The fame of Fermat’s Last Theorem comes solely from the sheer difficulty of proving it. An extra sparkle is added by the fact that the Prince of Amateurs said that he could prove this theorem that has since baffled generations of professional mathematicians. Fermat’s offhand comments in the margin of his copy of the Arithmetica were read as a challenge to the world. He had proved the Last Theorem; the question was, could any mathematician match his brilliance?
Fermat’s Last Theorem is a problem of immense difficulty, and yet it can be stated in a form that a schoolchild can understand. There can be no problem in physics, chemistry, or biology that can be so simply and unambiguously stated and that has remained unsolved for so long. In The Last Problem, E.T. Bell wrote that civilization would probably come to an end before Fermat’s Last Theorem could be solved. Proving Fermat’s Last Theorem has become the most valuable prize in number theory, and not surprisingly it has led to some of the most exciting episodes in the history of mathematics.
The riddle’s status has gone beyond the closed world of mathematics. In 1958 it even made its way into a Faustian tale. An anthology entitled Deals with the Devil contains a short story written by Arthur Porges. In “The Devil and Simon Flagg” the Devil asks Simon Flagg to set him a question. If the Devil succeeds in answering it within twenty-four hours then he takes Simon’s soul, but if he fails then he must give Simon $100,000. Simon poses the question: “Is Fermat’s Last Theorem correct?” The Devil disappears and whizzes around the world to absorb every piece of mathematics that has ever been created in order to prove the Last Theorem. The following day he returns and admits defeat:
“You win, Simon,” he said, almost in a whisper, eyeing him with ungrudging respect. “Not even I can learn enough mathematics in such a short time for so difficult a problem. The more I got into it the worse it became. Non-unique factoring, ideals — Bah! Do you know,” the Devil confided, “not even the best mathematicians on other planets — all far ahead of yours — have solved it? Why, there’s a chap on Saturn — he looks something like a mushroom on stilts — who solves partial differential equations mentally; and even he’s given up.”
–Simon Singh, Fermat’s Enigma: The Epic Quest to Solve the World’s Greatest Mathematical Problem
