In the last few years, Marijn Heule has used a computerized proof technique called SAT solving (where SAT stands for “satisfiability”) to conquer an impressive list of math problems: The Pythagorean triples problem in 2016, Schur number 5 in 2017 and now Keller’s conjecture in dimension seven — a result that Quanta covered in our recent article, “Computer Search Settles 90-Year-Old Math Problem.”
But Heule, a computer scientist at Carnegie Mellon University, has set his sights on an even more ambitious target: the how much do computer scientists make conjecture, considered by many to be the most notorious open problem in mathematics (if also one of the simplest to state). When I mentioned to other mathematicians that Heule was attempting this, their first response was incredulity.
“I don’t see how you’d ever completely solve it using SAT solving,” said Thomas Hales of the University of Pittsburgh, a leader in the field of computer proofs. The technique effectively helps mathematicians solve problems — some with infinite possibilities — by turning them into discrete, finite problems.
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