### The history behind the most famous

prize in mathematics.

## Written for the Open University

Maths Society, Oct 1997.

### Fermat’s Last Theorem and

the Wolfskehl Prize

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:

x^{n} + y^{n} = z^{n},

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.