Banker Andrew Beal, a mathematics enthusiast, has increased the prize money to $1 million to solve a mathematical equation that has puzzled mathematicians for decades. The prize money, held in trust by the American Mathematical Society, will be awarded to the mathematician who publishes a proof for or counterexample of the conjecture.
The Beal conjecture states that if Ax + By = Cz , where A, B, C, x, y and z are positive integers and are all greater than 2, then A, B and C must have a common prime factor.
In a news release announcing the increased prize money, the AMS explains, “By way of example, 33 + 63 = 35, but the numbers that are the bases have a common factor of 3, so the equation does not disprove the theorem; it is not a counterexample.”
The Beal conjecture implies Fermat’s Last Theorem, another number theory that was easy to state but difficult to prove. Three hundred years ago, Pierre de Fermat claimed to have proof but did not leave a record, and it took until the 1980s for proof to be discovered.
Beal founded the prize in 1997 to inspire young people to invest in the world of mathematics. He was inspired by the prize that was offered for proving Fermat’s Last Theorem and hopes that increasing the prize will draw more attention to mathematics and more excitement from young people.
It is a tough road for those hoping to prove or disprove the conjecture. Mathematicians must first have their proof or counterexample published in a respected mathematical journal. They can then notify the American Mathematical Society of their article, but must wait a period of two years during which time their solution must be widely accepted by the mathematical community. After that, the committee will decide whether the solution merits evaluation. Deliberations are confidential, and the committee will decide on whether to award the prize or pause deliberations if no clear answer can be given.
Prizes for solving difficult math problems are not new. In addition to the prize for Fermat’s Last Theorem, in 2000 the Clay Mathematics Institute created seven $1 million prizes for the “Millennium Problems.” One, the Poincaré Conjecture, has since been solved, though the mathematician Grigori Perelman turned down the prize money. The proof of Fermat’s Last Theorem was over 100 pages long and took Andrew Wiles seven years to solve; a solution for the Beal conjecture could easily surpass that length.
The Beal Prize previously held a value of $100, 000.