What is the hardest math problem ever solved?

There is no official single "hardest solved problem" because difficulty can mean different things: longest unsolved, deepest theory required, hardest proof to verify, or biggest impact. Two famous candidates are: - Fermat's Last Theorem, unsolved for more than 350 years before Andrew Wiles proved it using deep modern number theory. - The Poincare conjecture, solved by Grigori Perelman using Ricci flow and geometric analysis. Fermat's Last Theorem is easy to state: $$x^n+y^n=z^n$$ has no positive integer solutions for $n>2$. That simple statement hid a proof requiring elliptic curves, modular forms, and the Taniyama-Shimura theorem. So it is a strong example of a problem whose surface looks elementary but whose solution needed a huge mathematical machine. The honest answer is: Fermat and Poincare are both reasonable answers, but "hardest" is not a mathematical invariant. It depends on what kind of difficulty you mean.