1. prime number research: Professor Zhang's main research field is prime number distribution. 20 13 proves a result about the irrelevance of prime algebra, which is called "a milestone in the field of prime numbers". He proved that there are infinite pairs of prime numbers, their sum is prime number, and their difference is also prime number. This result solved an unsolved problem that lasted for more than 70 years.
2. Riemann conjecture: Riemann conjecture is one of the most famous unsolved problems in the history of mathematics, which involves the distribution law of prime numbers. Professor Zhang has also made important contributions in this field. He proved that the real part of some nontrivial zeros of Riemannian zeta function is less than 1/2. Although this result cannot directly prove Riemann conjecture, it provides a new way to solve this problem.
3. Academic contribution: Professor Zhang's academic contribution is not only reflected in his research results, but also actively promotes the development of mathematics in China. He is the president of Peking University Institute of Mathematical Sciences, and devoted himself to training a new generation of mathematicians.
4. International recognition: Professor Zhang's research results have been widely recognized by the international mathematics community. In 20 14, he won the Sloan research prize, the highest prize in the field of prime number research.
Generally speaking, Professor Zhang's mathematical achievements are mainly reflected in his research on the distribution of prime numbers, especially the proof of the independence of prime algebra and the study of Riemann conjecture. His work not only promoted the development of mathematical theory, but also provided new ideas for solving other mathematical problems.