In keeping up with its tradition, Google has come up with an awesome doodle today to honour the birthday of the great Pierre de Fermat (kindly pronounce as “Ferma” . The ending ‘t’ is silent.) Hailed as a genius in the world of mathematics and physics, while being virtually unknown to the world outside, Fermat’s fame rests on two basic pieces of mathematical wizardry he presented to the world Fermat’s principle and Fermat’s Last Theorem.
The doodle looks like a board in the room of a mathematical genius. Maybe, if Fermat had a board on his wall, it would’ve looked something like this. Strangely though, out of the mathematical mess of seemingly random squiggles, emerge the letters G-O-O-G-L-Ein that order, while also maintaining complete mathematical harmony by spelling out the statement of Fermat’s Last Theorem. This is a masterstroke from the Google artist, unnamed as yet. Try a mouse-over and see the comment. Have patience – the explanation of the mouse-over comment is delicious.
The mathematician behind it
The life of Fermat is, however, way more awesome than the doodle. Starting off as a lawyer, he learned arithmetic, largely by himself. After shedding off the tag of being an amateur mathematician by discovering a method to calculate slopes of curved lines (which we regard as differential at a point), without having any knowledge of differential calculus (which came later), he moved onto things far greater. Newton would come half a century later and would develop calculus into a branch of mathematics.
Fermat’s great insight led him to discover the Fermat’s principle. This, in the garb of the language of modern optics, said that light always takes the path that lets it take the least time when it propagates from one point to another. Huygens, nearly two century later, would boldly propose the wave theory of light using Fermat’s principle to derive observed phenomenon of reflection and refraction. Now every branch of physics Classical mechanics, Relativity or even Quantum Mechanics uses this principle, in one form or the other.
But this was for technicians in the field. Fermat left behind a delicious puzzle for future generations. He conjectured (and never proved) that three positive integers, x, y and z, cannot possibly satisfy the equation xn + yn = zn, for any n>2 (For n=2, you’d recognise it as the Pythagoras theorem). Fermat supplied a proof for it for n=4, for not a general proof. In his copy of Arithmetica, a book written by the Greek Diophantus, he scribbled on the margin something which said that he had a proof but it was too big to fit in the margin.
Mouse over the doodle, and you’ll see that it says that the discovered proof is too big to fit in the doodle.
The general proof of Fermat’s last theorem is a stuff of legends now, with Andrew Wiles’ proof and his struggles to get to it having been made into TV shows, documentaries and books.
Fermat, pot-bellied and round-nosed, left behind a legacy too big to fit into this one article.