Wednesday, August 17, 2011
Fermat's last theorem
Today is Pierre de Fermat's 410th birthday. Google is celebrating it with a witty doodle that states: "I have discovered a truly marvelous proof of this theorem, which this doodle is too small to contain." It's a parody of the statement Fermat scribbled on the margin of a copy of the mathematical journal Arithmetica. The theorem he was referring to was later dubbed "Fermat's last theorem" and it made history. The proof was published in 1995, 358 years after Fermat first conjectured it.
Fellow math geeks out there, it's confession time: come on, admit it, we've all been fascinated by Fermat's last theorem. Why? Because of its simplicity! We were in high school (if not even younger) when we became old enough to understand it: x^n + y^n = z^n has no non-trivial integer solutions for any integer n>2. It had the innocent (and deceiving) appearance of an extension of the Pythagorean theorem, which we all knew. And the cherry on top was Fermat's tempting bait, right there: he'd found the proof, but darn it, it didn't fit the margin of the journal. So of course, we all thought good ol' Pierre was full of it and all we had to do was find four integers (x,y,z, and n) to disprove his claim.
It was so simple we all dreamed glory and fame spending countless night hours attempting to either prove it or find the four magic numbers.
And we all failed.
Why? Because we didn't have the tools in high school, nor we had them in our first years of college.
Luckily, Andrew Wiles proved it while I was still in college or else I may not have graduated. It took modular forms and elliptic curves to prove it, and even with all those tools, he had quite some obstacles to circumvent.
Pierre de Fermat is one of my old time heroes. Wiles started working on the proof in 1986 and published his final paper in 1995. And yet it will always be known as Fermat's theorem.
Nonetheless, hats off to Sir Wiles. I'm sort of jealous, though glad the proof ended up being far more complicated than we all envisioned back in high school.
Photo: oak leaf at the beach. Canon 40D, focal length 85mm, exposure time 1/30.