OpenAI says its models produced proofs for three open problems: local smoothing, the Exponential Time Hypothesis, and Yang-Mills existence
If these hold, formal verification becomes a much bigger part of AI-assisted research. A claimed proof, a machine-checked proof, and a proof the field accepts are three different milestones, and today’s news is at a different one for each problem. The ETH claim alone would have major implications for conditional hardness results.
One is formalised in Lean. One is being examined by the people who proposed the conjecture. One nobody outside David Gross’s group can see yet.
OpenAI calls the work raw research data at different verification stages. The Lean-formalised proof, it says, settles the local smoothing conjecture in every dimension, which would imply Kakeya and Stein’s restriction conjecture. The CS paper claims a subexponential deterministic SAT algorithm that refutes ETH, and OpenAI says Impagliazzo and Paturi, who proposed ETH, and Ryan Williams will shepherd public examination of the released data. The claimed Yang-Mills and QCD proof stays with David Gross’s group, with the artifacts withheld.
My read: if these hold, formal verification becomes a much bigger part of AI-assisted research. A claimed proof, a machine-checked proof, and a proof the field accepts are three different milestones, and today’s news is at a different one for each problem. The ETH claim alone would have major implications for conditional hardness results.
Your pick: get hands-on with formal verification tooling like Lean. Turning a generated proof into something people trust is going to matter as much as generating it.
12 months: AI-assisted proofs are routine in theory work.
24 months: formal verification is standard for major claims.
36 months: research splits into generation, verification, and explanation.
Why I may be wrong: these are OpenAI-produced claims, independent verification has barely started, and math advisers criticised the staged release.
Which of the three survives scrutiny?