Fermat’s last Theorem was first conjectured by French mathematician Pierre de Fermat in 1937. However, he did not provide the proof. (apparently he had omitted the proof as there was not enough margin space to write it down!)
We all know we can break down a squared number (25, that is 5^2) into sum of two squared numbers (16, that is 4^2 and 9, that is 3^2). This confirms to Pythogaras’ theorem.
What Fermat saw was that it is impossible to do that with any number raised to a power greater than 2. Put differently, the formula, x^n + y^n = z^n, has no whole number solution when n is greater than 2.
After more than 3 centuries, Andrew Wiles solved this problem in 1994 by way of the modularity conjecture for semistable ellipic curves.
He is offered the Abel Prize (“the Nobel of mathematics) for his stunning proof. [We believe that such effort should be recognized even more and should carry a financial reward more than what is currently offered.]