9.8 A Long-Standing Open Problem

Fermat’s Last Theorem Pondering Baudhayana triples led the brilliant French mathematician Pierre de Fermat, in the 1600s, to raise the stakes. Endlessly many squares can be split into a sum of two squares, but is there a cube that equals a sum of two cubes? A fourth power that splits into two fourth powers? Stated sharply, does x^n + y^n = z^n have any solution in natural numbers once n > 2?

Jotting in the margin of a book, Fermat claimed the answer is no, no solution exists for any power above 2, and left the most quoted note in all of mathematics:

“I have discovered a truly marvellous proof of this, which this margin is too narrow to contain.”

Fermat’s proof was never found. For over 300 years the finest mathematicians chipped away without success. Then, in 1963, a ten-year-old named Andrew Wiles came across the puzzle in a library book and resolved to crack it. He kept his word, finally proving Fermat’s Last Theorem in 1994.

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