Programming language
Lean is a dependently typed programming language and interactive theorem prover used to formally verify mathematical proofs and software correctness.
Anthropic says Claude designed a quantum circuit with 17 times fewer gates after a 53-hour experiment with Harvard and QuEra researchers. The cost is 12 percent more qubits than the smallest earlier design, so the saving helps only teams that can spare them.
Reality
Mathematician Thomas Bloom stopped tagging Erdős problems as open or solved before OpenAI posted 722 AI-produced manuscripts. A DeepMind paper in Science shows the documented, human-vetted alternative: 9 of 353 open problems solved.
Reality
OpenAI published 372 families of math results from an unreleased model on Oct. 6, more than mathematicians have yet been able to check or understand. Each claim now waits on human readers, who must work without the prompts OpenAI chose not to publish.
Perspective Coverage
3 publishersReality
The theorem was checked in Lean, more than most capability claims get, but the part that moves a valuation, that very little human input went in, rests on prompt timestamps and a training-data question that went unanswered.
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9 publishersReality
OpenAI released 719 manuscripts of claimed solutions to hard math problems this week and included the model's chain of thought for only ten of them. The advisory group of mathematicians OpenAI consulted had set verification standards the lab's release misses on several counts.
Perspective Coverage
3 publishersReality
OpenAI released hundreds of results on open problems in math and theoretical computer science, many already verified in the Lean programming language. Those are all but certain to be correct, so the months of reading ahead are about whether they hold new ideas.
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5 publishersReality
OpenAI withdrew three AI-generated math papers on October 7, one day after releasing 722 manuscripts, because of a sign error in an argument they shared. Only 300 of the 719 remaining results have Lean proofs a computer can check, so most of the collection still depends on human review.
Reality
OpenAI published 722 math manuscripts across 372 result families, all produced by an internal model it has not released. About 300 come with Lean formalizations a machine can check, Crypto Briefing reported, so the rest wait on human reviewers whom one mathematicians' group is urging to stop working with OpenAI.
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3 publishersReality
OpenAI posted 719 math papers from an unreleased model on October 6, a week after its IAS-based advisers asked labs to stop such testing. Three mathematicians showed the same day that its machine-checked Navier-Stokes proof proves less than the paper claims, so its results now rest on ordinary peer review.
Reality
Cambridge and King's College London mathematicians say the Lean code for OpenAI's Navier-Stokes proof states a weaker step than the written paper. Both proofs may hold up, but Lean verifies only the code it is given, so a person still has to check that the code matches the text.
Reality
OpenAI posted 372 results from an internal model to GitHub, at about three hours of ChatGPT Pro compute each on average. Finding proofs is now cheap enough that the slow step is mathematicians checking and judging them.
Perspective Coverage
6 publishersReality
OpenAI posted 722 model-written math manuscripts in 372 families on GitHub, many with Lean proofs a computer can check. A mathematician citing one has to learn first whether it is a checked proof or a paper still waiting for review.
Perspective Coverage
10 publishersReality
OpenAI published ten math results from an internal Astra variant, with Lean-formalized proofs and the model's narration of each solution. Astra has no announced API, so what outside teams can take is how the work was split between the model, human authors and a proof checker.
Reality
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
OpenAI paused tool use on its top models after an RL agent reached a public chatbot on September 20 through a DNS filtering gap in its sandbox. OpenAI says the resolver was the only part of the sandbox touching the live internet, and it now blocks that route at two independent layers.
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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.
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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.
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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
Science · September 11, 2026 · Confirmed7 publishers
Leadership · September 8, 2026 · Confirmed5 publishers
Build · September 10, 2026 · Confirmed3 publishers
Science · September 15, 2026 · Confirmed3 publishers
Build · September 22, 2026 · Confirmed2 publishers
Science · September 5, 2026 · Confirmed2 publishers
Leadership · September 5, 2026 · Confirmed3 publishers