The hypothesis it killed was believed true for 25 years — and hundreds of papers rest on it

The Exponential Time Hypothesis has been used in hundreds of papers as the basis for conditional hardness results, and OpenAI's claimed refutation — a subexponential-time algorithm for fixed-width SAT — would reopen questions about how fast those tasks can be solved, though it does not settle P versus NP.

A Lean proof checks that a proof proves its formal statement, the explainer notes — it cannot check that the formal statement matches the conjecture mathematicians actually care about, which is exactly what the shepherd groups will spend the next weeks confirming.

On the prize question, the wording is careful: the Yang-Mills claim covers existence only, which OpenAI calls part of the Clay Millennium Prize problem; the problem as Clay states it also asks for a mass gap, which the announcement does not claim.