Rohan Paul (@rohanpaul_ai) · 10/22/2026, 14:11:13
AI Agents Help Prove 31-Year-Old KLS Conjecture
Microsoft researchers proved the long-standing Kannan-Lovász-Simonovits (KLS) conjecture using AI agents that explored over 100 research trajectories. The resulting 140-page proof validates a human-directed search model where AI handles derivation and checking while humans define core methods.
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Rohan Paul (@rohanpaul_ai) · 2026-10-22 06
A math problem older than Google has been solved, with AI doing much of the searching.
Microsoft researcher proved this 31-year-old Math conjecture (Kannan-Lovász-Simonovits conjecture) after AI agents explored over 100 approaches.
A 140-page proof, more than 100 AI-explored paths now have closed a question mathematicians had been working on since 1995.
A human-directed search, with AI agents exploring roughly 100 research trajectories while a researcher cut weak directions between rounds, produced the criterion underpinning Song and Zhang’s proof of the Kannan-Lovász-Simonovits (KLS) conjecture.
The AI explored candidate approaches, carried out derivations, helped prepare the manuscript and ran internal proof checks, while the recursive method and the error bound that finished the proof are credited to the 2 researchers.
About the Kannan-Lovász-Simonovits conjecture: Picture a random walker wandering inside a convex shape: the conjecture says no secret narrow passage can trap it, so it can explore the whole shape efficiently, even in huge dimensions.
