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