Joyeux anniversaire, Pierre de Fermat! Today is the French mathematician's 410th birthday.
Fermat is best known as the originator or Fermat's Last Theorem, which consists of a deceptively simple-looking formula famously scrawled in a book's margin, where he claimed the proof was too large to fit. The theorem's fame grew because – despite the efforts of countless mathematicians – four centuries would pass before the publication of a successful proof in 1995 by Sir Andrew Wiles, a Royal Society Research Professor at Oxford.
Fermat's birthday is marked today with a Google doodle, and in a wry reference to the mathematician's original margin note, if you hover your mouse over the doodle the alt text is "I have discovered a truly marvelous proof of this theorem, which this doodle is too small to contain."
According to the theorem, for any integer n greater than two, there are no positive integers a, b, and c that can satisfy the equation:
an + bn = cn
You may recognise from your school days the simple case when n = 2 as Pythagoras' Theorem.
Perhaps Fermat would have preferred to be remembered for something other than a small comment in the margin of a book? Here are some of the things that you may not know about Pierre de Fermat.
• Pierre de Fermat is not Pierre de Fermat. He studied to be a lawyer at the University of Orleans, and went on to be the councillor at the High Court of Judicature in Toulouse. Here he became entitled to change his name from Pierre Fermat to Pierre de Fermat.
• Fermat has his own number. Fermat numbers have been found to be good at generating sequences of random numbers that are ideal for data encryption on computers, keeping all your banking and personal files safe.
• Fermat also has a little theorem. Fermat's Little Theorem is used in something called Fermat's Primality Test. The test tells us whether a whole number is a probable prime. Whereas a prime number is strictly a number only divisible by one and itself, a probable prime has similar properties but may be easier to generate. These numbers are very important in cryptography and internet security.
• Fermat is one of the founders of probability theory. Through his close relationship with Blaise Pascal, a mathematician and philosopher, he studied how chance behaves in games with dice. An exchange of letters between the two mathematicians developed a general formulation of probability theory – work which still provides the basic principles of how sporting odds are calculated today from horse racing to football.
It is a measure of Fermat's influence that many of his results are used today in computing and cryptography. However, he is well known for not giving rigorous mathematical proofs with his work. For example, the proof of Fermat's Little Theorem was first given not by Fermat but by Gottfried Leibniz.
This reticence has intrigued and frustrated mathematicians for centuries. On the plus side, there's still some of Fermat's work yet to be proven. So, given the inclination, you can try your hand at solving them.
