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Who is Andrew
Wiles?
I first met Andrew Wiles when I
began researching for a BBC documentary about his proof of
Fermat’s Last Theorem. Although he was clearly a man with a
brilliant mind, an immense determination and an obsession that
had haunted him since childhood, he came across as a modest,
diffident man. It was obvious that he hated publicity, so it
was not a complete surprise that initially he was
reluctant to have his story filmed for TV.
Eventually, my colleague, John
Lynch, persuaded him that it was his duty to be filmed. By
telling his story on screen, Wiles could inspire a new
generation of mathematicians and reveal the power of
mathematics to the public. Here was a story of passion and
intrigue that would enchant people around the
world. |
Andrew Wiles aged ten years, when he first
encountered Fermat's Last
Theorem |
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Wiles first became aware of the
Last Theorem when he was ten years old. On his way home from
school he popped into the Milton Road library and began
reading The Last Problem by Eric Temple Bell. From
that moment on, he dedicated his life to finding a proof, even
though this was something that had eluded the greatest brains
on the planet for three centuries.
He completed his PhD in mathematics under the supervision
of John Coates and eventually became a professor at Princeton
University. His research was in number theory, but was not
aimed at Fermat’s Last Theorem. Three hundred years after
Fermat had thrown down the gauntlet, mathematicians had
decided to put Fermat’s Last Theorem to one side because they
considered it impossible. For example, the mathematician David
Hilbert was asked why he did not attempt a proof of the Last
Theorem, and he replied, "Before beginning I should have
to put in three years of intensive study, and I haven’t that
much time to squander on a probable failure.”
But in the 1980s, work by Ken Ribet
and Gerhard Frey built a bridge between the Last Theorem and
mainstream mathematics, in particular the sort of ideas that
Wiles was already familiar with. To cut a long story short,
Wiles now had to prove the Taniyama-Shimura conjecture, a
problem that had been around for decades and which was
considered impossible. Nevertheless, as far as Wiles was
concerned, anything that led to Fermat’s Last Theorem was
worth pursuing. For the next seven years, Wiles worked in
complete secrecy, formulating the proof of the
century.
Wiles’s incredible journey is too
long to even begin to explore on this page, but it is best
summarised by the following quote by Andrew Wiles, which draws
an analogy between doing mathematics and exploring a dark
mansion:
“You enter the first
room of the mansion and it’s completely dark. You stumble
around bumping into the furniture but gradually you learn
where each piece of furniture is. Finally, after six months or
so, you find the light switch, you turn it on, and suddenly
it’s all illuminated. You can see exactly where you were. Then
you move into the next room and spend another six months in
the dark. So each of these breakthroughs, while sometimes
they’re momentary, sometimes over a period of a day or two,
they are the culmination of, and couldn’t exist without, the
many months of stumbling around in the dark that precede
them.” |
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In 1995,
Wiles's proof was officially published and accepted by the
mathematical community. The story of Fermat’s Last Theorem had
come to an end. We now know that Fermat’s Last Theorem is
true, but one question remains. What was Fermat’s original
proof? Wiles’s proof is too complicated to be the same as
Fermat’s, so some people continue to search for the original
proof – if, indeed, such a proof exists – it could be that
Fermat made a mistake and never had his own proof. If you
think you have discovered Fermat’s proof, then please do not
send them to Andrew Wiles as he does not have the time to look
at such proofs. Similarly, I have neither the time, nor the
expertise, so please do not send proofs to me.
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On 27 June, 1997, Wiles collected
the Wolfskehl Prize, which was worth roughly $50,000. This is
much less than Wolfsekhl had intended a century earlier, but
hyperinflation had eroded its value. The mathematical
equivalent of the Nobel Prize is the Fields Medal, but winners
must be younger than forty, so Wiles just missed out. Instead,
he received a special silver plaque at the Fields Medal
ceremony in honour of his momentous
achievement.
Wiles also won the prestigious Wolf
Prize, the King Faisal Prize and numerous other international
awards. But money, awards and honour were not the driving
force behind Wiles’s achievement. As he said in the BBC
documentary:
‘This was my childhood
passion. There’s nothing to replace that. I had this very
rare privilege of being able to pursue in my adult life what
had been my childhood dream. I know it’s a rare privilege, but
if you can tackle something in adult life that means that much
to you, then it’s more rewarding than anything imaginable.
Having solved this problem there’s certainly a sense of loss,
but at the same time there is this tremendous sense of
freedom. I was so obsessed by this problem that for eight
years I was thinking about it all the time – when I woke up in
the morning to when I went to sleep at night. That’s a long
time to think about one thing. That particular odyssey is
over. My mind is at rest.’
Want to find out more about
Wiles? See the history of maths
website. |
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