For those who don't know, Jordan Ellenberg (the author of this blog) is a relatively famous and extremely well-regarded math professor at the University of Wisconsin. I was fortunate enough to have him on my Ph.D. thesis committee.

Terence Tao (see the blog comments), as many HN readers know, is a Fields medalist and quite brilliant. Brian Conrad (again, see the blog comments) is a professor at Stanford who is incredible, he knows algebraic number theory as well as anyone, and he has a great nose for bullshit (as well as no patience for it).

This paper is outside my immediate area, so I can't comment scientifically. But I can speak for the culture of mathematics. Evidently, this paper is not a bunch of obvious BS. The paper could be correct, perhaps not. It could be like Wiles's first proof of Fermat's Last Theorem, which contained a fairly serious gap, which was nevertheless later fixed.

In short, outstanding people are taking this seriously.