system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: What Fermat's Last Theorem is and why its important that it's solved.
gpt
Fermat's last theorem states that for integer values a, b and c the equation a^n + b^n = c^n is never true for any n greater than two. So for example a=1 b=2 c=3 n=4 gives you  1+16=81 which is obviously false. This is rather simple, but proving that it was true turned out to be an utter bear. 

Proving Fermat's last theorem itself wasn't all that important, although it was very interesting since the proof had eluded mathematicians for nearly 400 years. Which actaully makes that pretty important in it's own right given that Wiles managed to solve something some of the smartest people in the world had failed at, and had mostly given up on as unsolvable. 

The more obviously important part comes from the methods Wiles' used in the proof itself, which involved approaches and tools brand new to mathematics. In particular those tools could be applied to solve other difficult problems. Wile's didn't just prove  Fermat's last theorem, in doing he kicked open a whole new door in the field of mathematics.