1, p and NP problems: a problem is called p if it can be solved by an algorithm that runs polynomial times (that is, the running time is at most a polynomial function with an input size). If the proposed solution can be tested by polynomial algorithm, then the problem becomes NP problem.
2. Riemann hypothesis/Riemann conjecture: Every nontrivial zero of Riemann zeta function has a real part equal to 1/2.
3. Poincare conjecture: Any simply connected three-dimensional closed flow is an embryo in a three-dimensional sphere.
4.Hodge conjecture: Any Hodge class about nonsingular complex projective algebraic family is a rational linear combination of some algebraic closed-chain classes.
algebraic number theory
1847, Cuomo founded algebraic number theory, an important modern discipline. He also proved that Fermat's last theorem holds when n ~ 100, except for irregular prime numbers such as n=37, 59 and 67, which is a great leap.
In history, Fermat's Last Theorem had its climax and legend. Its amazing charm saved the lives of suicide youths at the last moment. He is the German Wolff Kirli. 1908, he set up a prize of 65438+ million marks (equivalent to the current 1600000 USD) for Fermat's Last Theorem, with a term of 1908-2007.