4 ms·

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

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.

williamstein 10y ago
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.)
- saalweachter 10y ago
  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.
  - Jweb_Guru 10y ago
    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.
    - mafribe 10y 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.
      - tacomonstrous 10y ago
        And that doesn't even make it unusual. Most mathematical results are first presented at conferences or workshops, sometimes long before publication.
      - moomin 10y ago
        I was around at the time. I remember the buzz after day one of his two day workshop. Everyone knew where he was going.
  - JCzynski 10y ago
    Wiles was weird at the time. Math is done in public, he just really wanted to be the one to have the final valid proof of Fermat's Last Theorem.
    - jacobolus 10y ago
      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.
      - bonzini 10y ago
        Technically he was working on the Taniyama conjecture (now known as the modularity theorem), not on Fermat's last theorem.
      - digler999 10y ago
        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.
- cromwellian 10y ago
  If only the ABC conjecture proof was handled as transparently.
  - aalireza 10y ago
    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.
    - cromwellian 10y ago
      What I meant is, the author of the theory for a long time refused to travel and present his theory in person to walk others through it. Things might have gone faster if the author had taken the time to teach others and help them understand it.
stablemap 10y ago
I want to point out two more differences: in Wiles's case it took about a year of work with Richard Taylor to patch things up.
- tacomonstrous 10y ago
  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 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.

williamstein 10y ago

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.)

saalweachter 10y ago
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.
- Jweb_Guru 10y ago
  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.
  - mafribe 10y 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.
    - tacomonstrous 10y ago
      And that doesn't even make it unusual. Most mathematical results are first presented at conferences or workshops, sometimes long before publication.
    - moomin 10y ago
      I was around at the time. I remember the buzz after day one of his two day workshop. Everyone knew where he was going.
- JCzynski 10y ago
  Wiles was weird at the time. Math is done in public, he just really wanted to be the one to have the final valid proof of Fermat's Last Theorem.
  - jacobolus 10y ago
    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.
    - bonzini 10y ago
      Technically he was working on the Taniyama conjecture (now known as the modularity theorem), not on Fermat's last theorem.
    - digler999 10y ago
      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.
cromwellian 10y ago
If only the ABC conjecture proof was handled as transparently.
- aalireza 10y ago
  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.
  - cromwellian 10y ago
    What I meant is, the author of the theory for a long time refused to travel and present his theory in person to walk others through it. Things might have gone faster if the author had taken the time to teach others and help them understand it.

stablemap 10y ago

I want to point out two more differences: in Wiles's case it took about a year of work with Richard Taylor to patch things up.

tacomonstrous 10y ago
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.