The story of the most famous problem in mathematics, Fermat's Last Theorem, has all the ingredients of a real-life treasure hunt: a cryptic note left behind by the French mathematician Pierre de Fermat; a sizable reward offered by a German physician in his 1906 will; finally, a solution found in 1994 by the reserved Princeton University mathematician, Andrew Wiles. Now, a Dallas banker has launched a new twist on the famed hunt, offering a bounty of up to $50,000 for a proof of a more general version of Fermat's Last Theorem.
"I've always loved brain teasers and logical puzzles," says Andrew Beal, the president of Dallas' largest locally owned bank. Beal, who never studied mathematics in college, first heard about Fermat's Last Theorem when Wiles announced his proof. After studying the problem himself, Beal and mathematician Daniel Mauldin of the University of North Texas in Denton hatched the idea for the new prize. "I was particularly thrilled to have someone ... who's not a mathematician be interested in promoting mathematics," Mauldin says.
Fermat's original problem states that if two positive integers are raised to the nth power, then added together, the sum can never be the nth power of another integer if n is greater than 2. But Beal wondered if a similar prohibition governs the outcome of equations whose exponents vary. Some examples of powers that add up to another power are known: For instance, 23 + 23 = 24 and 35 + 114 = 1222. But in all such known equations, either two integers have a common factor, as in the first example, or one of the exponents is 2, as in the second. Beal is offering $5000 to the first person who can prove that one of those two conditions always holds. Like a lottery, the prize will rise by $5000 each year, up to a maximum of $50,000.
According to number theorists, the money is fairly safe for now. "It's unlikely that anyone's going to get anywhere on it with the current techniques," says Andrew Granville of the University of Georgia, Athens. But then again, people said the same thing before Wiles proved Fermat's Last Theorem. Says Beal, "I would love to award the prize."