## Fermat: this column is too short for a full biography…

Pierre de Fermat was born either in 1601 or in 1607 (in which case he is his own younger brother). In 1653 he contracted plague and was, for a while, “counted among the dead”, and then he wasn’t, and then in 1667 he was again, this time for good.  Fermat was of Basque origin and spoke that language fluently. A life-long town councillor in Toulouse, he was a noted poet in many languages and a connoisseur of Greek manuscripts. A high school in Toulouse is named after him, a crater on the moon, and a street in Paris. He was described as secretive and taciturn, and also as preoccupied and confused. He was certainly preoccupied with mathematics even though he published next to nothing and considered himself an amateur; he contributed enormously to many areas and was held in high esteem by the likes of Descartes and Pascal.

Of course he is best known for the conjecture that if $n$ is an integer larger than 2, there are no positive integers $x$, $y$ and $z$ so that $x^n+y^n=z^n$. He famously claimed to have proved this statement and that unfortunately the “truly remarkable proof” was too long for the margin in his copy of Diophantus’ Arithmetica. Judging by the complexity of the eventual 1994 proof by Andrew Wiles, Fermat most probably fibbed. But then he also thought that all Fermat numbers, numbers having the form $2^{(2^n)}+1$, are prime, which was shown to be wrong by Euler.

Apart from his work in number theory, Fermat clarified the laws of probability and helped lay the foundations of calculus.  He would have contributed even more to the development of calculus were he not held back by the antiquated notation he used. To top all these achievements, Fermat also enunciated the remarkable principle of optics that the path between two points taken by a ray of light is the one that minimises the traversal time, a statement that helped pave the way to the very fruitful marriage of physics and calculus of variations.  Such variational principles were very suspect in the 17th century, as was Newton’s action at a distance in the 18th. That we accept these without batting an eyelid only shows how much more intellectually demanding people were in the past.

(MG)