Seventeenth-century lawyer and mathematician Pierre de Fermat was one of the greatest thinkers in history. In addition to his pioneering work in analytic geometry, he basically created differential calculus and devised dozens of theorems that influenced everyone from Rene Descartes to Sir Isaac Newton. But for all that he did, Fermat is most remembered for something he never finished.
One day in 1637, while reading a copy of Diophantus’ Arithmetica, Fermat had an idea. He jotted down the following, in Latin, in the margin of the book:
It is impossible to separate a cube into two cubes, or a fourth power into two fourth powers, or in general, any power higher than the second, into two like powers.
In short: an + bn can never equal cn, if a, b, and c are positive integers and n is greater than two.
But what about the proof of this theorem? Therein lies the problem. Fermat’s jotted note continues:
I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.
To his dying day, 28 years later, Fermat never revealed his “truly marvelous proof.” Mathematicians have spent 400 years trying to prove what has been dubbed Fermat’s Last Theorem; many had chipped away at it, proving the theorem for a few numbers, but no one had gotten close to the universal proof. The Guinness Book of World Records even named it the World’s Most Difficult Math Problem.
Fermat’s Last Theorem was finally solved in 1994 by British mathematician Andrew Wiles. It took seven years and more than 100 pages to prove the theorem, using advanced algebraic geometry that wasn’t even available in the seventeenth century. (Wiles received a knighthood for his work.)
The irony is that if Fermat had divulged his marvelous proof before he died, the problem would have just been another in a long list of his theorems. Instead, Fermat’s single uncompleted work made him one of the most famous math geniuses in history.