In May 1997, I published a book entitled
"Fermat’s Last Theorem" - the story behind the most notorious
problem in mathematics. I had spent the previous year
researching everything from the origin of the problem to the
most recent attempts to solve it, including the breakthrough
made by Professor Andrew Wiles of Princeton University in
1995. Hence, it was disconcerting to discover within a month
of publication that historians had found evidence that
conflicted with one hitherto accepted part of the Fermat saga.
Fermat’s Last Theorem was created by the seventeenth
century French mathematician Pierre de Fermat, who stated that
there are no non- trivial whole number solutions to the
following:
xn + yn
= zn,
where n is greater than
2.
Unfortunately,
the mischievous Frenchman never wrote down the proof behind
his theorem. Instead he merely scribbled a tantalising note in
a book he happened to be studying: "I have a truly marvellous
demonstration of this proposition which this margin is too
narrow to contain".
For the next three hundred years
there were strenuous efforts to prove Fermat’s Last Theorem,
and at the beginning of this century interest increased
further when Paul Wolfskehl, a mathematician born in 1856 in
Darmstadt, bequeathed a reward of 100,000 Marks (equivalent to
£1 million in today’s money) to whoever could rediscover
Fermat’s proof. But why did Wolfskehl offer such an enormous
prize for the proof? The motivation behind the Wolfskehl Prize
has been at the centre of a recent controversy.
For many years, the accepted version of
events concerned Wolfskehl’s romantic attachment to a
mysterious young lady, who has never been identified.
Depressingly for Wolfskehl, the woman rejected him, and he was
left in such a state of utter despair that he decided to
commit suicide. He would shoot himself through the head at the
stroke of midnight, but to while away the intervening hours he
went to his library and began browsing through the
mathematical publications.
It was not long before he found himself
staring at the work of Ernst Kummer, who had recently tried to
demonstrate that there was a fundament flaw in an attempted
proof of the Last Theorem by Augustin Cauchy. Wolfskehl soon
became engrossed in trying to prove that Kummer was wrong, and
that Cauchy’s approach could be repaired and made to work. He
explored Kummer’s paper in detail, and by dawn his work was
complete. The bad news, as far as mathematics was concerned,
was that Kummer was right, and the Last Theorem remained in
the realm of the unattainable, for the time being at least.
The good news was that the appointed time of the suicide had
passed, and Wolfskehl was so enthused by his calculations that
he abandoned his death wish. Mathematics had renewed his
desire for life. Wolfskehl rewrote his will in the light of
what had happened that night - the reward of 100,000 Marks was
his way of repaying a debt to the conundrum that had saved his
life.
This story was documented in 1969 by
Philip Davis and William Chinn in their book "3.1416 and all
that", who had in turn heard the story from the renowned
mathematician Alexander Ostrowski. According to Davis,
Professor Ostrowski himself had heard the story many years
earlier and maintained that there was more to it than mere
legend. As Ostrowski died in 1986, the details about his
source can no longer be ascertained.
However, Prof. Dr. Klaus Barner at the
Universität Gesamthochschule Kassel has published a paper in
the November issue of the Notices of the American Mathematical
Society which puts forward two other theories. First, Barner
states that Wolfskehl initially undertook a career in
medicine. However, soon after graduating as a doctor in 1880,
he began to display the first symptoms of multiple sclerosis.
He soon realised that he would not be able to practise as a
doctor for very long, and so, according to Barner, Wolfskehl
decided to study mathematics, a subject he would be able to
pursue even when confined to a wheelchair. Consequently, the
prize may have been Wolfskehl’s way of acknowledging that
mathematics had offered him a new opportunity, when the onset
of multiple sclerosis was forcing him to abandon his intended
career.
Barner’s alternative theory claims that
the motivation was not gratitude, but rather spite. Because
Wolfskehl was severely invalided, his family forced him to
wed, but the only woman who would marry him was Marie
Fröhlich, the 53 year-old daughter of tax advisor August
Fröhlich. Unfortunately, Marie turned out to be an evil shrew
who made her husband’s life hell during his last years. Hence,
perhaps he changed his will in January 1905 in order not to
leave all of his money to his despicable wife.
Barner’s reason for researching the
history behind the Wolfskehl Prize was that on June 28th,
1997, almost a century after Wolfskehl’s death, the prize was
awarded to Andrew Wiles for his proof of Fermat’s Last
Theorem. However, the prize, which was originally worth £1
million, had suffered because of the hyperinflation which
followed the First World War and the introduction of the
Deutschmark in 1948, and as a result Wiles received only
£30,000. As far as Wiles is concerned, the prize money is not
important. Fermat’s Last Theorem had obsessed him since he was
a boy, and so discovering a proof was the realisation of a
childhood dream.
