Not a mathematician, but I've kept up with this story as a non-mathematician. > For instance, imagine the proof is made of 50 lemmas. One could check the main

Not a mathematician, but I've kept up with this story as a non-mathematician. > For instance, imagine the proof is made of 50 lemmas. One could check the main theorem derives from the 50 lemmas. And checking each individual lemma could be left to other mathematicians. To my understanding, some mathematicians have gone ever further and checked the work themselves. Peter Scholze (a 32-year-old who won the Fields medal a couple of years ago and seems to be in the sweet spot of expertise and stamina to really audit this thing) has identified a specific result ("Corollary 3.12") that he says does not follow from the results leading up to it [1]. This is pretty weird because "Corollary" is usually reserved for things that are immediate consequences of previous results. Based on the featured article, Scholze's position hasn't changed. There is a specific objection and the two sides just...disagree. For those interested, you can look at the papers yourself if you want to. Here's the one containing the controversial result [2]. Theorem 3.11 is on p153, and the statement alone is 5 pages long. The proof is 3 lines and asserts that it's obvious from definitions and previous statements. Corollary 3.12 is on p173. As an outsider, I am amazed at Scholze's ability to work through all of this and identify a specific criticism. [1] https://inference-review.com/article/a-crisis-of-identification https://inference-review.com/article/a-crisis-of-identificat... [2] http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%20Teichmuller%20Theory%20III.pdf http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%20...