mathematics

Google DeepMind's AlphaProof Nexus solved nine of 353 open Erdős problems and proved 44 OEIS conjectures, according to a study published in Science. The system pairs Gemini 3.1 Pro with the Lean proof assistant, and the work went through peer review, unlike other recent AI-math releases.

The Association for Human Mathematics (AHM), chaired by Fields Medalist Terence Tao, is urging mathematicians to stop working with OpenAI after the company released more than 700 AI-generated manuscripts at once. The group says the release violates scientific norms. Critics say many of the papers are too dense to verify without AI assistance.

OpenAI released 719 manuscripts claiming solutions to open math problems, but only 10 include the model's chain of thought. A Cambridge and King's College London paper also documents at least two discrepancies between the natural-language and Lean versions of OpenAI's Navier-Stokes-derived result.

OpenAI has published 372 mathematical results generated by an unnamed internal frontier model, hosted on GitHub instead of in peer-reviewed journals. The company claims each result solves or substantially advances an open problem, at an average of about three hours of ChatGPT Pro Thinking compute per result. Many include Lean formalizations, but independent validation of significance is still pending.

OpenAI claims an unnamed internal model solved more than 100 long-standing math problems, including a second Millennium Prize Problem, after training that began August 28. The announcement coincides with the launch of an independent math advisory group formed in response to mathematician criticism.

Axiom Math's AI system AxiomProver has formally verified the proof of the '246 theorem,' a landmark result from the Polymath8b collaboration on prime gaps. The company says the achievement builds a reusable library for future formalization work and points toward AI verification of software code.

Anthropic says an as-yet-unreleased model significantly increased the lower bound of solutions for which the 150-year-old Riemann hypothesis holds true, coordinating 60 sub-agents across 650 tested ideas. The result was verified by in-house mathematicians and formalized in the Lean proof assistant.

OpenAI claims an internal version of its next major model, Astra, produced solutions to ten mathematical and theoretical computer science problems that had seen no progress in at least a decade. The company says each solution cost less than $2,000 in GPT-5.6 Sol token pricing, and published Lean 4 formalizations along with a paper describing the results.

OpenAI published a counterexample disproving the Unit Distance Conjecture, a geometric graph theory problem open since 1946, in what many mathematicians call the most significant AI math result yet. Reactions range from Terence Tao's cautious optimism to Timothy Gowers describing 'mixed feelings' about having the rug pulled out from under him.

OpenAI claims its new reasoning model has produced an original mathematical proof disproving a geometry conjecture first posed by Paul Erdős in 1946. The company says this is the first time AI has autonomously solved a prominent open problem central to a field of mathematics, with verification from mathematicians including Thomas Bloom and Noga Alon.

Zyphra has released ZAYA1-8B, a mixture-of-experts language model with 760M active parameters and 8.4B total parameters. The model scores 89.1% on AIME 2026, competitive with models exceeding 100B parameters, while maintaining efficiency for on-device deployment.

OpenAI's GPT-5.4 Pro model has reportedly solved Erdős open problem #1196 in approximately 80 minutes, with another 30 minutes to format the solution as a LaTeX paper. Mathematician Terence Tao notes the solution reveals a previously undescribed connection between integer anatomy and Markov process theory.