Science

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Why Pierre de Fermat is the patron saint of unfinished business

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In 1637, French mathematician Pierre de Fermat jotted a cryptic conjecture in the margins of a textbook. On Fermat's birthday Google celebrates Fermat's Last Theorem, which managed to drive mathematicians bonkers for the next four centuries.

By
Eoin O'Carroll, Staff /
August 17, 2011

Most of history's great thinkers are remembered for their completed works. Think of Newton's *Principia,* Kant's *Critique of Pure Reason, *or Darwin's *Origin of Species. *These are people who slaved away for decades, each producing works that are today widely regarded as masterpieces.

Not so for 17th century French mathematician Pierre de Fermat. To be sure, Fermat accomplished many feats. He helped develop analytic geometry along with fellow Frenchman RenĂ© Descartes. He planted the seed that would blossom into differential calculus. He made important contributions to optics, probability theory, and most of all, number theory. He was fluent in five languages. And he managed all of this while holding down a job as a lawyer.

But Fermat is best remembered not for what he did, but for what he left undone. One day in 1637, while perusing his copy of an ancient Greek text by the 3rd century mathematician Diophantus, Fermat jotted a note in the margins that would drive mathematicians crazy for the next four centuries.

Fermat's marginalia, which was written in Latin and later discovered by his son after he died, read: "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. I have discovered a truly marvelous proof of this, which this margin is too narrow to contain."

In other words, *a*^{n} + *b*^{n} can never equal *c*^{n}, as long as *a*, *b*, and *c* are positive integers and as long as *n* is greater than two.

Go ahead and plug in some numbers for *a*, *b*, *c*, and *n*, and you'll see that they don't add up (or just take our word for it). But it turns out that coming up with a mathematical theorem proving it for *every* integer greater than two is really, really, really hard.