## Homer Simpson and Fermat

Simon Singh writes in the Guardian about mathematics gags in episodes of The Simpsons:

My favourite freeze-frame gag appears in “The Wizard of Evergreen Terrace” (1998), in which Homer tries to become an inventor. In one scene, we see him busily scribbling equations on a blackboard. One of the equations relates to the mass of the Higgs boson, another concerns cosmology and the bottom line explores the geometry of doughnuts, but the most interesting equation is the second one, which appears to be a counterexample to Fermat’s last theorem.

Although it was only on screen for a moment, this equation immediately caught my eye, because I have written a book on Fermat’s last theorem. Homer’s scribble sent a shiver down my spine. I was so shocked that I almost snapped my slide rule.

In order to appreciate my reaction, it is necessary to be aware of the colourful history behind Fermat’s last theorem. In short, a 17th-century French mathematician called Pierre de Fermat believed that it was impossible to find numbers that fitted a particular equation, and he left a tantalising note proclaiming that he had a proof of this fact, but he never wrote down the proof itself. For more than 300 years, mathematicians desperately tried and failed to rediscover Fermat’s proof, which only made his inadvertent challenge even more infamous. Eventually, in the 1980s, Professor Andrew Wiles (now Sir Andrew Wiles) worked in secrecy for seven years to fulfil a childhood dream and build a proof that confirmed that Fermat was right, inasmuch as the following equation has no solution: xn + yn = zn, for n > 2. It is neither necessary to understand the proof nor to examine the equation in detail, except I should stress again that both Wiles and Fermat claimed, indeed proved, that this equation has no solutions, yet Homer’s blackboard proves the opposite!

3987^12 + 4365^12 = 4472^12.Check it for yourself on your phone calculator and you will find that the equation balances! I realise that I have used two exclamation marks in two consecutive sentences, but this is an extraordinary mathematical circumstance. Homer had the audacity and genius to defy two of the greatest mathematicians in history.

The resolution, and more, is in the article.

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