I remember the same thing originally happened with Wile's proof of FLT. It's heartwarming to know that scholars continue to skeptically check each other's work for factual correctness.
Even better -- this situation is much more public and open than the situation with Andrew's FLT proof. I remember when Wiles proof was announced, when there was a gap, etc. only a select few got to actually look at the proof. It was only published after it had been very carefully checked. I started studying number theory exactly during this strange period of secrecy in 1993. Incidentally, exactly at that time, I used to play around writing computer games with Harald Helfgott, who is the guy who just found the mistake with Graph Isomorphism a few days ago... (He's a fantastic mathematician.)
I can't help but wonder if the qualitative difference in the problems -- graph isomorphism is an important, active area of applied mathematical research in search of a better algorithm, FLT was a multi-century abstract mathematical puzzler -- makes for a difference in the groups of people working on the problems and their attitudes.
Saying you’re working on FLT in the late 20th century is a good way to make everyone think you’ve gone nuts and are wasting your time. It makes some sense to make sure you have something solid before you mention it.
or conversely, if they believe you, they could try to sniff your approach and take the credit for it. given the fame of FLT I dont blame him for doing it undercover.
Graph isomorphism isn't that important practically (subgraph isomorphism is, but it's NP-complete and, IIRC, APX-hard as well) and the hard graph cases don't come up much in practice (despite being a relatively large percentage of random graphs, AFAIK). I think it reflects a difference in how mathematics is done; the quasipolynomial result was first presented at a conference, not in a paper, which definitely wouldn't have been the case 20 years ago.
Wiles' original FLT result was first presented at a workshop in Cambridge, although he didn't explicitly state that he had succeeded (sans the gap) in proving FLT, he left that for the audience to infer.
What you're saying implies that a situation is -even- theoretically possible such that a radically new mathematical theory with near-completely novel underlying frameworks that's essentially developed by a single guy over the span of almost a decade that necessarily resulted in a deviation from the route focused by the majority of researchers, could be `quickly` understood/vetted by other mathematicians via traditional methods of un-automated peer-review process.
I guess if that was true, we would have been a significantly smarter species, or at a the very least, had god-like context-switching or learning abilities.
On the other hand, Wiles's work was quite a bit more complex conceptually just in terms of the sheer number of moving pieces involved, though the level of cleverness required is probably comparable in the two cases.
I don't think this is finished yet. The paper is very complex, and not completely checked yet. Other issues will possibly arise. That's part of any large maths proof.
Babai commented that the new work-around requires a 2-page proof and makes 10 existing pages obsolete. So, a net savings of 8 pages, in theory! We'll see how it turns out.
It should be noted that Helfgott (who found the issue in the proof) is scheduled to talk about Babai's work at the famous Bourbaki seminar next saturday: http://www.bourbaki.ens.fr/seminaires/2017/Prog_janv17.html
The seminar is broadcast live on youtube, notes and video are available afterwards.
Yeah, I read more about it, only subgraph isomorphism is known to be NP-complete...of course the complexity of that will remain a mystery for a long time.
