Claude produces O(n^1.9992) 3SUM algorithm with Lean proof, vetted by top experts
thegautamkamath · x · 2026-10-06
Ilya Razenshteyn reports that Claude obtained an O(n^1.9992)-time algorithm for the classic 3SUM problem (finding whether three of n integers sum to zero), long conjectured to be impossible below O(n^2), complete with a Lean proof. Leading fine-grained hardness experts Josh Alman and Virginia Williams checked and digested the algorithm, giving Razenshteyn 99.99% a priori confidence it's correct. If it holds up, this is a landmark for AI-assisted mathematics and threatens the many hardness results built on the 3SUM hypothesis.
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