Fermat's Last Theorem!

Even if you're not into math, you've probably heard of this one. Back in
1637, Pierre de Fermat conjectured that no three positive integers a,
b, and c could satisfy the equation a^n + b^n = c^n for any integer
value of n greater than two. He scribbled this conjecture in the margin
of a copy of Arithmetica. Fermat went on to claim he had a proof for
this, but it was too long to fit in the margin. By the time of his
death, he had not produced this proof.

A few mathematicians tackled this problem over the years. Okay, more
than a few. More like nearly every mathematician for the next 358 years.
Finally, in 1995, Andrew John Wiles managed to prove it... his proof
was over 100 pages long, took seven years of research, and made use of
techniques that did not exist in Fermat's time. Wiles was knighted for
his contribution to mathematics.

I remember my first encounter with the Last Theorem. Back in high
school, in the first linear algebra class I'd ever taken, on the first
day of class, we were asked disprove the theorem as homework, the
equation scrawled on the whiteboard in the last few moments of class as
if it was no big deal. Now, back in those days my Google-fu was weak and
my work ethic was strong, so I went at it with a gusto. And I arrived
at class the next day feeling utterly despondent, having found exactly
zero solutions and having no idea why. Oh math... I think that's the day
I fell in love with you.

I feel like I should talk about Fourier analysis and how it can do
anything if you're clever enough, or Fibonacci numbers and how they're
already doing everything whether you're clever or not... but instead,
I'll just ask this: do you think Fermat had a solution? Or was he just
another mathematical rebel without a cause (more on that tomorrow)?

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