## Fermat’s last theorem

Today I discovered that Pierre de Fermat (or just Fermat, as he is most commonly called), one of the most famous mathematicians of all time, was of Basque origin. I’d like to share with you the story of his so-called Last Theorem.

Pierre de Fermat (1601-1665) was a French lawyer of Basque ancestry, but he is remembered today mostly as a great mathematician. Even though math was just a hobby to Fermat, he made groundbreaking contributions in number theory, probability and analytic geometry.

Pierre de Fermat

Fermat shared his work with others mostly in letters, often stating results he found without giving proofs. This nonchalant attitude often drove his correspondents crazy when they failed to find a proof themselves. The most striking example of this is Fermat’s last theorem, which states that for $n\geq 3$ the equation

$\displaystyle{ a^n+b^n=c^n}$

has no solutions where $a$, $b$ and $c$ are non-zero integers. In his notes Fermat stated this result and wrote (in Latin)

“(…) demonstrationem mirabilem sane detexi. Hanc marginis exiguitas non caperet.”

“I have found a truly marvellous proof. This margin is too narrow to contain it.”

He never gave a proof, and for over 300 years nobody managed to come up with one. In 1996, at last, Andrew Wiles found a proof of Fermat’s claim, in 108 pages of mathematics far beyond anything known in the 17th century. Wiles received several awards for his contribution, among which a knighthood. Today, it is considered highly unlikely that Fermat actually ever had a correct proof of his result.