Explainer19 min read
Is AI using up math's open problems? Terence Tao's warning after OpenAI's 722 papers
Terence Tao warns that AI is mining math's best open problems as a non-renewable resource. What he said, why some mathematicians now withhold problems, and how to share one.
A month ago, on 6 October 2026, OpenAI put 722 AI-generated mathematics manuscripts on GitHub at once. Its README groups them into 372 "families" of results and says the unreleased internal model behind them "was posed approximately 4,000 problems".1 Within days, mathematicians were writing about problems they had worked on for years, some since their PhDs, appearing in the list with claimed solutions.
Terence Tao's warning came before the release. In a run of posts on Mathstodon from early September, he argued that good open problems, the ones worth years of work, are scarce, and that "the collection of good, fruitful open problems is now being mined in a non-renewable fashion".2 He added that the incentives "may now be pointing in the direction of no longer sharing any promising research directions with the broader community". On 6 October he wrote that this was already happening: "promising open directions are now being withheld from the public in fear that this will cause their own research to be 'scooped'".3
That matters beyond mathematics. Open problems are how a field trains its students and shows newcomers where the interesting ground is. Stop posting them and that is lost; keep posting them without new norms and they may be answered by sweeps that nobody learns from.
Below: what OpenAI released, what Tao said and when, whether AI is really "using up" open problems (with a weekly count from Papex's listing of AI-assisted claims), why some mathematicians now keep problems to themselves, what has been proposed instead, and how to post an open problem today so that it keeps its value. Every source was checked on 5 November 2026.
What did OpenAI release on 6 October?#
A GitHub repository, openai/math. Its README at the first commit said: "The current catalogue contains 722 manuscripts organized into 372 families."1 A family "groups related papers, which may include a principal result, companion arguments, consequences, or alternative proofs". So 372 is not a count of solved problems, although some reports described it that way: Retraction Watch wrote of "progress in solving 372 math problems".4
The README also says how the catalogue was chosen from those 4,000: "Aggregating the output into result families and manuscripts and requiring an appropriate level of significance led to the catalog outlined above." It does not say how many the model failed on; some may have been solved but judged not significant enough to include.
| What | Figure | Where it is stated |
|---|---|---|
| Manuscripts at release, 6 October | 722 | README, first commit1 |
| Result families | 372 | README, first commit |
| Problems posed to the model | About 4,000 | README |
| Average compute per result | About three hours of ChatGPT Pro thinking | README |
| Withdrawn, 7 October | 3, after a sign error | Repository history5 |
| Revised, 7 October | 14, plus 13 updated only to cite revised companions | Repository history |
| Top-line results formalized in Lean | 300 of 719, about 42% (7 October entry) | Repository history |
| Catalogue today | 721 manuscripts in 373 families, after two were added on 26 October | README, current6 |
| Funding promised | $5 million to a Simons Foundation initiative (15 October update) | OpenAI's announcement7 |
The repository's history file records the first changes: three Hodge-conjecture manuscripts withdrawn because "a sign error invalidates a stabilization-trace cancellation argument", and 14 others revised "with proof repairs, corrected statements, clearer hypotheses and dependencies".5 We explained the withdrawals in Why OpenAI withdrew three Hodge conjecture papers. An OpenAI spokesperson told Retraction Watch that roughly 50% of the results were released unconfirmed.4 The current README adds a line the first one did not have: "We defer to the math community completely on matters of credit, precedence, and concurrent work."6
OpenAI's announcement says it consulted "the independent Advisory Group on Mathematics and Artificial Intelligence at the Institute for Advanced Study" (AGMAI) and has "drawn on their advice and public recommendations".7 Those recommendations, dated 29 September, open with a request that the announcement does not mention: "we ask them to stop testing advanced mathematical problems on proprietary models."8 On release day, AGMAI, nine mathematicians who take no payment for the work, wrote that its advisory role "should not be interpreted as a judgment of the impact of these results or an endorsement of the process by which OpenAI obtained them."9
What exactly did Terence Tao say about open problems?#
Tao, a Fields medalist at UCLA, made the argument in a series of Mathstodon threads in September and restated it in October. The quotations here are from his own posts. His website also keeps a "living summary" of his views, which he calls "AI-maintained";10 we quote the posts it summarizes instead.
| Date | Where | What he said |
|---|---|---|
| 2 September | Mathstodon | Like pre-atomic steel, open problems from before the AI era have become "something resembling a non-renewable resource"11 |
| 3 September | Mathstodon | The production of answers and the production of insight have become "negatively correlated"; three AI companies raced to improve Julia Stadlmann's new prime-gap bound12 |
| 5 September | Mathstodon | AI companies should compete to "be the first to announce a new mathematical insight", not a solution13 |
| 7 September | Mathstodon | Open problems in pure mathematics "are being mined as a non-renewable resource"14 |
| 8 September | Mathstodon | Good problems are scarce though problems are infinite; the incentives point toward no longer sharing; some problems should require careful analysis2 |
| 6 October | Mathstodon | Promising directions "are now being withheld from the public"; solutions are "being harvested at large scale in an unsustainable fashion"3 |
| 8 October | Proofs and Prompts | He is "horrified" that years of patient research by students and postdocs are "casually disrupted or destroyed"15 |
| 9 October | Caltech lecture, Math 2.0 | "the future frontiers of mathematics will always continue to expand", but blind optimization of problem solving is "now actively harmful"16 |
Read together, the argument has four steps.
Good problems are scarce, even though problems are not. Tao's analogy: "a country or region can suffer a critical shortage of drinking water while simultaneously being surrounded by a massive ocean."2 Anyone can ask for the 10^10^10th digit of pi, but most such questions "show no particular propensity to reveal any further insights or connections to other questions". Deciding which questions are worth a career is, he writes, "a lengthy, deliberate, and subjective process", and it depends on knowing a field's "difficulty landscape": what is easy, what is hard but reachable, and what is out of range.
Solving is irreversible. His 2 September thread compares a known answer to a movie spoiler.11 On 6 October he put it plainly: "a problem that has been 'solved' cannot be somehow reverted to become 'unsolved', and even the mere knowledge that a solution exists 'contaminates' efforts by both humans and AI to find alternate routes to the problem that reveal additional insights."3
The landscape has been flattened without a map. New techniques have always made problems easier, but they usually open a new boundary to explore. This time, he writes, there are "no clear frontiers that are separating the 'AI-feasible' problems from the 'AI-hard' problems", a situation "compounded by the refusal of AI companies to disclose their negative results, or reveal the process towards obtaining their solutions."2
So the scarce resource is the promising problem itself. "We have now seen 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."2 If people respond by keeping their directions private, that "would reverse centuries of traditions of open science and do serious long-term damage to the future of the field."
He does not argue against AI as such. "A priori, there is no reason that AI use necessarily has to perform this tradeoff," he wrote on 3 September, pointing to AI literature search as a use that adds insight.12 His objection is to "pointing a powerful AI tool at the task of answering a problem X, unguided by any human expert in the field X resides in".
Is AI really "using up" open problems?#
In one sense, no, and Tao says so. His Caltech slides of 9 October: "Despite the impression given by press releases and social media, most of the problems at the current frontier of mathematics remain unsolved, even with massive computational expenditure."16 OpenAI's own numbers point the same way: about 4,000 problems posed, 372 families released.1
In another sense, yes. The stock that matters is the set of problems a community has already identified, explained and agreed are worth working on, and much of that stock was hit at once. Hugo Duminil-Copin, a Fields medalist, wrote in a collection of reactions published on 8 October: "Not a single one of the major open problems I have publicly mentioned throughout my career (whether in a talk, a lecture, an article, or even a grant proposal) was left untouched by the announcement."15 In the same collection, Tristan Humbert wrote that Katok's entropy conjecture, "the subject of my PhD", had been claimed that morning, and that he spent the morning rewriting his research plan while applying for postdocs.
Frank Calegari, in a guest post on Tao's blog on 1 November, answered that "when we talk about the central problems in any area, we are merely discussing the most natural boundaries of our understanding", and that crossing them is "the first step to finding new playgrounds to explore".17 His suggestion is to make new problems on purpose: he encourages senior mathematicians "to take up the work of creating future problems and exploring new ideas rather than simply using AI to answer existing questions." Tao made a related point on 7 September about the Equational Theories Project, which "was deliberately chosen to open up a new source of problems to study, rather than to exhaustively mine out an existing productive vein of problems."14
What Papex's own listing shows
Papex lists AI-assisted claims on named open problems at /ai-claims, each as its source states it and unchecked by us. As listed on papex.org/ai-claims on 5 November 2026, there are 375 claims on 312 problems. Of these, 232 claims on 198 problems are dated 6 October to 4 November, the 30 days before this post. Three are withdrawn: the three Hodge papers.
| Week starting (Monday) | AI-assisted claims listed, by the claim's own date |
|---|---|
| 31 August | 16 |
| 7 September | 5 |
| 14 September | 9 |
| 21 September | 5 |
| 28 September | 16 |
| 5 October | 135 |
| 12 October | 6 |
| 19 October | 7 |
| 26 October | 39 |
| 2 November (to 4 November) | 46 |
The week of 5 October is almost all OpenAI: 125 of the 127 claims dated 6 October come from the openai/math repository. Those are only the release's claims that address a problem in our catalogue, not all 372 families. The rise since late October has a different source. Of the 105 claims dated 7 October to 4 November, 79 were posted to Hexagon and 19 to arXiv. Hexagon, announced on Tao's blog on 6 October, is a repository for the mathematical sciences and theoretical computer science that "allows submissions entirely generated by LLMs and even where the submitters claim no human understanding".18 The 79 Hexagon entries come mostly from individual researchers and small teams. In their AI declarations, 36 describe the work as primarily AI-generated and 41 as a mix of human-written and AI-generated; 49 name a model, most often a version of Claude or GPT.
Two cautions. These are claims, not results: each problem's status stays its source's, and Papex has not checked any of the claims. And the counts measure what we list as well as what was posted: we add problems and sources over time, and since 31 October we have read arXiv, Hexagon and the openai/math repository every day, so recent weeks are covered more fully than earlier ones.
One problem shows Tao's point in miniature. Julia Stadlmann's preprint lowering the bounded-gaps bound from 246 to 240 was posted to arXiv in August, written, in Tao's description, "with the assistance of traditional numerical computation, but not modern AI tools".19 The twin prime conjecture page on Papex lists three AI-assisted claims dated 3 and 4 September that improve on her bound, to 186, 212 and 182, and a fourth, posted to Hexagon on 4 November, that improves one of her exponents. Tao's comment at the time was that he was "very glad that Stadlmann was able to complete her analysis just in time before the problem became contaminated".12
Why would mathematicians keep problems to themselves?#
Because a problem stated in public can now be pasted into a model by anyone, and some researchers have watched that happen to their own work. The evidence so far is first-hand accounts, not a survey. No one has measured how many problems are being withheld.
- Tao, 6 October: promising open directions "are now being withheld from the public in fear that this will cause their own research to be 'scooped'".3
- Antonio Auffinger, 22 September, in a guest post on Tao's blog: "In the past few weeks, I have had colleagues reach out for advice and tell me they will no longer post on arXiv." He adds: "I am also part of the problem, as I have started advising my students to be extra careful when sharing work in progress."20
- Thomas Bloom, 6 October, on erdosproblems.com, which he runs: "many have stopped thinking about Erdős problems believing that they cannot compete with AI."21 We covered his site's changes in How many Erdős problems has AI solved?
- Tao, on Alpöge and Buckmaster's blowup result for the Euler equations in September: "they had to release far earlier than planned due to external events".22
- Dana Moshkovitz of UT Austin, who had worked on one of the claimed problems for over a decade, on NPR's Short Wave on 4 November: "this was a life-- a life plan for me, right? And now it's gone".23
The cost falls hardest on students, because open problems are how they are trained. The declaration "A Severe Misalignment of AI in Mathematics", signed by Fields medalists including Tao, says: "For students we often suggest problems with the core intention of developing skills making them well-positioned for advances in research and elsewhere."24 Duminil-Copin asked in August: "How can they build mathematical abilities when the most accessible problems may fall at any moment under the battering ram of compulsive users of AI models?"25
Withholding has its own cost. Bryna Kra, among the 8 October reactions: "The mathematics community has mostly been collaborative: we share questions, talk about work in progress, and give others ideas on how to approach a problem."15 Auffinger's worry "is that this unselfish openness will become a thing of the past."20
Keeping answers back can also be deliberate and useful. In the first stage of the SAIR/LMFDB inverse Galois challenge that Tao co-organizes, contestants did not share their polynomials, which slowed the solving but "allowed us to create a valuable map" of how hard each case was. Releasing them all for the collaborative second stage "permanently degraded the ability to crowdsource this type of difficulty map in the future", a trade the organizers made knowingly.11 An unsolved status can be information in itself.
What has been proposed instead?#
None of these proposals binds anyone. AGMAI itself says: "we do not have decision making power at any AI company".9 But together they sketch the norms people are trying to build.
| Proposal | Who, when | What it changes |
|---|---|---|
| Designate problems that call for "a careful analysis", where a raw answer counts for little2 | Tao, 8 September | What counts as a contribution on that problem |
| Keep some classes of problems off-limits to automated solvers, while opening others to them11 | Tao, 2 September | Which problems are fair targets |
| Compete to be first to a new insight, not a new solution13 | Tao, 5 September | What labs race for |
| "Open exposition problems": explain results whose proofs are opaque16 | Tao, Caltech slides, 9 October | Gives AI a target that adds understanding |
| Stop testing advanced problems on proprietary models; say how problems were chosen and how many failed; post in repositories no lab controls8 | AGMAI, 29 September | How labs run and release their work |
| No problem statuses, no ownership language, more weight on exposition21 | Bloom, erdosproblems.com, 6 October | Removes the open-to-solved scoreboard |
| Find a mathematical counterpart to genomics' Bermuda Principles and Fort Lauderdale Agreement, which paired rapid release with recognition20 | Auffinger, 22 September | How credit follows early sharing |
| Senior mathematicians create new problems17 | Calegari, 1 November | Replenishes the supply |
The first is the one most often reported. Tao wrote that "we can still designate many classes of problems as being desirous of a careful analysis that not only solves the problem, but identifies insights from the solution process", and for which "raw solutions without such analysis would be of negligible or even negative value".2 He compares it to a food drive that no longer accepts every donation that is merely edible, but sets standards for what is actually sought. Decrypt summarized the idea as marking problems "analysis-required";26 the label is Decrypt's, not Tao's.
How can you share an open problem now without losing its value?#
There is no standard yet. This sequence is our synthesis of the proposals above, not a rule from any of them. It cannot stop anyone from running a model on your problem, but it says what you are asking for, puts a date on it and makes the answers comparable.
- State it exactly, and say why it matters. Give the statement with definitions, the known partial results with references, and what partial progress would teach. Tao's questions make a good outline: "What are the main difficulties to overcome to resolve X?", "Why are existing techniques insufficient to solve the problem by itself?", "What are some natural related or followup questions".12 If you can, add a formal statement in Lean, so that a claimed formal proof can be checked against what you meant. Bloom asks for formalizations to be registered on Palomar because it "makes it easy to check the formal statement correctly matches the problem statement".21
- Say what kind of attempt you want. Open to AI-assisted attempts; set aside for a student or a seminar until a date; or posed as an exposition problem. Tao's protected problems rest on this kind of social signal, which he compares to the social pressure that discourages spoiling films.11
- Say what a good answer must contain. For example: the key idea, why earlier methods failed, and which nearby questions change. That is the careful analysis Tao describes. A bare answer can still be recorded, as a claim.
- Ask attempts to disclose AI use. AGMAI asks labs to "make public the name of the model, the prompts used, a (summarized) chain of thought, the time taken, and the estimated cost of computation";8 a lighter version suits any attempt. Bloom asks that papers acknowledge their sources and say honestly how AI was used. Our guide to writing an AI disclosure statement has templates.
- Put a date on it, somewhere fixed. A preprint, a problem list, your own page with an archived copy, or a signed and timestamped record. Say how you would like the problem cited. What each option proves is in How to protect a research idea from being scooped.
- Keep a public log of attempts, failures included. Date, who, which tools, and the outcome, including "this approach fails because". Tao's slides say the lessons from attempts, "whether they succeed, fail, or achieve partial progress", are often worth more than the answer.16 A failure log is also a piece of the difficulty map that, in Tao's account, the labs do not publish. We looked at why negative results go missing in Do AI research agents hide negative results?
Put together, a problem post might read like this (placeholders in brackets):
Problem. [Exact statement, with a definition or reference for each term.] Posted [date] by [name] at [link]. Please cite as [form].
Why it matters. [What a solution would connect to, what fails with known methods, references.]
What counts as progress. [Special cases or bounds that would already be interesting.]
Attempts. [AI-assisted attempts are welcome.] or [Please do not run automated solvers on this before [date]; it is set aside for a student project.]
A good answer explains the key idea and why earlier approaches failed. A formal proof is welcome; please compare its formal statement with the one above.
Disclosure. Name the AI tools and versions used, and say what they did.
Log. [Link to a dated list of attempts, including the ones that failed.]
Where does Papex fit?#
Papex keeps a record of how research is made, and two parts of this post map onto it. A conjecture can be written as a Papex Hypothesis, whose fields include the claim, why it matters and what would show it wrong. The person accountable signs one exact version, and a salted fingerprint of that version is timestamped with OpenTimestamps and anchored in Bitcoin; anyone can check the signer, version and date at /verify without an account. An attempt can be signed as a Discovery or Publication that says how AI was involved, as the authors state it, and later versions stay linked to earlier ones. Problem pages, such as Navier–Stokes, show a problem's status as a named source gives it, the AI-assisted claims we list at /ai-claims, and public Papex records linked to the problem.
A Papex record shows who signed which version, when, and what they said the tools did. It is not proof that the mathematics is right, it is not peer review, and the model and tool names in it are self-reported.
Sources#
- openai/math, README at the first commit (OpenAI, 6 October 2026), checked 5 November 2026 a b c d
- Terence Tao, thread on open problems as drinking water beside an ocean (Mathstodon, 8 September 2026), checked 5 November 2026 a b c d e f g
- Terence Tao, thread on "Math 1.0" and "Math 2.0" (Mathstodon, 6 October 2026), checked 5 November 2026 a b c d
- OpenAI withdraws three preprints a day after releasing 722 manuscripts on unsolved math problems (Retraction Watch, 8 October 2026), checked 5 November 2026 a b
- openai/math, history.md (OpenAI, entries from 7 to 29 October 2026), checked 5 November 2026 a b
- openai/math, README, current version (OpenAI, last changed 26 October 2026), checked 5 November 2026 a b
- Sharing AI progress in mathematics (OpenAI, 6 October 2026, updated 15 October 2026), checked 5 November 2026 through the Internet Archive copy of 29 October 2026, because openai.com blocked automated reading a b
- Responsible Release of AI-Generated Mathematics (Advisory Group on Mathematics and Artificial Intelligence at IAS, 29 September 2026), checked 5 November 2026 a b c
- AGMAI statements, including About AGMAI (22 September 2026) and On OpenAI's Release of Mathematical Results (6 October 2026), checked 5 November 2026 a b
- Terence Tao, Math 2.0 (Terence Tao's blog, 10 October 2026), checked 5 November 2026 ↩
- Terence Tao, thread on open problems as a non-renewable resource (Mathstodon, 2 September 2026), checked 5 November 2026 a b c d e
- Terence Tao, thread on answers versus insight (Mathstodon, 3 September 2026), checked 5 November 2026 a b c d
- Terence Tao, post proposing a competition for insight (Mathstodon, 5 September 2026), checked 5 November 2026 a b
- Terence Tao, thread on the Equational Theories Project (Mathstodon, 7 September 2026), checked 5 November 2026 a b
- 100+ reactions to 100+ solutions (Proofs and Prompts, 8 October 2026, reactions added to 19 October), checked 5 November 2026 a b c
- Terence Tao, Math 2.0, slides of the Caltech public lecture (9 October 2026), checked 5 November 2026 a b c d
- Frank Calegari, Mathematics has changed. Let's act like it (guest post on Terence Tao's blog, 1 November 2026), checked 5 November 2026 a b
- Ben Antieau, Hexagon (guest post on Terence Tao's blog, 6 October 2026), checked 5 November 2026 ↩
- Terence Tao, post on Julia Stadlmann's prime-gap preprint (Mathstodon, 1 September 2026), checked 5 November 2026 ↩
- Antonio Auffinger, Open problems, open mathematics (guest post on Terence Tao's blog, 22 September 2026), checked 5 November 2026 a b c
- Thomas Bloom, Changes to the Erdős problems web site (guest post on Terence Tao's blog, 6 October 2026), checked 5 November 2026 a b c
- Terence Tao, post on Alpöge and Buckmaster's blowup result (Mathstodon, 7 September 2026), checked 5 November 2026 ↩
- OpenAI published tranches of math proofs. Is it hurting the field? (NPR Short Wave, transcript, 4 November 2026), checked 5 November 2026 ↩
- A Severe Misalignment of AI in Mathematics (declaration, 11 September 2026), checked 5 November 2026 ↩
- Hugo Duminil-Copin, Care for a little more AI? (Proofs and Prompts, 30 August 2026), checked 5 November 2026 ↩
- AI Is Solving Math's Best Problems Faster Than They Can Be Replaced, Terence Tao Warns (Decrypt, 9 September 2026), checked 5 November 2026 ↩