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AI Mathematicians Timeline: OpenAI’s 722 Papers, DeepMind’s Erdős Proofs and What Is Verified

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AI and mathematicians are in the news because of two releases in one week: Google DeepMind’s Erdős-problem proofs in Science and OpenAI’s mass release of research manuscripts. This timeline keeps to what the labs, the journal and the foundation have published.

Two verified facts anchor the story: Google DeepMind’s AlphaProof Nexus reported Lean-verified proofs of 9 of 353 Erdős problems and 44 of 492 OEIS conjectures (Science, Oct 8, 2026), and OpenAI published 722 manuscripts on Oct 6 that it then reduced to 719 after withdrawing three, with about 42% of top-line results formalized in Lean; whether the results are correct, new and understood is still being settled by mathematicians.

Read on 2026-10-18: OpenAI’s Oct 6 post and its Oct 15 update, OpenAI’s public math repository and its history file, Science’s news report of Oct 13 and its AlphaProof Nexus paper page, the arXiv paper, DeepMind’s results repository, the Simons Foundation’s Oct 15 announcement, and official X posts by @OpenAI, @AnthropicAI, @SimonsFdn and DeepMind’s Pushmeet Kohli. Scope: the AI-and-mathematicians story, which X’s own trending summaries on Oct 10–17 centre on. We did not check any proof ourselves.

Timeline

  1. Pushmeet Kohli of Google DeepMind announces AlphaProof Nexus on X as “an agentic framework for formal proof search powered by Gemini”. The thread says the agent autonomously solved 9 open Erdős problems from a set of open formal math problems and links the formal proofs in Lean. The accompanying arXiv paper (2605.22763) describes agents that alternate LLM proof generation with checking by the Lean compiler.

    Pushmeet Kohli on X: AlphaProof Nexus

  2. Science, describing OpenAI’s earlier work, says the company’s “headline-grabbing Navier-Stokes breakthrough last month” took a swarm of 10,000 agents working continuously for 88 hours, likely at a cost of millions of dollars. We can source this only to Science’s description, not to a primary OpenAI page we read, so it is included as context and not as a verified result.

    Science: OpenAI just changed math forever

  3. OpenAI publishes “Sharing AI progress in mathematics” and a repository of manuscripts produced by an unreleased internal model, saying it consulted the independent Advisory Group on Mathematics and Artificial Intelligence at the Institute for Advanced Study. The repository describes 372 result families; the model was posed roughly 4,000 problems and the average result used the equivalent of about three hours of ChatGPT Pro thinking. Science counts 722 preprints at release. OpenAI’s post on X went out at 22:19 UTC.

    OpenAI: Sharing AI progress in mathematics

  4. OpenAI’s repository history records the first withdrawals. A sign error in a paper on algebraicity of Weil classes on split abelian eightfolds invalidates an argument that two dependent papers also use, so three manuscripts are withdrawn, including one titled “The rational Hodge conjecture for products of K3 surfaces”. Fourteen other manuscripts are revised, and the history gives the new total as 719 manuscripts with 300 formalized, about 42%.

    OpenAI math repository: history

  5. Science publishes the AlphaProof Nexus paper by Tsoukalas and colleagues. Its summary: an AI agent for formal proof search that autonomously resolved nine of 353 open Erdős problems, including two open for 56 years, proved 44 of 492 open conjectures from the On-Line Encyclopedia of Integer Sequences, resolved an open question in algebraic geometry and improved a known bound in min-max optimization. Kohli posts a thread the same day, crediting the formal mathematics community and Lean’s Mathlib.

    Science: Advancing mathematics research with AI-driven formal proof search

  6. Science’s news report appears online. It quotes mathematicians including Olga Holtz (“One must distinguish a claimed result, an independently verified result, and a result that has been understood and absorbed into mathematical culture”) and notes that a preprint found the Lean formalization of OpenAI’s Navier-Stokes result does not match the proof in its paper. It reports the advisory group asked OpenAI to stop testing open problems on unreleased models mathematicians cannot access, and that OpenAI has so far declined.

    Science: OpenAI just changed math forever

  7. The Simons Foundation announces that it, Anthropic and OpenAI will commit $15 million in combined funding and resources to help mathematicians evaluate AI-assisted results, learn new tools and set standards, with the Foundation managing awards and an open call. OpenAI’s X post says it is contributing $5 million and adds an update to its Oct 6 page; Anthropic says on X that it has committed $5 million as well.

    Simons Foundation: $15M effort to help mathematicians navigate the AI era

Background: why mathematicians are in the news

Mathematics has an unusually clean test for machine reasoning: a proof can be checked. That is why the field became the place where claims about AI progress get sharpest, and why two announcements in one week moved it from a research curiosity to a news story. The first is about a method, formal proof search, in which a language model proposes a proof and a proof assistant called Lean checks every step. The second is about volume: a single lab putting out hundreds of manuscripts at once.

It helps to separate three things people mean by a result. A claimed result is what the lab says. A verified result has been checked, by a computer in a formal system or by independent experts. An absorbed result has been understood, written up in a form others can use and taught. Holtz’s sentence in Science separates exactly these three, and the timeline above is arranged around which of the three each node supports.

The title uses “AI mathematicians” to mean AI systems that produce research-level mathematics, together with the working mathematicians reacting to them. We found no single official product named “AI mathematician”, so this is a story about several systems and communities. Our earlier post on Terence Tao’s reaction covers one person’s arc in depth; this one is the wider record. See Terence Tao vs OpenAI for that angle.

Thread one: DeepMind’s AlphaProof Nexus and Lean-verified proofs

AlphaProof Nexus is a framework, built by Google DeepMind and powered by Gemini, for agents that write formal proofs and get feedback from the Lean compiler. The paper describes a basic agent where sub-agents independently search for proofs, and a full-featured agent where sub-agents are coordinated with an evolutionary algorithm and can call AlphaProof, an earlier reinforcement-learning system for olympiad-level Lean proving, as a tool. The paper reports that the full agent solved 9 of 353 attempted Erdős problems at an inference cost of a few hundred dollars per problem, and says that even a basic agent replicated the Erdős successes.

What makes this thread easy to state precisely is that the output is code. DeepMind’s public repository holds the Lean proofs and prose proofs for the problems the agent solved, and a list of the Erdős problems that were attempted. After each solve, the authors say experts on the team checked that the Lean statement faithfully captured the original conjecture, which is the step that guards against a proof of the wrong statement. The paper says the results were logged on Terence Tao’s wiki of AI contributions to Erdős problems.

A hit rate of 9 of 353 means the agent failed on most of what it tried, so the claim covers some open problems and not most. A paper in Science also remains a claim about priority. Formal-conjecture repositories are public, and a third-party analysis we found argues that one of the nine, problem 846, was already implied by earlier work, so the count of newly resolved problems might be eight. We list that analysis under unverified items because it is not a primary source and we have not checked the underlying papers.

Thread two: OpenAI’s mass release, and how fast it changed

OpenAI’s October 6 post says it is releasing “a broad range of new mathematical results produced by an internal frontier model”, shares Lean formalizations of many proofs, and adds summaries of the model’s reasoning and compute estimates. The repository says the manuscripts are organized into families, that the vast majority were obtained by one procedure on an unreleased model, and that results are classified by discipline from number theory to partial differential equations.

What the repository does not do, by its own description, is certify the English claims. Science notes that Lean confirms a proof establishes the statement as coded, not the statement the paper states in English, and that some formalizations may be of something weaker. So the formalized fraction of about 42% (300 of 719) cannot be read as 42% of results being verified.

The correction came quickly. On the day after the release, a sign error in one paper took out two dependent manuscripts and a stated resolution of a Hodge-type conjecture for products of K3 surfaces. OpenAI recorded the withdrawals in a public history file with notices on the papers, and revised fourteen more. Errors were found and logged in public within a day, and the headline count of 722 did not hold: the repository gave 719 after the withdrawals.

There was also a dispute about process. Science reports that the independent advisory group asked OpenAI to stop testing open problems on unreleased models that mathematicians cannot access, and that OpenAI rejected that request while agreeing in spirit with others, such as depositing results in independent repositories and disclosing the prompts behind each result. OpenAI’s own post says it is continuing to explore community-hosted alternatives to GitHub for the release.

Thread three: the human response and the money

The response is documented in several places. Science quotes Constantin Kogler, an IAS researcher who found OpenAI’s proof of the exact overlaps conjecture while still at a party and posted his own paper four hours later, as well as Steven Sivek of the Association for Human Mathematics, who called the paper closest to his own work “completely unreadable”, and Max Lieblich, who sees a chance to rethink what the discipline is for. Edward Witten, who belongs to the advisory group, is quoted as saying a human who understood the results could write them more clearly.

On October 15 the Simons Foundation announced the $15 million effort. By its own text the money supports workshops and initiatives to help researchers evaluate AI-assisted results, learn tools, share perspectives and shape collective standards, and OpenAI and Anthropic will provide tools and compute to supported researchers. OpenAI’s update to its own post frames its $5 million as support for examining and building on AI-produced results, including those in the October 6 release. Neither source says the funding was a response to criticism; we state the order of events and nothing more.

Three places record changes as the story develops: OpenAI’s repository history, which logs every withdrawal and revision, the Simons Foundation’s call for proposals, and the Erdős-problem tracker pages that record AI contributions. We will add dated nodes here when one of them changes.

How to read any new “AI solved it” claim

  • Ask who made the claim, and whether a non-lab expert has said it is correct. A lab’s post is a claim; an expert’s written check is evidence.
  • Look at what was formalized. A Lean file proves what the Lean statement says; confirm that statement matches the English theorem.
  • Look for priority. Open-problem databases and preprint servers are public; look for earlier or simultaneous work.
  • Look at the denominator. Nine of 353 problems, or 372 result families from about 4,000 problems posed, is a very different picture from a headline count.
  • Watch the history file as well as the headline. The three withdrawals in OpenAI’s repository changed the count within a day.

What is not verified

  • That any specific OpenAI result, including the Hodge-type and Navier-Stokes claims, is correct. Science reports that the Navier-Stokes Lean formalization does not match the paper’s proof; researchers say this does not mean the result is wrong.
  • That AlphaProof Nexus’s problem 846 is newly resolved. A third-party analysis argues the count may be eight; we have not verified it.
  • Allegations about priority or plagiarism on specific OpenAI results. They appear in secondary news coverage, and we did not find primary statements from the people involved on pages we could read.
  • Individual reactions that circulate on X, including accounts of specific mathematicians’ distress, which we saw only in X’s auto-generated trending summaries.
  • Terence Tao’s remarks in a Numberphile interview, which appear in X’s summaries but which we did not read at the primary source. His own page is covered in our Tao post.
  • Anything about an unreleased model beyond what OpenAI says in its post and repository: name, size and training.

Where this connects to other Front stories

The same labs that are publishing mathematics are also shipping general models. Google’s Argon launch included math and science claims, including Lean-verified quantum-circuit work, in its October 13 post; see the Google Argon timeline and the practical companion What you can do with Google Argon today, which includes a long-decode example asking for a proof. For another dated, sourced story about a lab’s claims against what its own pages show, read Grok 4.8: what xAI has actually said. All posts are at the blog index.

Keep reading on Front

Every post, newest first, is on the Front blog index.

FAQ

What does “AI mathematician” refer to here?

It refers to AI systems producing research-level mathematics, mainly Google DeepMind’s AlphaProof Nexus and OpenAI’s unreleased internal model, and to the mathematicians responding to them. No product is officially named AI mathematician.

How many papers did OpenAI release?

722 preprints on October 6, 2026, covering 372 result families. After three withdrawals the repository lists 719 manuscripts.

Are the OpenAI proofs verified?

Partly. OpenAI says about 42% of top-line results (300 of 719 manuscripts) are formalized in Lean, and Science notes Lean checks the coded statement, not necessarily the paper’s English claim. Independent expert verification is ongoing.

What did AlphaProof Nexus prove?

Per the Science paper: nine of 353 attempted Erdős problems (two open 56 years) and 44 of 492 OEIS conjectures, each with Lean proofs published in DeepMind’s repository.

What is the Simons Foundation initiative?

A $15 million combined commitment announced October 15, 2026 with Anthropic and OpenAI to support workshops, tools and standards for mathematicians evaluating AI results.

Update log

  • — First published. Checked OpenAI, DeepMind, Science, Simons Foundation and official X posts through Oct 18, 2026 (UTC+8).

Sources