OpenAI releases 700-plus claimed math proofs, prompting scrutiny and open-source training environments

Mathematicians dispute OpenAI's description of its potential Navier-Stokes proof, saying its resemblance to the cited approach is superficial, Scientific American reports. The 166-page proof is written in Lean and remains under review by the Clay Mathematics Institute. OpenAI researcher Noam Brown also says the contribution of about 10,000 model instances remains unclear without comparison tests, attributing less than 10 percent of the success to the multi-agent setup.

We turned @OpenAI's math problems into open-source RL environments on @huggingface! They are early and rough, and the verifier only accepts the exact original formalization, so an equivalent proof can still score 0. I find this an exciting direction for turning open research into executable environments anyone can build on to train better open models! https://huggingface.co/datasets/FineEnvs/openai-math

OpenAI and Anthropic announced a broad set of model, product, and access changes this week. OpenAI rolled out GPT-6 with Intelligent UI in ChatGPT, with GPT-6 Sol on paid plans and GPT-6 Luna on Free and Go, and said GPT-6 Astra scored 55.0% versus GPT-5.6 Sol’s 41.6% on 11 contracting tasks. Anthropic released Claude Haiku 5.5 at $0.10 / $0.50 per million tokens for prompts up to 100K, with a 1M context window.

Terence Tao argues that AI is making mathematical proofs abundant, ending a Mathematics 1.0 era built on proof scarcity. He warns that solving problems is not the same as understanding them, calls for reporting failed attempts and compute costs, and says the bottleneck for Mathematics 2.0 is imagination. He also questions whether a PhD still matters when answers come easily.

On October 7, OpenAI released 722 mathematics manuscripts, including two on the Kakeya conjecture: a 97-page paper claiming a three-dimensional maximal-function result stronger than Wang and Zahl's, and a 175-page paper claiming the four-dimensional Hausdorff dimension case. Both are attributed to OpenAI, are not Lean-formalized or peer-reviewed, and OpenAI's README says some unformalized results may be flawed.

A mathematician makes an Opus 5.5 music video in response to OpenAI’s proofs. Pretty great.

OpenAI released more than 700 manuscripts on October 6, 2026, claiming solutions to hundreds of open math problems, and the blog Proofs and Prompts collected over 100 researcher responses. Some papers were withdrawn or criticized as hard to read, while Fields Medalists Peter Scholze and Terence Tao urged patience and solidarity. Many mathematicians described shock, paralysis and fears about their profession.