Pierre de Fermat is one of the top ten greatest mathematicians in history. Alongside Blaise Pascal, he established the foundations of probability theory, which is the mathematics of gambling, risk and change. Also, when Newton was asked where he got the idea of calculus from, he credited “Monsieur Fermat’s method of drawing tangents”. Already it is clear that Fermat has changed the world we live in, because everybody from insurance companies to stock markets use probability theory and everybody from architects to NASA use calculus.
But Fermat’s greatest ideas are in the area of number theory, a subject which has virtually no practical applications. Number theory is the purest form of mathematics, concerned with the study of whole numbers, the relationships between them, and the patterns they form.
For example, Fermat showed that 26 is the only number trapped between a square and a cube, because:
52 = 5×5 = 25 and 33 = 3x3x3 = 27
Fermat was able to use mathematical logic to prove that no other numbers from zero to infinity have this property. (If you go below zero, then -1 also has this property.)
By the way, Fermat lived in the 17th century near Toulouse in southwest France, and his day job was as a judge dealing with some of the nastiest cases imaginable, including the condemnation of priests to be burned at the stake. Judges were generally discouraged from socialising within the community in order to avoid a conflict of interests, so Fermat would spend his evenings hidden in his study, pursuing his mathematical interests. He was a truly amateur academic and E.T. Bell called him the Prince of Amateurs. However, when Julian Coolidge wrote Mathematics of Great Amateurs, he excluded Fermat on the grounds that he was ‘so really great that he should count as a professional.’
It was during one of these amateur interludes that Fermat created the infamous Last Theorem. You can find out more about the Last Theorem in the suitably titled What is the Last Theorem? section, but in essence Fermat invented a problem, then solved it, but he never wrote down the solution. In the margin of a notebook he scribbled:
“I have a truly marvellous demonstration of this proposition
which this margin is too narrow to contain…”
This was typical of Fermat. He was a mischievous mathematician, who was forever tormenting his rivals. René Descartes called Fermat ‘a braggart’ and the English mathematician John Wallis called him ‘that damned Frenchman’.
Fermat wrote several other notes, saying things like ‘I can prove such and such but I have to feed the cat’, or ‘I can solve a particular equation but I have to wash my hair’, and all of these notes were discovered after his death. Mathematicians across Europe studied Fermat’s observations and attempted to rediscover the proofs behind the theorems. Over the course of the next century, each theorem was proved, except for the one, which would become known as Fermat’s Last Theorem.
You can find out more about Pierre de Fermat by visiting the excellent History of Mathematics website. This site will also tell you more about the other mathematicians mentioned on this page, including Blaise Pascal.