http://www.nytimes.com/1995/01/31/science/how-a-gap-in-the-fermat-proof-was-bridged.html?pagewanted=all&src=pm
[previous in 1993 was:
http://www.nytimes.com/1993/06/24/us/at-last-shout-of-eureka-in-age-old-math-mystery.html?pagewanted=all&src=pm
but this is from the 1995, (first url) ]
Dr. Wiles, cautious and a bit nervous, decided not to circulate copies
of his manuscript widely among mathematicians but instead to wait
until a select few experts who were reviewing it before publication
proclaimed it sound. Writing a complex proof, he said, "is like
writing in a foreign language -- you are bound to make a few
grammatical errors." If there were any faults, as often happens with
complicated proofs, he wanted to fix them himself rather than share
the glory.
"It's a very competitive environment," Dr. Wiles explained, and, after
working for seven years and after getting so close, he wanted the
victory to be his alone. The Gap A 'Minor' Problem Turns Into a Crisis
Several minor faults were found and Dr. Wiles fixed them. But then, in
the fall of 1993, a reviewer asked him to justify an assertion, in the
midst of his proof, that a certain estimate was correct.
The gap at first seemed to be a minor one. But though the estimate
seemed intuitively to be correct, proving it was a different matter.
...In the outside world, Dr. Wiles'ssecretiveness irritated many and
touched off a betting game on what he was up to and whether he would
succeed.
"I noticed he was stuck and I was very pessimistic," said Dr. Gerd
Faltings, a mathematician at the Max Planck Institute in Bonn,
Germany.
Dr. Kenneth Ribet of the University of California at Berkeley said
that although he was rooting for Dr. Wiles, as time went by the
unfilled gap in the proof was becoming something of an
embarrassment. "A proof that is unfinished is no proof at all,"
Dr. Ribet said. "I had heard from people in other parts of mathematics
that this whole algebraic geometry group has egg on its face, that we
can't get our act together. They would say that we don't know a proof
when we see one, so how could anyone believe what we say."
...
And it was getting harder and harder to think clearly. "I was very
tired," he said. "I'd been working very hard, and I needed someone to
check every statement I made. I needed someone to talk to all the
time." But Dr. Wiles needed a collaborator who would allow him to call
the shots. "I wanted to choose the direction -- I didn't want someone
to come in with lots of new methods," Dr. Wiles said. Before he gave
up and let the world in on the problem, he said, "I wanted to make
sure that I had completely explored the ideas that I had and that I
hadn't missed something obvious."
The glory of being the person to have proved the theorem was too
overwhelming to give up without a fight. Dr. Wiles quoted Enrico
Bombieri, a mathematician at the Institute for Advanced Study in
Princeton, who said: "Everyone has their price. For mathematicians,
it's Fermat's last thoerem or the Riemann hypothesis." Riemann is
another outstanding unsolved problem.