The Providence, Rhode Island-based American Mathematical Society (AMS) on Tuesday said $1 million will be awarded for the publication of a solution to the Beal Conjecture number theory problem.
Dallas banker D. Andrew Beal first offered the Beal Prize in 1997 for $5,000. Over the years, the amount has grown.
AMS spokesman Michael Breen says a solution is more difficult than the one for a related problem – Fermat’s Last Theorem – which didn’t have a published solution for hundreds of years.
Mr Beal is a self-taught mathematician and founder of the Beal Prize. He says he wants to inspire young people to pursue math and science.
An AMS-appointed committee will award this prize for either a proof of, or a counterexample to, the Beal Conjecture, published in a refereed and respected mathematics publication.
The prize money is being held in trust by the AMS until it is awarded.
Income from the prize fund is used to support the annual Erdős Memorial Lecture and other activities of the Society.
According to the AMS website, the $1million prize will be awarded to anyone who can solve and fulfill the following:
Quote
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 administration of the Beal Prize is overseen by a Beal Prize Committee (BPC) to be appointed by the President of the AMS.
The formal charge of the BPC and the ‘Procedures for Determination of an Award of the Beal Prize’ are subject to the review and approval by the Council of the AMS.
The Beal Prize Fund is held as a restricted asset of the American Mathematical Society (AMS), with US$1,000,000 to be awarded if, in the judgment of the BPC, the 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 Beal Prize Committee, or to Mr Beal. Unpublished manuscripts will not be considered.
The BPC will consider a proposed solution if it is a complete mathematical solution of the Beal Prize Problem. Before consideration, a proposed solution (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 decides may qualify).
In the case of a counterexample, the proposed solution will be subject to independent verification. Upon publication, the author(s) of the Work should notify the AMS and the BPC.
The Work must be widely accepted by the mathematics community following a two-year waiting period after publication.
In the case of a counterexample, that recognition and acceptance by the community may happen much sooner.
Following the waiting period, the BPC will decide whether the Work merits detailed evaluation.
If the Work is to receive detailed evaluation, the BPC and the AMS 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.
Upon completion of the evaluation, if the BPC can make a clear decision, it may award the prize and determine attribution of credit for a solution.
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