Why was proving Fermat’s Last Theorem such a big deal?

Question

Why was proving Fermat’s Last Theorem such a big deal?

In: 2

Answer 1

Here’s the claim:

> It is impossible to separate a cube into two cubes, or a fourth power into two fourth powers, or in general, any power higher than the second, into two like powers. I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.[30][31]
https://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem

I.e. you can’t have a^n + b^n = c^(n), where a, b, c, and n are integers, with n>2. The claim seems reasonable enough, and was proved for various values of n, and was finally proven in general in the 20th century. But *nobody* has come up with that simple, elegant proof that Fermat claimed to have. So … did he see something that everyone else has missed, or did he just make a mistake about that.