After all the hype around “Fermat’s Last Theorem,” I must say I was tres disappointed when I learned in Michael Bradley’s Age Of Genius: 1300- 1800 just what the theorem is.
The theorem is this… that for the equation…
x^n + y^n = z^n
…the only possible integer-values for “n” are 2, 1, or 0.
This theorem was found in the notes of Pierre de Fermat [fair MAH] or [ FER mat] (1601- 1665) five years after his death. Fermat had left no proof of his assertion, but then again, this was not uncommon for him.
For centuries after this unproved theorem’s discovery, mathematicians amused and/or befuddled-frustrated themselves with trying to find ways to prove it or disprove it… neither of which happened until 1994, when some Englishman (Andrew Wiles) was given credit for proving that Fermat had been RIGHT all along.
I would one day like to study Wiles’ proof. I’m always skeptical when people claim to have found something that they’ve really, really wanted to find for a very long time. For example, I’m convinced that not every extra-solar-system “planet” scientists have claimed to find will actually turn out to be a planet. It’s possible of course… and if we’ve got the basic picture of our Universe more-or-less right (if, in other words, the stars we see really are fundamentally similar to that mind-boggling immense and unimaginably hot bright ball we call the Sun)– then I think the odds are good that other stars could capture plenty of large asteroids, if not legit planets.
But I’m skeptical… There are many people with powerful occupational, egotistical, and psychological reasons for wanting to find other planets… and there are relatively few people who desperately want there NOT to be other extra-solar planets.
But back to Fermat’s Last Theorem… Not to take away from either Fermat or Wiles, but I had been hoping that the vaunted Last Theorem would be something with a little more, I don’t know… pizzazz.
While we’re on the subject, there are a couple of other mathematical obsessions I just don’t get…
Pi. Why was its value to the 1,000th decimal place and beyond such a Holy Grail for mathematicians for so many centuries?
Prime Numbers. Mathematicians seem to love discovering primes and coming up with rules about them. I have no idea why. One of the most famous rules for prime numbers is Fermat’s Theorem (not to be confused with Fermat’s “Last” Theorem)… if, he stated, “a” is an integer and “p” is a prime number, then [ (a^p) – a ] is divisible by p. Oh yay.