DescriptionIn 2016, Marijn Heule, Oliver Kullmann, and Victor Marek used a Boolean satisfiability (SAT) solver running on a supercomputer to resolve the decades-old Boolean Pythagorean triples problem, showing that the integers up to 7,825 can be two-colored avoiding any monochromatic Pythagorean triple, but no coloring works beyond that point. The resulting proof certificate was approximately 200 terabytes, requiring around two days of computation on 800 processor cores, and it was reported at the time as the largest mathematical proof ever produced, illustrating both the power and the verifiability challenges of computer-generated mathematics.
Formal questionThe 2016 resolution of the Boolean Pythagorean triples problem — whether the positive integers can be two-colored so that no Pythagorean triple (a,b,c) with a^2+b^2=c^2 is monochromatic — produced a machine-checkable proof of approximately 200 terabytes, the largest mathematical proof by size at the time of its publication.
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