language
Lean is a dependently typed programming language and interactive theorem prover used to formally verify mathematical proofs and software correctness.
No evidence-backed relationships are recorded.
Ramana Kumar used AI to exploit a different bug in each of two Lean kernels, passing off a false Collatz disproof as machine-checked in July. AI labs rely on Lean to vouch for their maths results, so those claims hold only as well as the checker does.
Reality
OpenAI says about 10,000 AI agents produced a proposed finite-time singularity for the forced 3D Navier-Stokes equations in 88 hours. The construction fits one route the Clay rules allow and leaves unforced smoothness open, while the mathematicians whose forced-Euler work came first ask whether their Codex drafts reached the model.
Reality
An interview with Lean's founder says an AI translated C zlib into Lean and proved compress-then-decompress round-trips in about a week. The remaining work is optimization without breaking the proof.
Reality
Anthropic's own account has dozens of agents writing 13 million machine-checked lines in 11 days, about 7% of them dead ends, and only after a Columbia team built the shared to-do list that stopped them duplicating work.
Reality
Kevin Buzzard holds a five-year grant to do the same job by hand. He compiled Anthropic's 13 million lines himself and says the result teaches mathematicians nothing and anyone running agent fleets quite a lot.
Reality
Trail of Bits' agent-built Lean model of the Miden VM, backed by 95 machine-checked proofs, surfaced a way for a malicious prover to forge Falcon signatures. A dev.to account says the agents built tooling first, so that Miden's stack assembly could be reviewed at all.
Reality
A proof checker confirmed the steps of OpenAI's Navier-Stokes result within days. The argument now running through mathematics is over who explains the 166 pages and who gets the credit for them.
Perspective Coverage
7 publishersReality
OpenAI says no specific user data was accessed to solve the problem, and that it cannot rule out that de-identified data derived from two mathematicians' use of its products improved its models. A procurement team has to read both sentences.
Perspective Coverage
5 publishersReality
OpenAI's write-up gives the token counts, the agent count and the verification time for its Navier-Stokes result. The verification time is the number that decides whether the method transfers to anyone else's workload.
Perspective Coverage
3 publishersReality
With Navier-Stokes claimed and five Millennium problems left, the ordering of what falls next turns on which conjectures a single counterexample would settle. Five million dollars of Clay prize money is still unclaimed.
Perspective Coverage
3 publishersReality
OpenAI says its new nine-member mathematics advisory group will not advise on the pace of its internal research, and the group's own website says the decisions rest with the AI companies.
Reality
Ten Claude Opus 5.5 agents produced the algorithm and a machine-checked proof of its runtime bound in about 15 hours. The theorem covers sparse directed graphs, and the margin over Dijkstra grows as the twelfth root of log n.
Reality
Six months before the review of Miden's zero-knowledge VM began, Trail of Bits set its agents to writing developer tooling for the project's custom assembly language, then reviewed the code with it.
Reality
A Caltech open letter says research mathematicians end up verifying and correcting what AI companies announce, without pay or credit. OpenAI's sponsorship was $1m in credits, and it took them back.
Reality
Nvidia's Nemotron scored 30 of 42 at IMO 2026 writing proofs in ordinary prose, and the September 9 paper publishes the data, the code and the acceptance rule that decided which candidate proofs survived.
Reality
Tristan Buckmaster says OpenAI accelerated onto Navier-Stokes after learning of his work with Anthropic's Levent Alpoge, and that the answer he got about his prompt history addressed lookup rather than training.
Reality
The blue check marks in the editor gutter assume an honest author, and they stay blue when a dependency contains sorry. That is why the manual escalates to axiom listings and to re-checking .olean files.
Reality
The Navier-Stokes result cost more in compute than the Clay Institute's award, and the interesting line in OpenAI's blog post is the one conceding it cannot rule out that customers' de-identified prompts helped.
Reality
OpenAI says the result resolves statement C of the official Millennium formulation, then says it will not claim the $1M prize. The smooth force applied to its fluid throughout is why that second sentence carries the weight.
Reality
OpenAI says roughly 10,000 agents produced a Navier-Stokes singularity proof in about 88 hours, but the only proofs an outsider can run belong to two mathematicians who posted Lean formalisations with their preprints.
Reality
Science · September 5, 2026 · 2 publishers
Leadership · September 5, 2026 · 3 publishers
Build · September 6, 2026 · 1 publisher
Build · September 5, 2026 · 1 publisher
Build · August 29, 2026 · 1 publisher
Build · August 18, 2026 · 1 publisher
Build · August 17, 2026 · 1 publisher