Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang

To give a sense of the scale of this claim: If correct, Zhang's work is the most significant progress towards the Generalized Riemann Hypothesis in a century. Moreover, I think this result would not only be a more significant advance than Zhang's previous breakthrough, but also constitute a larger leap for number theory than Wiles' 1994 proof of Fermat's Last Theorem (which was, in my opinion, the greatest single achievement by an individual mathematician in the 20th century).

Some discussion / explanation of Siegel zeros and Zhang's claim can be found here:

https://old.reddit.com/r/math/comments/y93a86/eliundergradua...

https://mathoverflow.net/questions/433949/consequences-resul...

An account of Zhang's remarkable story (and his previous breakthrough) can be found here. Famously, prior to his breakthrough, he worked at Subway and lived in his car:

https://www.newyorker.com/magazine/2015/02/02/pursuit-beauty

1. Zhang posted an attempt at solving this problem in 2007 that he later more or less admitted was flawed: https://mathoverflow.net/questions/131221/yitang-zhangs-2007.... But speaking with mathematicians who are intimately familiar with Zhang's previous work, there seems to be good reason to be optimistic nevertheless. First, the idea behind Zhang's proof is similar to the zero-repulsion ideas appearing in known results about Siegel zeros, and is thus reasonable. Second, Zhang seems to have matured late, and unlike the flawed 2007 paper, his 2013 paper on bounded gaps in primes is meticulously written. He came a long way between those two papers, and he may have come even further since then.

2. Zhang is 67 years old. If the paper is correct, then Zhang constitutes a strong counterexample to G.H. Hardy's famous claims that "mathematics is a young man's game" and nobody alive today could say, as Hardy did, that "I do not know an instance of a major mathematical advance initiated by a man past fifty."

> Prior to getting back to academia, he worked for several years as an accountant and a delivery worker for a New York City restaurant. He also worked in a motel in Kentucky and in a Subway sandwich shop. A profile published in the Quanta Magazine reports that Zhang used to live in his car during the initial job-hunting days.

https://en.wikipedia.org/wiki/Yitang_Zhang