Why is the Fermat's theorem so important today?

Answer 1

It's important as a theorem that's very simple to explain; most school children know Pythagoras's theorem about right angle triangles (a2+ b2 = c2), Fermat proposed that there were no whole number solutions for an + bn = cn for n other than 1 or 2. Fermat wrote in his notebook that he had a "wonderful" proof, but didn't have room to write it down. It was 300 years before it was proved - and for some time it was thought that it might be unprovable. (Gödel's incompleteness theorem states that there are true things that can't be proved true and I was taught that Fermat's might be such a thing).