On July 12, 2016, Prof. Zhang Yitang, a famous mathematician, was invited to the 77th SUSTech Lecture and delivered an inspiring lecture on twin primes for the teachers and students of SUSTech in No. 110 Lecture Hall. Some of teachers and students of Shenzhen University and Peking University ShenZhen Graduate School also attended the lecture chaired by Vice President Tang Tao.

On behalf of SUSTech, Tang Tao extended warm welcome to Prof. Zhang.

Prof. Zhang Yitang is a famous Chinese mathematician. In 1978, he was admitted to the Department of Mathematics of Peking University; in 1992, he graduated and received his doctor’s degree at Purdue University. He is currently a professor at the Department of Mathematics at University of California, Santa Barbara. In May 2013, Prof. Zhang made a breakthrough in the twin primes research. He proved a weakened form of the twin prime conjecture. Without relying on unproven premises, he announced a proof that states there are infinitely many pairs of twin primes that differ by 70 million or less, which solved a major issue of the twin prime conjecture and greatly pushed forward the research in the twin prime conjecture. With this major achievement, Prof. Zhang was awarded the 2014 Frank Nelson Cole Prize in Number Theory by American Mathematical Society and the MacArthur Fellowship.

At the beginning of the lecture, Prof. Zhang answered the attendants’ questions about the nature of the research on the number theory, “When I was an undergraduate at Peking University, Prof. Wang Yuan once gave a science lecture and said research on the number theory was like experimental science. What do you use to do experiments? In the number theory, you use numbers, formulas and symbols. The manuscripts of Prof. Chen Jingrun are so many that they can fill several sacks. It is a truth because he had to do a lot of calculation experiments.” It also took Prof. Zhang decades of painstaking research and experiments that he finally discovered a new path for the twin primes issue.

Prof. Zhang admitted that he completed the proof of twin primes based on the work of several mathematicians. Starting from the easy issues and then to the hard ones, Prof. Zhang talked from the infinity of prime numbers and gradually to the twin prime conjecture of (p, p + 2). Later, he explained in detail the weakened form of the twin prime conjecture.

Prof. Zhang briefly showed the main formulas in his mathematical proof. With his step by step deduction and clear explanation, the audience were deeply impressed by his rigorous and meticulous research spirit. He said during the entire process, one major difficulty was to control the deviation within a quarter. To solve this problem, Mathematical Sciences Research Institute convened leading mathematicians in 2008, who concluded that the current approach could not solve the problem after a week’s work. Prof. Zhang said he was not present at the discussion, which roused a burst of laughter from the audience because it was Professor Zhang who finally solved the important problem.

After Prof. Zhang published his research results, mathematicians have lowered the difference between the prime numbers from 70 million to 246. Professor Zhang believes the result can still be improved, but there is still a long way to go before finally proving the twin prime conjecture and lowering the difference to 2.

After the lecture, Prof. Zhang answered the questions from teachers and students patiently. When some students asked what was the motivation that supported his decades of painstaking research, Prof. Zhang summarized in one phrase– “Love for science”.