Mathematician Yitang Zhang Claims to Have Proven Riemann Hypothesis Problem

Yitang Zhang is reported to have said he proved the Landau-Siegel zeros theory in an online salon organized by the Peking University Alumni Association. The article links that claim to the Riemann hypothesis and says it had not yet been fully verified.

Reading notes

#

• Zhang reportedly made the claim on October 15 in an online salon organized by the Peking University Alumni Association.
• The Landau-Siegel zeros theory is described as related to the Riemann hypothesis and to the distribution of prime numbers.
• The text says the claim had not yet been fully verified, and that a paper of more than 100 pages was expected to be sent to a preprint site in early November.
• It presents Landau-Siegel zeros as one of the hardest problems in number theory and as a weak form of the Riemann hypothesis.
• The article says that if Zhang had really proved that Landau-Siegel zeros exist, the Riemann hypothesis would be wrong.
• It also says many people were more inclined to believe Zhang proved the opposite result.
• Zhang had previously said he was paying attention to the Riemann hypothesis.
• In 2007, he submitted a paper on the Landau-Siegel zeros conjecture on arXiv and later said it had bugs.
• In 2019, he said he had made gratifying progress on the conjecture.
• The article recalls his 2013 paper on bounded gaps between primes, which proved there are infinitely many pairs of primes with gaps of less than 70 million.
• It says that paper was reviewed and accepted by The Annals of Mathematics in just over a month.
• Henryk Iwaniec is quoted as supporting acceptance of that paper and saying no flaws were found.
• The article says Zhang has published few papers over more than 40 years of research, and that two other papers were related to the Riemann hypothesis.