Fermat's Last Theorem 

Fermat's Last Theorem was the last equation in a book written by Pierre de Fermat's that was the last to be solved. The equation was x^n+y^n=z^n. Pierre said that he had proof that this equation could never be proven if n was larger than 2.

He wrote this in 1637 and it hasn't been proven until 1993(1995 for perfected) by Andrew Wiles. Andrew proved this after working on the equation for 7 years. Solving it was a dream of his since he was a young boy. Andrew received worldwide recognition for his proof. Andrew solved this by also proving the Taniyama-Shimura Conjecture, which states that every elliptic curve is also modular. Andrew solved this by turning the elliptic curves into Galois representations and turning the equation into a class number formula. Many had tried before Andrew but none succeeded for 300 years.

Many doubt if Fermat had any real proof but it was still a mathematical marvel of a challenge and we can hope another such equation will pop up.

"It is impossible for a cube to be the sum of two cubes, a fourth power to be the sum of two fourth powers, or in general for any number that is a power greater than the second to be the sum of two like powers. I have discovered a truly marvelous demonstration of this proposition that this margin is too narrow to contain." - Pierre de Fermat

Every mathematician hates and loves Andrew Wiles for his proof of Fermat's Last Theorem

Fermat's Last Theorem by Bacon In the Soap January 2, 2012

Fermat’s Last Theorem 

Arguably the most notorious problem in the history of mathematics: mathematicians’ secret desire to solve it to achieve mathematical fame and immortality had saved a few lives, whose suicidal minds were so absorbed in their proofs that they forgot to end their lives prematurely.

A generalized version of the Pythagorean theorem, the Fermat’s Last Theorem was finally put to rest by Prof. Wiles, after an error was exposed in the first proof he unveiled to the mathematical brethren.

Fermat’s Last Theorem by MathPlus February 13, 2018