many scholars from 1960 to 1970.
8. Behr and Swenorton-Dale conjecture: Behr and Swenorton-Dale conjecture that the size of rational point group and the behavior of a related Zeta function z(s) near point s= 1 are particularly interesting. If z( 1) is equal to 0 and there are infinite rational points, then if it is not equal to 0,
7. Four-color theorem: 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. Many people have proved that it is impossible to construct five or more connected regions on the two-dimensional plane, but it does not rise to the level of logical relationship and two-dimensional inherent attributes, which leads to many wrong counterexamples. But these are precisely the textual research and development promotion of the rigor of graph theory. The computer proves that although we have made tens of billions of judgments, we have only succeeded in a huge number of advantages, which does not conform to the strict logic system of mathematics, and there are still countless math enthusiasts involved.
6. Goldbach conjecture: Goldbach put forward the following conjecture in the letter to Euler from 1742: 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. 1966 Chen Jingrun proved that "1+2" holds, that is, "any sufficiently large even number can be expressed as the sum of two prime numbers, or the sum of a prime number and a semi-prime number".
5. Fermat's Last Theorem: It was put forward by French mathematician Pierre de Fermat in the 7th century. It asserts that when the integer n
& gt2, the equation about x, y and z x n+y n = z n.
There is no positive integer solution. After it was put forward, it was proved by British mathematician andrew wiles in 1995 after more than 300 years of history.
4. Riemann hypothesis: Riemann hypothesis is that all meaningful solutions of equation z(s)=0 are on a straight line. This point has been solved countless times and proved to bring light to many mysteries surrounding the distribution of prime numbers. The general formulas of pseudo prime numbers and prime numbers tell us that prime numbers and pseudo prime numbers are determined by their variable sets. So her assumption is wrong.
3. Hodge conjecture: He conjectures that for the so-called projective algebraic family, a branch called Hodge closed chain is actually a (rational linear) combination of geometric branches called algebraic closed chain.
2. Poincare conjecture: Poincare conjecture is a conjecture put forward by French mathematician Poincare. In 2006, the mathematical community finally confirmed that perelman's proof solved Poincare's conjecture. 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.
1, NP complete problem: If a person tells you that your number 137 1742 1 can be written as the product of two smaller numbers, he tells you that it can be decomposed into 3607 times 3803, which is verified by the computer. People want to know whether it is possible to calculate directly or find the correct answer in polynomial time. This is NP=P? If there is no hint, it will take a lot of time to answer.