Fermat's Last Theorem
This is amazing.
Andrew Wiles proceeded to solve Fermat's last theorem (For n>2, the equation a^n + b^n = c^n has no solutions for non zero a,b and c) by proving Taniyama - Shimura Conjecture. Does it not sound incredible that a man who lived about 400 years ago could come up with a different solution, which even the greatest mathematicians of our time have not been able to reproduce ? It speaks volumes of that man's incomparable genius.