The Beal Prize is funded by D. Andrew Beal, a prominent banker who is also a mathematics enthusiast. An AMS-appointed committee, the Beal Prize Committee, will recommend awarding this prize for either a proof or a counterexample of the Beal Conjecture published in a refereed and respected mathematics publication. The prize money—now US$1,000,000—is being held by the AMS until it is awarded. The spendable income from investment of the prize money is used to fund the annual Erdős Memorial Lecture and other activities of the Society that benefit early-career mathematicians.
Beal’s conjecture is a generalization of Fermat’s Last Theorem. It states: If Ax + By = Cz, where A, B, C, x, y and z are positive integers and x, y and z are all greater than 2, then A, B and C must have a common prime factor.
The rules and procedures governing the Beal Prize are available at http://www.ams.org/profession/prizes-awards/ams-supported/beal-prize-rules.
The Beal Conjecture and Prize were announced in an article that appeared in the December 1997 issue of Notices of the American Mathematical Society. The early history of the Beal Conjecture is described here.
One of Andrew Beal's goals is to inspire young people to think about the equation, think about winning the offered prize, and in the process become more interested in the field of mathematics.