Funny you should mention Annals. A journal famous for publishing two papers in three years by the same author, one proving some theorem, and the other disprovin

Funny you should mention Annals. A journal famous for publishing two papers in three years by the same author, one proving some theorem, and the other disproving the theorem. Sure, tons of other journals have done so, but Annals is definitely the highest profile one. Maybe take a look at https://mathoverflow.net/questions/282742/endless-controversy-about-the-correctness-of-significant-papers https://mathoverflow.net/questions/282742/endless-controvers... or https://mathoverflow.net/questions/35468/widely-accepted-mathematical-results-that-were-later-shown-to-be-wrong https://mathoverflow.net/questions/35468/widely-accepted-mat... It's also a nice way to pad your CV if you manage to get the wrong theorem published - you get two Annals papers for the price of one. It is of course true that published papers have been vetted. But very often, it simply means that 1. an editor glanced at it, 2. (optional) a peer provided a positive quick opinion on the paper, without checking the correctness, 3. one or two independent referees presumably read the paper and produced a report on it. It's not nothing, but it doesn't mean you should accept blindly as truth everything published. For context, I'm an associate professor of mathematics at a large research university.