A proposed solution of the prize problem may not be submitted directly to the AMS, or to the Beal Prize Committee, or to Mr. Beal. Unpublished manuscripts will not be considered.
Beal Prize Rules and Procedures
The Beal Prize is awarded in accordance with the procedures set forth below under the heading “Procedures for Determination of an Award of the Beal Prize.” The prize amount – US $1,000,000 (the “Prize Money”) – was donated to the American Mathematical Society (the “AMS”) by D. Andrew Beal, a prominent banker who is also a mathematics enthusiast. The Beal Prize Committee, an AMS-appointed committee, will award the Prize Money for either a proof of, or a counterexample to, the Beal Prize Conjecture, assuming one or the other is published in a refereed and respected mathematics publication. In accordance with a Memorandum of Understanding effective as of May 22, 2013 between the AMS and Mr. Beal (the “MOU”), the Prize Money is being held in the Beal Prize Fund as a restricted asset of the AMS. In accordance with the MOU, spendable income from the Beal Prize Fund shall be used by the AMS to support the annual Erdős Memorial Lecture and other activities of the AMS that benefit early career mathematicians. The Beal Prize Conjecture and original prize were announced in an article that appeared in the December 1997 issue of Notices of the American Mathematical Society. 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.
Beal Prize Conjecture
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.
[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.]
Procedures for Determination of an Award of the Beal Prize
The administration of the Beal Prize is overseen by the Beal Prize Committee (the “BPC”), to be appointed by the President of the AMS. Decisions made by the BPC shall be made by a majority of the members of the BPC. The formal charge of the BPC and these “Procedures for Determination of an Award of the Beal Prize” are subject to the review and modification from time to time by the Council of the AMS.
The Beal Prize Fund is held as a restricted asset of the AMS, with US$1,000,000 to be awarded if, in the sole judgment of the BPC and subject to the subsequent approval by the Executive Committee and Board of Trustees of the AMS (the “ECBT”), the Beal Prize Conjecture is proved or a counterexample is presented.
A proposed solution of the Beal Prize Problem may not be submitted directly to the AMS, or to the BPC, or to Mr. Beal. Unpublished manuscripts will not be considered.
The BPC will consider a proposed solution (the “Work”) if it is a complete mathematical solution of the Beal Prize Conjecture. Before consideration, the Work must be published in a refereed mathematics publication which is respected and, in the opinion of the BPC, maintains the highest editorial standards (or published in another form as the BPC, in its sole discretion, decides may qualify). In the case of a counterexample, the Work will be subject to independent verification by the BPC Expert Advisors (as defined below). Upon publication, the author(s) of the Work should notify the AMS and the BPC by sending an email to firstname.lastname@example.org or by sending mail to:
Beal Prize Committee
c/o Executive Director
American Mathematical Society
201 Charles Street
Providence, RI 02904 USA
The Work must be widely accepted by the mathematics community following a waiting period of at least two (2) years after the publication of the Work, the determination of such acceptance by the mathematics community within the sole discretion of the BPC. (In the case of a counterexample, that recognition and acceptance by the mathematics community may happen sooner.) Following the two-year waiting period (or in the case of a counterexample, such shorter period, as determined in the sole discretion of the BPC), the BPC will decide whether the Work merits detailed evaluation.
If the Work merits detailed evaluation, the BPC will identify at least two experts who can verify the correctness of the Work and who are not members of the BPC to assist in the evaluation, and such experts shall be approved by the Executive Committee and Board of Trustees of the AMS (collectively, the “BPC Expert Advisors”). The BPC Expert Advisors will report to the BPC within a reasonable time. Based upon the report of the BPC Expert Advisors and potential additional evaluation, if the BPC can make a clear decision, it may (subject to the approval of the ECBT as provided above), award the Prize Money and determine attribution of credit for a solution. The BPC shall consider whether a solution relies directly on contributions of others published prior to the Work and it may, in its sole discretion and subject to the approval of the ECBT, divide the Prize Money among multiple contributors.
If the BPC cannot make a clear decision based upon the report of the BPC Expert Advisors and potential additional evaluation, the BPC may, in its sole discretion, decide that the Prize Money shall not be awarded at that time. The BPC may, in its sole discretion, revisit a decision to make no award if new information becomes available, provided that the approval of the ECBT shall be required prior to the payment of any award.
All deliberations of the BPC or of the BPC Expert Advisors assisting in an evaluation are confidential. No records of deliberations or related correspondence shall be made public unless approved by the BPC and the AMS Board of Trustees.
No prize shall be awarded to any person who (a) is a “disqualified person” (as such term is defined in Section 4946 of the Internal Revenue Code of 1986, as amended) in connection with the AMS or (b) is a then serving member of the BPC.