AI proves long-standing mathematical conjecture

Machines generate text and code, but proving a theorem remained another challenge. This time, models claim to have proven a problem that had remained open for decades. AI in mathematics is now tackling questions that researchers had never resolved.

OpenAI publishes new proofs

OpenAI announced in a publication released at the end of October 2026 that its models had produced unprecedented proofs in fundamental sciences, published for researchers to verify. The most striking result concerns a conjecture in wave theory, which had remained unproven since 1991.

Local smoothing conjecture solved

AI in mathematics is now addressing long-standing open problems, but these proofs still await validation from the community. Among the most remarkable results is the local smoothing conjecture, formulated in 1991 by mathematician Christopher Sogge. It concerns equations describing the propagation of waves, including those of sound and light.

Understanding wave behavior

Specifically, it seeks to understand how their solutions gain regularity during their evolution. Until now, mathematicians had only managed to prove this property in certain cases. A manuscript published by OpenAI claims to now provide a proof valid in all spatial dimensions.

Advancements in computer science

Another claimed advancement concerns theoretical computer science, with a possible refutation of the exponential time hypothesis. This hypothesis assumes that certain problems require computations whose duration increases extremely quickly with their size. It serves as an important reference for numerous research areas, including biology, geometry, and databases. If this hypothesis were indeed refuted, new...