The Beal Conjecture: an unsolved problem worth $1,000,000.
In the 1990s, Andy Beal was exploring patterns in number theory when he identified a conjecture he could not prove. Rather than set it aside, he proposed it formally and offered a prize for its proof or disproof. The conjecture remains unsolved.
At a Glance
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Current prize amount
- $1,000,000
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Current status
- Unsolved
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Prize administrator
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AMS
(American Mathematical Society)
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Origin of the Beal Conjecture
Andy Beal is self-taught mathematician with an interest in numbers theory. In 1993, he publicly stated a generalization of Fermat’s Last Theorem which has become known as the Beal Conjecture. The conjecture has been widely accepted as correct among the academic community.
To encourage a solution, Mr. Beal has personally funded a standing prize of $1,000,000 for the proof or disproof of the Beal Conjecture. The funds are held in trust by the American Mathematical Society, and an informational website on the Beal Conjecture is hosted by the University of North Texas.
The conjecture in plain language.
If you take three whole numbers and raise each one to a power greater than 2, and those three results add up perfectly (the first plus the second equals the third), then the three base numbers must share a common prime factor.
More formally, the exact conjecture is stated as:
where
A
,
B
,
C
,
x
,
y
,
z
are positive integers
and
x
,
y
,
z
> 2
then A , B , and C must share a common prime factor.
The $1,000,000 prize.
The prize for whomever can prove the conjecture or provide a counterexample is administered by the American Mathematical Society (AMS), the primary professional organization for mathematicians in the United States. The award currently stands at $1,000,000. Any proposed proof or disproof must be published in a refereed mathematics journal and survive peer review before a prize committee considers it.
For more information and full rules, please visit the American Mathematical Society (AMS).
Why a bank founder offers a math prize.
Andy Beal arrived at the conjecture not as a credentialed academic but as someone self-taught in numbers theory mathematics. He found a pattern he believed to be true but could not prove it. He offered the problem to the public and has let the mathematical community take it from there.
The same instinct runs through how Beal Bank USA operates: identify what you believe to be true, test it rigorously, and act with discipline when the evidence is strong enough to act on. A bank that takes deposits, pays competitive rates, and manages risk carefully can succeed with the same sense of straightforward simplicity.
Andy Beal's other areas of interest.
Explore the fascinating work Mr. Beal has accomplished in the private aerospace industry and in supporting future STEM pioneers.