Andrew Wiles — English Mathematician born on April 11, 1953,

Sir Andrew John Wiles, KBE, FRS is a British mathematician and a Royal Society Research Professor at the University of Oxford, specialising in number theory. He is most notable for proving Fermat's Last Theorem... (wikipedia)

The definition of a good mathematical problem is the mathematics it generates rather than the problem itself.
I don't believe Fermat had a proof. I think he fooled himself into thinking he had a proof.
Pure mathematicians just love to try unsolved problems - they love a challenge.
However impenetrable it seems, if you don't try it, then you can never do it.
I hope that seeing the excitement of solving this problem will make young mathematicians realize that there are lots and lots of other problems in mathematics which are going to be just as challenging in the future.