OpenAI's new result proves 2005 edit-distance embedding optimal; researcher distills proof to 2.5 pages with AI help
thegautamkamath · x · 2026-10-08
Among OpenAI's released results is a sharp lower bound confirming that the 2005 embedding of edit distance into l1 (optimal distortion exp(sqrt(log n log log n))) is optimal. Ilya Razenshteyn used the occasion to finally work through the finicky original proof, and by iterating prompts with Astra produced a cleaner 2.5-page version of the upper bound—1.5 pages of which are entirely standard—showing how AI can help reconstruct and simplify complex mathematical proofs.
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