John Pavlus in Quanta:
The mathematical conundrums that Marijn Heule has helped crack in the last decade sound like code names lifted from a sci-fi spy novel: the empty hexagon(opens a new tab). Schur Number 5(opens a new tab). Keller’s conjecture, dimension seven. In reality, they are (or, more accurately, were) some of the most stubborn problems in geometry and combinatorics, defying solution for 90 years or more. Heule used a computational Swiss Army knife called satisfiability, or SAT, to whittle them into submission. Now, as a member of Carnegie Mellon University’s Institute for Computer-Aided Reasoning in Mathematics, he believes that SAT can be joined with large language models (LLMs) to create tools powerful enough to tame even harder problems in pure math.
“LLMs have won medals in the International Mathematical Olympiad, but these are all problems that humans can also solve,” Heule said. “I really want to see AI solve the first problem that humans cannot. And the cool thing about SAT is that it already has been shown that it was able to solve several problems for which there is no human proof.”
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