I upvoted this post; it’s really well written. The introduction made the conjecture less scary, which I appreciated. :)
It’s good to know that the post was accessible—it’s something I can never quite be sure of when reviewing it on my own.
The fact that there could be a correct proof but there aren’t very many people qualified enough to actually verify it is funny to me. Is that normal? It seems like a bit of a problem, if people care about determining the correctness of this type of conjecture.
It’s not normal. The problem with Mochizuki is that he has been working by himself on IUT for one to two decades and in 2012 the only people who had any expertise on his theory were his own graduate students and associates. Nobody outside of his “network” was following his work that closely, and people had to scramble to see what it was all about when he claimed a proof of the conjecture in 2012. His work is particularly dense and so it took years for anyone to even acquire a sufficient understanding of it to try to figure out if his proof was valid or not.
Generally mathematicians aren’t this solitary when working—most mathematics is done in a more interactive and social way nowadays. There are a few exceptions, however: Andrew Wiles, Grigori Perelman and Shinichi Mochizuki are all mathematicians who worked in isolation from the rest of the mathematics community. Mochizuki’s difference from the others is that he seems to have built up a whole theoretical apparatus with much more ambitious goals than just proving the abc conjecture. For him this conjecture is just a corollary, not something that he set out to prove. Since he has this vast machinery that he’s built up over the years, it makes it that much harder for anyone to understand a proof which heavily relies on it.
It’s good to know that the post was accessible—it’s something I can never quite be sure of when reviewing it on my own.
It’s not normal. The problem with Mochizuki is that he has been working by himself on IUT for one to two decades and in 2012 the only people who had any expertise on his theory were his own graduate students and associates. Nobody outside of his “network” was following his work that closely, and people had to scramble to see what it was all about when he claimed a proof of the conjecture in 2012. His work is particularly dense and so it took years for anyone to even acquire a sufficient understanding of it to try to figure out if his proof was valid or not.
Generally mathematicians aren’t this solitary when working—most mathematics is done in a more interactive and social way nowadays. There are a few exceptions, however: Andrew Wiles, Grigori Perelman and Shinichi Mochizuki are all mathematicians who worked in isolation from the rest of the mathematics community. Mochizuki’s difference from the others is that he seems to have built up a whole theoretical apparatus with much more ambitious goals than just proving the abc conjecture. For him this conjecture is just a corollary, not something that he set out to prove. Since he has this vast machinery that he’s built up over the years, it makes it that much harder for anyone to understand a proof which heavily relies on it.