From: David Bernier <bernier@my-deja.com>
Subject: Re: JSH: Email revisted re my proof of FLT
Date: Mon, 30 Aug 1999 21:43:07 GMT
Newsgroups: sci.math
Keywords: Wiles on the discovery of the gap

In article <37CAA7C5.5C6B8696@math.okstate.edu>,
  "David C. Ullrich" <ullrich@math.okstate.edu> wrote:
> James Harris wrote:
>
> > [...]
> >
> > What I find most interesting about this email is that the emailer has
> > indicated  understanding exactly what I'm doing and has raised what one must
> > suppose is their biggest objection.  I've handled the objection without real
> > difficulty, so it's reasonable for me to suppose that there remains no
> > mathematical or logical reason for the emailer to think it's not a proof.
>
>     That's not how it works. People keep pointing out errors and
> incoherencies (aka undefined terms), and you keep "answering"
> them, then saying "aha, so it's right". You should conclude that
> someone thinks you have a correct proof when someone actually
> says that they think your proof is correct.

So what is rigor really?  How does someone convince "the world"  :)
that an argument is valid?  First of all, by answering all questions
like "what does this mean?" or "please explain this point further,
I don't understand..."

Copying from the transcript of the  NOVA episode "The Proof" [1] :

ANDREW WILES: It was a wonderful feeling after
          seven years to have really solved my problem. I'd finally
          done it. Only later did it come out that there was a
          problem at the end.

          NICK KATZ: Now, it was time for it to be refereed,
          which is to say, for people appointed by the journal to
          go through and make sure that the thing was really
          correct. So, for two months, July and August, I literally
          did nothing but go through this manuscript line by line,
          and what this meant concretely was that essentially
          every day, sometimes twice a day, I would e-mail
          Andrew with a question: "I don't understand what you
          say on this page, on this line. It seems to be wrong," or
          "I just don't understand."

          ANDREW WILES: So, Nick was sending me e-mails,
          and at the end of the summer, he sent one that seemed
          innocent at first, and I tried to resolve it.

          NICK KATZ: It's a little bit complicated, so he sends me
          a fax, but the fax doesn't seem to answer the question,
          so I e-mail him back, and I get another fax, which I'm still
          not satisfied with. And this, in fact, turned into the error
          that turned out to be a fundamental error, and that we
          had completely missed when he was lecturing in the
          spring.

          ANDREW WILES: That's where the problem was, in the
          method of Flach and Kolyvagin that I'd extended. So,
          once I realized that at the end of September, that there
          was really a problem with the way I'd made the
          construction, I spent the fall trying to think what kind of
          modifications could be made to the construction. There
          are lots of simple and rather natural modifications that
          any one of which might work.
[...]

[1]  http://www.pbs.org/wgbh/nova/proof/


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==============================================================================
[The video is available as an "educator video" and appears in the list of
titles as "Proof, The". The current URL seems to be
     http://www.pbs.org/wgbh/shop/novavideo.html#educator
--djr]