Has AI solved a Millennium Prize Problem? All seven, October 2026

Not officially. As of 15 October 2026, the Clay Mathematics Institute (Clay), which set the seven Millennium Prize Problems in 2000, has recognised no solution produced with AI. Its pages mark one problem as solved, the Poincaré conjecture, proved by Grigoriy Perelman, and five as "Unsolved". The seventh, Navier–Stokes, is now marked "Active": OpenAI said on 8 September 2026 that an internal model had proved one of the four statements Clay accepts, and Clay said three days later that the problem "has apparently been settled", in a process that is "deliberately unhurried". Clay considers a prize only after publication in a refereed outlet, two years and general acceptance. For the Riemann hypothesis, the Hodge conjecture and the Birch and Swinnerton-Dyer conjecture, AI companies have published partial results, not proofs. We found no AI claim on P vs NP or Yang–Mills.

Below: all seven problems, the Navier–Stokes claim in depth, the partial results, the rumour about Claude, the Erdős problems and a checklist for the next headline. Statuses come from Clay's pages and claims from the claimants' own pages, checked on 15 October 2026; the sources note where we used an archived copy.

How many Millennium Prize Problems are solved?

One of seven is solved by Clay's count: the Poincaré conjecture. Five are listed as unsolved, and Navier–Stokes is listed as active.

The solved one. Clay's Poincaré page credits Perelman's preprints of 2002 and 2003, built on Richard Hamilton's Ricci flow. Clay announced on 18 March 2010 that it had awarded him the prize, and the Associated Press reported on 1 July 2010 that he had declined the $1 million.

The labels. On Clay's overview page, Navier–Stokes now sits alone under "Active problems". Internet Archive copies of its problem page show the label changed from "Unsolved" to "Active" between 9 and 10 September 2026. The summary changed too, from "there is no proof for the most basic questions one can ask" to "for many decades no proof was found answering the most basic questions one can ask".

Is the Navier–Stokes problem solved?

Not officially. OpenAI claims a solution and Clay has relabelled the problem, but under Clay's rules no prize can be considered until two years after publication in a qualifying outlet.

What the prize asks. Charles Fefferman's official problem description asks "for a proof of one of the following four statements". Statements (A) and (B) say that, with no external force, smooth solutions exist for all time from any smooth starting velocity, in all of three-dimensional space (with bounded energy) and on a periodic box. Statements (C) and (D) say the opposite can happen: there exist a smooth starting velocity and a smooth force for which no such solution exists for all time. So a single carefully built example with a smooth force would answer the problem. Clay's rules say that for Navier–Stokes and P vs NP "a resolution in either direction will be evaluated by the standard evaluation procedure".

What OpenAI claimed. On 8 September 2026 OpenAI published a research post, "On the Navier–Stokes Millennium Prize Problem", with a 166-page paper and a Lean repository. The post says: "This resolves the Navier–Stokes Millennium Prize problem by establishing statement “C” (and also “D”) in the official Millennium Prize formulation". The paper constructs, for every positive viscosity, a flow that "starts from rest and develops unbounded velocity in finite time while maintaining uniformly bounded kinetic energy", driven by "a smooth force compactly supported in space and time".

OpenAI says the result came from "a system of coordinating agents powered by our internal model", with "on the order of 10,000 concurrent agents" in the group that found it, about 88 hours after the first agents started. The same release claims finite-time blowup for the Euler equations without a force; Fefferman notes that the Euler equation "is not on the Clay Institute’s list of prize problems". OpenAI also wrote: "We do not intend to claim the Millennium Prize for this result."

The revision. On 10 September OpenAI updated the post's "Concurrent work" section, the part about the dispute below. The first version said: "While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models". The update removed that sentence and added: "Following an investigation, we have confirmed that Buckmaster’s Codex prompts over the two months preceding this announcement and paper on September 8, 2026, could not have influenced the system in any way, including through training." The mathematical claim was not changed.

What Clay says. Clay's statement of 11 September reads: "Today, CMI shares in the excitement of the global mathematical community as we contemplate the announcement that the Navier-Stokes problem has apparently been settled." It adds that the rules describe "the process for evaluating what has been achieved and for assigning credit. The process is deliberately unhurried, but we will provide updates." Clay's rules page sets three conditions before it will consider a proposed solution: "(i) the proposed solution must be published in a Qualifying Outlet (see §6), and (ii) at least two years must have passed since publication, and (iii) the proposed solution must have received general acceptance in the global mathematics community". A Qualifying Outlet is, in the rules document, "a refereed mathematics publication of worldwide repute" or a publication approved under relaxed conditions. "CMI does not accept direct submission of proposed solutions." OpenAI's paper is posted on its own website; under the rules, the two years run from publication in a qualifying outlet.

What does a Lean proof of Navier–Stokes show?

It shows that a formal statement follows from Lean's rules and the libraries used. Whether that settles the prize depends on whether the formal statement says what Fefferman's statement (C) says, and that check is done by people.

OpenAI's repository states the Lean result in words: "There exist smooth initial data and forcing for which no global smooth solution with uniformly bounded kinetic energy exists." It provides challenges for Comparator, a tool that compares the proved theorem with a separately written statement and checks which axioms the proof uses. Its instructions say that statement was adapted from the Formal Conjectures project's Lean version of the problem.

Thomas Hales, in a guest post on Terence Tao's blog on 9 October, puts the point plainly: "a proof in Lean should not be accepted until a human audit is performed to ensure statement fidelity." For this case, "a human should check that the statement in Lean corresponds with Fefferman’s statement of the Millennium Prize Problem". He reports that the formalization "has already been confirmed by more than a dozen proof-checkers" and adds: "Cross-checking the proof by different kernels does not remove all doubt."

Two papers question what has been shown. Alexander Bastounis, Fabian Circelli and Anders C. Hansen argue (6 October) that AI translation into Lean can lose meaning, and state: "we show that the formalised Lean proof does not correspond to the NL proof of blow-up of solutions to the Navier-Stokes equations." Their claim concerns the match between the Lean proof and the written argument. Peter Constantin, Mihaela Ignatova and Vlad Vicol prove (17 September) that in constructions with the features of OpenAI's, the force "can neither vanish identically near the singular point, nor be real analytic". Constructions of this kind need a force near the singularity, so they do not settle the unforced question.

What is the Navier–Stokes priority dispute?

It is a disagreement over credit and conduct between OpenAI and two mathematicians, Tristan Buckmaster of New York University and Levent Alpöge, an Anthropic employee, whose results on the Euler equations appeared hours before OpenAI's announcement. Below is each side's account in its own words.

Buckmaster and Alpöge. On 8 September (UTC) Buckmaster announced with Alpöge "finite-time blowup with smooth forcing for incompressible porous media, for Boussinesq, and for 3d incompressible Euler", verified in Lean. His statement credits the underlying programme to Diego Córdoba and Luis Martínez-Zoroa, says "We used several LLMs throughout: Anthropic’s Claude, OpenAI’s Codex", and calls the work "a purely personal collaboration". It describes calls with OpenAI on 6 September and says: "Sebastien twice asserted that he wanted Levent removed from authorship". It records the line "Why would you ruin your career?" and states what he does not claim: "I have not seen OpenAI’s proof. I do not know what their model did, or how. I do not know whether our data was used. I am not accusing anyone of anything." Later that day he asked: "Is it ethical to use customer's data to try to scoop their customer?" Alpöge wrote that "so far the proof looks more along the lines of another euler blowup proof we had".

OpenAI. The research post says: "We recognize the priority of their work on forced Euler and congratulate them on their remarkable mathematical achievement." It says its researchers and agents "did not see any of their work through any means until they released it publicly", and the updated version says "Alpöge and Buckmaster proved a result with external forcing, while OpenAI’s system proved a result without external forcing." OpenAI researcher Sébastien Bubeck wrote on 8 September: "I never ever asked for Levent to be removed from authorship of his own work". He said the option discussed was Buckmaster as lead author on a rewrite of OpenAI's proof, and that he felt "it would be inappropriate for an Anthropic employee to author OpenAI’s work". Of his remark about Buckmaster's career he wrote: "I deeply apologize for this extremely poor choice of words". OpenAI's chief executive, Sam Altman, wrote: "We would have greatly preferred coordination."

The earlier work. Córdoba and Martínez-Zoroa, in a guest post of 4 October, describe their cascade method and write: "At this moment we are not in a position to say anything substantive about a comparison between OpenAI’s constructions and our cascade methods." Clay's rules anticipate such questions: "CMI will pay special attention to the question of whether a Prize solution depends crucially on insights published prior to the solution under consideration."

What have mathematicians said about the Navier–Stokes claim?

Views range from a major advance to doubts about what has been checked and what the race does to the field. Zhen Lei and Xiao Ren, who wrote a readable version of part of the construction, state: "We regard OpenAI's work as a major advance on the Navier-Stokes Millennium Prize Problem." Córdoba and Martínez-Zoroa write that the forced claim, "if verified under the stated hypotheses, would establish an allowed breakdown alternative in the Millennium Problem formulation." Tapio Schneider, in a guest post, notes: "(The unforced version of the problem, whether smooth solutions exist for all time without external forcing, remains open.)"

Terence Tao wrote on 8 September that "even the rumor of someone working on a problem can trigger a massive amount of AI-powered effort to flatten it before the original research project has time to reach its full potential." On 11 September he posted a declaration, "A Severe Misalignment of AI in Mathematics", with 25 initial signatories, all Fields Medallists; its site, mathandai.org, lists 28 Fields Medallists as of 15 October 2026. The declaration names no company and says: "The goals of the AI companies and the goals of the mathematical community are severely misaligned." On how results are released: "Often these solutions are announced in a rush, leaving no time for a proper writeup, the isolation of new methods and ideas, and citing relevant previous work of others." Timothy Gowers explained on 17 September that he did not sign, "despite agreeing with much of what it said", because it could be read as making conceptual understanding the only right priority.

Has AI made progress on the Riemann hypothesis?

Yes, on related questions; no one claims a proof of the hypothesis. The Riemann hypothesis says that all non-trivial zeros of the zeta function have real part 1/2. Two kinds of partial result have appeared.

Anthropic, August 2026. Anthropic reported on 10 August that "An unreleased research version of Claude has improved on a longstanding lower bound for the fraction of zeros of the Riemann zeta function that satisfy the Riemann hypothesis", raising it "from 41.6% to 67.2%". A staff member had asked Claude to attempt the hypothesis itself, and Anthropic says that "it didn’t succeed". By Anthropic's account, two of its mathematicians validated the paper, two outside experts examined it and a Lean formalization passes Comparator; the post was updated on 13 August with a revised paper. Anthropic adds: "We don’t expect that the techniques Claude used will lead to proving the Riemann hypothesis." The arXiv version lists Levent Alpöge and Ralph Furman as authors, with the note "Proof discovered autonomously by Claude (Anthropic); verified and communicated by the listed authors." Youness Lamzouri has since given a new proof that he calls "conceptually simpler".

OpenAI, October 2026. OpenAI's 6 October release, "Sharing AI progress in mathematics", published results in a GitHub repository that now holds 719 manuscripts. Two concern the quasi-Riemann hypothesis: that zeta has no zeros with real part above some fixed number less than 1. One paper, formalized in Lean, claims this with the bound 7/8 for every Dirichlet L-function, zeta included; another claims the bound 11/12 by a different route. The first says: "The theorem does not establish the Riemann hypothesis or its generalized versions, which place nontrivial zeros on ℜs = 1/2." The repository notes that this work was an exception to its standard procedure and that the 11/12 writeup "was human edited for readability".

Frank Calegari wrote on 8 October that he had thought such zero-free regions were near the limit of analytic methods: "Obviously, I was totally wrong, and something was clearly missed." He still believes, "although perhaps with slightly less conviction, that improvements to these analytic arguments are not going to be sufficient to prove the full Riemann hypothesis." Baiying Liu has improved the 7/8 slightly using the same strategy.

What has AI claimed on the Hodge and Birch–Swinnerton-Dyer conjectures?

Special cases only. OpenAI's October release includes papers that prove each conjecture for restricted families, and three of its Hodge papers have been withdrawn.

Hodge. Clay's overview says the conjecture "is known in certain special cases". OpenAI's current papers claim it for complex abelian varieties with complex multiplication and for self-powers of other special varieties: certain abelian sixfolds, K3 surfaces in a defined locus and Jacobians of abelian covers. None has a Lean formalization in the repository. Three other papers, on Weil classes on split abelian eightfolds, Kuga–Satake correspondences and products of K3 surfaces, were withdrawn on 6 October after a sign error was found; each notice says: "This withdrawal concerns the proof; it does not assert that the mathematical statement is false." For context, Burt Totaro's guest post of 11 September calls Eyal Markman's 2025 proof for abelian varieties of dimension 4 and 5 "a monumental piece of work".

Birch and Swinnerton-Dyer. OpenAI's paper claims the full leading-term formula for every elliptic curve over the rationals whose q-power Selmer group has corank zero or one at some prime q. The conjecture covers all ranks. Calegari's first impression is "that these are technical improvements on results already in the literature, and that they represent no genuine progress towards the higher-rank version of BSD." Ashay Burungale, in a guest post on Calegari's blog on 15 October, writes: "The correctness of the announced proofs remains under investigation."

Has AI solved P vs NP or the Yang–Mills mass gap?

No. We found no claim from an AI company on either problem, and none of the 372 result families listed in OpenAI's repository is about either one. Clay's overview describes Yang–Mills in one line: experiment and simulation suggest a mass gap, "But no proof of this property is known." For P vs NP, Lance Fortnow wrote in June: "I do not believe we will see a P v NP proof in my lifetime proven by man or machine, separately or working together."

Did Claude solve Navier–Stokes?

No. As of 15 October 2026, Anthropic's news and research pages and its sitemap show no Navier–Stokes paper or claim; its August mathematics post is about zeta zeros. A rumour circulated before either September announcement. On 5 September Tao posted: "A clarification in response to recent rumors about a possible solution to the Navier-Stokes problem: I am not aware of any significant developments in this regard".

OpenAI wrote: "On Tuesday, September 1, we heard rumors that two Millennium Prize problems had been resolved." Bubeck wrote of "viral twitter rumors that Anthropic had resolved 2 Millenium problems". Buckmaster's statement mentions "a rumor circulating that Anthropic had resolved a major open problem", adding that "it seems safe to assume I am" the person it attached to, and OpenAI says it later realised the rumour was related to Alpöge and Buckmaster. Their result was on the Euler equations, not Navier–Stokes, made with tools including Claude and OpenAI's Codex, and both describe it as personal work, not an Anthropic project.

Which Erdős problems has AI solved?

A number of them, but the counts depend on what is counted, and the main tracker stopped updating on 30 June 2026. Terence Tao's wiki "AI contributions to Erdős problems" separates full and partial results, incorrect work and unverified claims, and AI working alone from literature search and formalization. It warns: "This page is not a benchmark". Its header reads: "The wiki is no longer updated. The latest data is as of Jun 30, 2026."

The categories matter. On 17 October 2025 Thomas Bloom, who runs erdosproblems.com, replied to a post about GPT-5 by Kevin Weil, then at OpenAI: "this is a dramatic misrepresentation. GPT-5 found references, which solved these problems, that I personally was unaware of." Weil answered that he had misunderstood Mark Sellke's original post and would delete his own.

Two later results go further. On 20 May 2026 OpenAI reported that "An internal OpenAI model has disproved this longstanding conjecture", Erdős's 1946 conjecture on unit distances among points in the plane, and that "The proof has been checked by a group of external mathematicians". A Google DeepMind paper of 21 May, on the system its results repository calls AlphaProof Nexus, reports that its agent "autonomously resolved 9 of 353 open Erdős problems at the per-problem cost of a few hundred dollars", with proofs in Lean.

On 6 October Bloom announced that erdosproblems.com will freeze new proof claims and "will not display the statuses of any problems". His reason: the main public use of the site had become "to advertise their AI-generated proofs, often without any attempt to explain them".

How should you read an "AI solved X" headline?

Start from the problem's own statement and its keeper, not the announcement. Eight questions help:

1. Which exact statement? Forced or unforced, a special case or the whole conjecture, the quasi-Riemann hypothesis or the Riemann hypothesis. Compare the claim with the official wording, such as Fefferman's four statements.
2. Is there a paper with full proofs, and where? A blog post, a GitHub repository, arXiv and a refereed journal are different things. Clay counts only a qualifying outlet.
3. If there is a Lean proof, has a person checked the formal statement? A kernel check shows the formal theorem follows; a human audit shows the formal theorem is the one in the headline.
4. Who outside the company has checked it? Look for named experts writing in their own venues, and read what they actually say.
5. What does the keeper say? Clay's page labels, or the maintainer of a problem list, decide the official status.
6. Has it been revised or withdrawn? Check changelogs and version histories: OpenAI's post changed on 10 September, Anthropic's on 13 August, and three Hodge papers were withdrawn.
7. Who else was working on it? Look for earlier and concurrent work, and whether it is cited.
8. How was it found, and by what? Agent counts, human input and model names are reported by the company and usually cannot be checked from outside.

Where Papex tracks these claims

Papex keeps a catalogue of open problems, taken from named source lists, Clay's Millennium Prize Problems among them. Six of the seven have pages there, each sourced to Clay's own page. A page shows the source's status in Papex's labels, with the date it was checked: the five that Clay calls "Unsolved" appear as Open, and Navier–Stokes, which Clay now labels "Active", appears as Under review.

Some problem pages, such as Navier–Stokes, Riemann hypothesis, Hodge conjecture and Birch and Swinnerton-Dyer, carry an "AI-assisted claims" block: claims made elsewhere, quoted as their sources state them, with revisions, withdrawals and named responses. Its note reads: "Claims as their sources state them. Papex has not checked them; the status stays the source’s." Papex does not judge whether a claim is correct, does not check proofs and does not run Lean.

A researcher who works on an open problem, with or without AI tools, can keep a Papex record of the attempt. It stays a private draft until they sign. The signature links them to that exact version, which is timestamped with OpenTimestamps and anchored in Bitcoin, with no wallet needed; later edits become new versions. A public record can be linked to the problem and is listed on its page. Model names in a record are as the person declares them.

A record shows who signed which version and that it existed by a date. It is not peer review, it is not a journal, and it does not show that the work is correct, original or first.

Sources

• The Millennium Prize Problems (Clay Mathematics Institute), checked 15 October 2026
• Navier-Stokes Equation (Clay Mathematics Institute), checked 15 October 2026; earlier wording and label from Internet Archive copies of 9 September 2026 and 10 September 2026
• Riemann Hypothesis (Clay Mathematics Institute), checked 15 October 2026
• Hodge Conjecture (Clay Mathematics Institute), checked 15 October 2026
• Birch and Swinnerton-Dyer Conjecture (Clay Mathematics Institute), checked 15 October 2026
• P vs NP (Clay Mathematics Institute), checked 15 October 2026
• Yang-Mills & the Mass Gap (Clay Mathematics Institute), checked 15 October 2026
• Poincaré Conjecture (Clay Mathematics Institute), checked 15 October 2026
• First Clay Mathematics Institute Millennium Prize Announced Today (Clay Mathematics Institute, 18 March 2010), checked 15 October 2026
• Russian mathematician rejects $1 million prize (Associated Press via PhysOrg, 1 July 2010), checked 15 October 2026 (Internet Archive copy of 17 January 2012)
• Rules for the Millennium Prize Problems (Clay Mathematics Institute), checked 15 October 2026
• Millennium Prize Description and Rules (Clay Mathematics Institute, 26 September 2018), checked 15 October 2026
• Fefferman, Existence and smoothness of the Navier–Stokes equation (Clay Mathematics Institute), checked 15 October 2026
• Navier-Stokes Announcement (Clay Mathematics Institute, 11 September 2026), checked 15 October 2026
• On the Navier–Stokes Millennium Prize Problem (OpenAI, 8 September 2026, updated 10 September 2026), checked 15 October 2026 (Internet Archive copies of 8 September and 14 October 2026; the live page blocked automated access)
• Finite time blowup for Navier–Stokes (OpenAI), checked 15 October 2026
• openai/NavierStokesAndEuler, README and Comparator instructions (GitHub), checked 15 October 2026
• Hales, What mathematicians should know about the Lean Theorem Prover (guest post, What's new, 9 October 2026), checked 15 October 2026
• Bastounis, Circelli & Hansen, Navier-Stokes lost in translation (arXiv:2610.08144, 6 October 2026), checked 15 October 2026
• Constantin, Ignatova & Vicol, Regularity of asymptotically axisymmetric solutions to the 3D Navier-Stokes equations with analytic forcing (arXiv:2609.20803), checked 15 October 2026
• Buckmaster, announcement (Mastodon, 8 September 2026), checked 15 October 2026
• Buckmaster, statement (Courant Institute, NYU), checked 15 October 2026
• Buckmaster, post (Mastodon, 8 September 2026), checked 15 October 2026
• Alpöge, post (X, 8 September 2026), checked 15 October 2026 (read through the FixTweet API, api.fxtwitter.com; x.com requires sign-in)
• Bubeck, "I would like to clarify a few things" (X, 8 September 2026), checked 15 October 2026 (read through the FixTweet API)
• Bubeck, "Some more technical points" (X, 8 September 2026), checked 15 October 2026 (read through the FixTweet API)
• Altman, post (X, 8 September 2026), checked 15 October 2026 (read through the FixTweet API)
• Córdoba & Martínez-Zoroa, On classical solutions and singularity formation in incompressible fluids (guest post, What's new, 4 October 2026), checked 15 October 2026
• Lei & Ren, Finite-Time Blowup for Navier-Stokes with Smooth Forcing, Part I (arXiv:2609.35406), checked 15 October 2026
• Schneider, Headlines and inside stories (guest post, What's new, 23 September 2026), checked 15 October 2026
• Tao, post (Mathstodon, 8 September 2026), checked 15 October 2026
• A Severe Misalignment of AI in Mathematics (What's new, 11 September 2026), checked 15 October 2026
• A Severe Misalignment of AI in Mathematics (mathandai.org), checked 15 October 2026
• A Severe Misalignment of AI in Mathematics (Zenodo, 11 September 2026), checked 15 October 2026
• Gowers, Why I didn't sign the Fields medallists' letter (guest post, What's new, 17 September 2026), checked 15 October 2026
• Learning more about Claude's mathematical capabilities (Anthropic, 10 August 2026, updated 13 August 2026), checked 15 October 2026
• Alpöge & Furman, More than two thirds of the zeta zeros are simple and on the critical line (arXiv:2608.13637), checked 15 October 2026
• Lamzouri, A new proof that more than 2/3 of the zeros of the Riemann zeta function are simple and on the critical line (arXiv:2609.02882), checked 15 October 2026
• Sharing AI progress in mathematics (OpenAI, 6 October 2026), checked 15 October 2026 (Internet Archive copy of 12 October 2026; the live page blocked automated access)
• openai/math, README and history (GitHub), checked 15 October 2026
• The Quasi-Riemann Hypothesis: A Zero-Free Half-Plane ℜs > 7/8 (OpenAI, 30 September 2026), checked 15 October 2026
• The Quasi-Riemann Hypothesis, alternate 11/12 proof (OpenAI, 5 October 2026), checked 15 October 2026
• Calegari, A Brief Digest of Some New OpenAI Results (Persiflage, 8 October 2026), checked 15 October 2026
• Liu, Improved zero-free half-planes for the quasi-Riemann hypothesis (arXiv:2610.12234), checked 15 October 2026
• The rational Hodge conjecture for CM abelian varieties (OpenAI, 6 October 2026), checked 15 October 2026
• Weil classes and Hodge classes on abelian powers (OpenAI, 6 October 2026), checked 15 October 2026
• Algebraic Kuga–Satake correspondences and Hodge conjectures on a K3 quadratic locus (OpenAI, 30 September 2026), checked 15 October 2026
• Abelian covers, Gale correspondences, and the Hodge conjecture for powers (OpenAI, 6 October 2026), checked 15 October 2026
• Withdrawal notice: Algebraicity of Weil classes on split abelian eightfolds (OpenAI), checked 15 October 2026
• Withdrawal notice: Algebraicity of Kuga-Satake Correspondences for K3 Surfaces (OpenAI), checked 15 October 2026
• Withdrawal notice: The rational Hodge conjecture for products of K3 surfaces (OpenAI), checked 15 October 2026
• Totaro, On the Hodge conjecture (guest post, What's new, 11 September 2026), checked 15 October 2026
• Exact Birch–Swinnerton-Dyer Formula from Low Selmer Corank (OpenAI, 7 October 2026), checked 15 October 2026
• Burungale, BSD and the p-converse (guest post, Persiflage, 15 October 2026), checked 15 October 2026
• Fortnow, Respect the P v NP Problem (Computational Complexity, 10 June 2026), checked 15 October 2026
• Anthropic News (Anthropic), checked 15 October 2026
• Anthropic Research (Anthropic), checked 15 October 2026
• Sitemap (Anthropic), checked 15 October 2026
• Tao, post (Mathstodon, 5 September 2026), checked 15 October 2026
• AI contributions to Erdős problems (teorth/erdosproblems wiki, GitHub), checked 15 October 2026
• Bloom, reply to Kevin Weil (X, 17 October 2025), checked 15 October 2026 (read through the FixTweet API)
• Weil, reply (X, 17 October 2025), checked 15 October 2026 (read through the FixTweet API)
• An OpenAI model has disproved a central conjecture in discrete geometry (OpenAI, 20 May 2026), checked 15 October 2026 (Internet Archive copy of 11 October 2026; the live page blocked automated access)
• Tsoukalas et al., Advancing Mathematics Research with AI-Driven Formal Proof Search (arXiv:2605.22763), checked 15 October 2026
• google-deepmind/alphaproof-nexus-results (GitHub), checked 15 October 2026
• Bloom, Changes to the Erdős problems web site (guest post, What's new, 6 October 2026), checked 15 October 2026