How many Erdős problems has AI solved? October 2026

No one keeps a current count. The two public records that did have both stopped. A wiki on AI contributions to Erdős problems, started by Terence Tao, froze on 30 June 2026: by our count of its tables, 69 problems by then had at least one entry in which an AI system played the main role and the outcome was marked a full solution, a figure the wiki itself warns against reading as a score. erdosproblems.com, Thomas Bloom's database of 1,221 problems, stopped showing which problems are solved on 6 October 2026. Its last count, 586 solved (48%), covered human and AI work together and never separated the two. Since June, Google DeepMind has published AlphaProof Nexus in Science, with nine solved entries out of 353 attempted, and OpenAI has released manuscripts with claims on 25 Erdős problems that Bloom says "should be read as 'claims'". Much of the first wave of "AI solved an Erdős problem" was literature search: AI found papers that had already answered problems listed as open.

Below: the counts and where they come from, what AlphaProof Nexus and OpenAI's unit distance result show, how much was literature search, the other notable claims, why the counting stopped, how mathematicians now ask for AI help to be credited, and six questions for the next headline. Every page was checked on 21 October 2026; the sources note where we used an archived copy, and the one count we made ourselves says how it was made.

How many Erdős problems are there, and how many are solved?#

erdosproblems.com lists 1,221. Its last published figure, on 5 October 2026, was 586 solved (48%). Since 6 October the site shows no statuses at all.

The site is the main online list of problems posed by Paul Erdős, run by Thomas Bloom of the University of Manchester. Until October its home page gave a running total, and Internet Archive copies show how it grew:

"Solved" here meant that the site had changed a problem's status, to proved, disproved or otherwise resolved, sometimes long after the fact. The site's own list of status changes said it "is just when their status was changed on this site, and has no meaning beyond that". For a sense of the earlier pace, Quanta Magazine reports that in 2024 and the first eight months of 2025, "the statuses of 111 problems on the list were changed from 'open' to 'solved'".

A community database on GitHub, teorth/erdosproblems, still publishes totals. On 20 October 2026 it gave 579 solved (336 proved, 139 disproved and 101 "otherwise solved") and 593 that "appear to be completely open", with the rest in smaller categories. It calls these statuses "an unofficial crowdsourced classification", and since 6 October keeps the totals off its front page "so that a visitor arriving at the repository is not shown a tally of solved problems by default". Neither source explains the gap between 586 and 579.

How many Erdős problems has AI solved?#

There is no current figure. The most detailed record, the wiki "AI contributions to Erdős problems", opens with: "The wiki is no longer updated. The latest data is as of Jun 30, 2026."

Tao created the page on 27 December 2025; by the freeze, most of its 1,096 edits were by Nat Sothanaphan. It sorted each AI contribution by the role the AI played and by what was already in the literature. The definitions below are the wiki's; the counts are ours.

How we counted: in the frozen page, the distinct problem numbers in rows whose outcome starts with the wiki's green mark and "Full solution" ("Full solution found" in 2(a)). A problem can sit in more than one section, so the first four rows add up to 72 entries for 69 problems. The page also logs partial results, unverified claims and incorrect work: section 1(a) alone has 10 rows marked incorrect.

The wiki asks readers not to do what this table invites. Its first disclaimer is "This page is not a benchmark", and it advises "against direct comparison of raw counts of problems solved by different methodologies, as this could be comparing apples to oranges". Tao added a summary line in January: "The evaluation of AI contributions to these problems is actually incredibly complex and subtle, and cannot be reduced to a simple leaderboard or a numerical metric."

Since the freeze, no source we found sorts AI contributions this way. erdosproblems.ai, launched in October by the company Plasma AI, marks each problem open, claimed or solved (on 21 October, 494 open, 110 claimed and 617 solved) and asks people submitting proofs to list "the contributors and tools involved". It says it is "operated independently and does not imply his endorsement", meaning Bloom's. Its home page gives no count of AI results.

What did AlphaProof Nexus solve?#

Nine entries out of 353 attempted, each with a Lean proof. The paper, "Advancing mathematics research with AI-driven formal proof search" by George Tsoukalas and 20 co-authors at Google DeepMind, Google and Aarhus University, appeared in Science on 8 October 2026, after a preprint in May. Its abstract: "We built an artificial intelligence agent for formal proof search that autonomously resolved nine of 353 open Erdős problems".

How the 353 were chosen. Not by hand. The team ran the agent on "all Lean statements of Erdős problems available in the Formal Conjectures repository … as of early February 2026 – 353 problems in total", and notes that "this process has a bias toward problems amenable to formalization in Lean".

What "solved" means. The agent had to produce a complete Lean proof, one with no gaps left, of the formal statement. Then, the paper says, "experts on our team validated that the Lean statement faithfully captured the original conjecture". For two problems the statement itself changed: the word "density" was amended to "lower density" and "upper density" after the agent found proofs that used it in a different sense. People wrote the proofs in ordinary mathematical language: the paper's statement of contributions says six team members "wrote the natural language proofs, with HM providing agent-generated drafts".

The nine. The paper's Table 1 lists them by erdosproblems.com number. Some are parts or variants of a problem:

A simple agent did it too. "Remarkably, the basic agent solved all 9 problems, though at a higher cost on the harder problems", the preprint says; Science's abstract keeps the point: "Even a basic agent … replicated the Erdős successes." The June version of the preprint also tried two coding agents on the nine: "Codex solved 7/9 problems, failing to solve Problems #152 and #125 within 12 hours. We could not get Claude Code to solve any of the problems." We read the arXiv version of 8 June; the full Science text was not available to us, and its abstract no longer gives the preprint's cost of "a few hundred dollars" per problem. The preprint adds that "identifying tractable problems was itself a significant computational investment".

Bloom, speaking to Science News, called the results "not really at the top level of importance" and said Google DeepMind was "trying to be more responsible with the science". The same issue of Science carries a Perspective by Jeremy Avigad and Matthew Ballard titled "AI for research mathematics has arrived".

Did AI solve the Erdős unit distance problem?#

It disproved Erdős's conjecture, and mathematicians outside OpenAI have checked and refined the proof. This is erdosproblems.com's problem #90.

Erdős asked how many pairs among n points in the plane can be exactly distance 1 apart, and conjectured in 1946 that the number grows only slightly faster than n. On 20 May 2026 OpenAI wrote: "An internal OpenAI model has disproved this longstanding conjecture, providing an infinite family of examples that yield a polynomial improvement." The construction gives, for infinitely many n, sets of n points with at least n^(1+δ) unit-distance pairs for a fixed δ > 0, and Will Sawin of Princeton showed the same day that more than n^1.014 is possible. OpenAI says the proof came from "a new general-purpose reasoning model", which it does not name.

Nine mathematicians, among them Noga Alon, Bloom and Tim Gowers, posted a companion paper the same day: "a short, digested, human-verified version" whose argument "relies crucially on ideas that may, at least in retrospect, be attributed to Ellenberg-Venkatesh, Golod-Shafarevich, and Hajir-Maire-Ramakrishna". Melanie Matchett Wood, one of the nine, told Scientific American: "We recognized that there were very similar ideas in the literature that weren't credited. If a human had been familiar with those results and not credited them, then that would be professional malpractice." Gowers, in a statement on OpenAI's page, wrote that if a human had submitted it to the Annals of Mathematics, "I would have recommended acceptance without any hesitation". Daniel Litt told the magazine: "This is the unique interesting result produced autonomously by AI so far."

Six days later Levent Alpöge, who works at Anthropic, posted that he had checked "whether mythos is able to solve the erdos unit distance problem, aka erdos problem #90. the answer is: yea", with a write-up on Anthropic's site that names no author or model. A participant on the problem's erdosproblems.com forum noted that it covers only the weaker form of the conjecture, with the bound n^(1+O(1/log log n)) rather than n^(1+o(1)); Bloom replied that the method would give the stronger result with a better choice of parameters, adding that he was not "vouching for its correctness".

The problem's page shows the site's new style. In May it read "This was disproved by an internal model at OpenAI"; since mid-October it reads "This has been disproved", followed by the result and links to the papers.

Was most of it literature search?#

At first, yes. In October 2025 several contributors to erdosproblems.com began using AI research tools to look for literature on problems marked open. On 16 October 2025 Tao counted six problems whose status had been "upgraded from 'open' to 'solved' by this AI-assisted approach".

The next day Kevin Weil, then at OpenAI, posted: "GPT-5 just found solutions to 10 (!) previously unsolved Erdös problems, and made progress on 11 others. These have all been open for decades." Bloom replied: "this is a dramatic misrepresentation. GPT-5 found references, which solved these problems, that I personally was unaware of. The 'open' status only means I personally am unaware of a paper which solves it." Weil deleted his post, and Demis Hassabis of Google DeepMind replied to a similar, also deleted, post by OpenAI's Sébastien Bubeck: "this is embarrassing". Bubeck wrote: "Only solutions in the literature were found that's it, and I find this very accelerating because I know how hard it is to search the literature."

Bloom later summed up the shift: "At first this was as a super-powered literature search, turning up many previously unknown solutions and papers. In the last month we have started to see actual solutions generated by AI." That was in January 2026. Tao had explained why the two blur: the problems AI could pick off first are "precisely the category of nominally open problems that are most likely to have been solved in the literature". On Christmas Day 2025 a claimed autonomous AI solution of problem #333 turned out, within hours, to be in a 1977 paper by Erdős himself. A Google DeepMind case study of January 2026 reported 13 problems marked open: "5 through seemingly novel autonomous solutions, and 8 through identification of previous solutions in the existing literature", concluding that "the 'Open' status of the problems was through obscurity rather than difficulty".

Which other Erdős problems has AI solved?#

The best-known claims of 2026, as their sources describe them:

On the October release, Bloom's overview says the papers are "at a glance, very poorly written, in the usual AI fashion" and that he expects most of them to be "(a) correct yet (b) capable of being substantially simplified and improved given expert attention". The repository's own README says: "Some of the unformalized results could have issues." On 7 October OpenAI withdrew three manuscripts unrelated to Erdős problems and revised 14 others.

Why did the counting stop?#

Because the counts had become the goal. On 6 October Bloom announced four changes: a freeze on new problem comments and proof claims, no statuses, no "credit-giving language for a result (human or AI)", and more emphasis on expositions. His reason: "The main way that people publicly interact with the site now is to advertise their AI-generated proofs, often without any attempt to explain them, but as a way to record a (increasingly meaningless) priority claim."

Removing statuses, he wrote, is meant "to disincentivise people who are simply glory-chasing and copying problems into their AI to get an OPEN->SOLVED dopamine hit", and "prevents people drawing wrong conclusions from the 'rate of solved problems'". Results are still recorded, in a new form: "instead of saying 'Bloom proved that x > y', I will write 'It is known that x > y -- an explanation of the proof is provided by Bloom [link]'." On places that collect AI proofs he wrote: "I personally don't want to manage one. Just as one does not open a restaurant in an abattoir, it is important that there be a separation between such repositories and a site which aims to promote the actual questions".

The wiki gives no reason for its freeze. Its main maintainer, Sothanaphan, wrote in July that "the format was implicitly constraining what counted as a contribution. In particular, proof generation was given priority over proof verification and proof digestion, which I viewed as no less important."

Money is now going into the checking. On 15 October the Simons Foundation announced that it, Anthropic and OpenAI "will commit $15 million in combined funding and resources" for work that helps researchers "evaluate recent AI-assisted results, learn and use new tools, share perspectives and shape collective standards for AI use". OpenAI and Anthropic each say they are giving $5 million. A related call, Targeted Grants to Math+AI Institutes, closes on 1 December 2026.

How should AI help on a proof be credited?#

Mathematicians are still deciding, but a few rules are written down.

• Disclose the tools, keep the credit with people. The Leiden Declaration of June 2026, which its site says is endorsed by the International Mathematical Union, asks authors to "Transparently disclose the use of automated tools, including large language models" and states: "Credit and responsibility continue to belong to humans within the mathematical community and should not be given to automated systems."
• Disclose how AI was used, or lose a place on the list. Bloom's October post: "Papers should acknowledge their sources and honestly disclose how AI was use[d]; where there is evidence of plagiarism or misrepresentation about AI use, I may decline to feature the submission, even if the proof is correct."
• Say how a Lean proof was made. The Palomar registry of Lean-verified results asks each entry for a formalization.yaml file whose required automation field takes one of "manual | copilot | agent | autonomous | other".
• Attribute the result to the system that produced it. OpenAI takes this line for its own results: "claiming human authorship for a proof generated entirely by an AI system would misrepresent both the system's contribution and the nature of genuine human intellectual work".

Tao has gone further, on priority itself. On 6 August he proposed that "we should no longer assign priority to the first to release a preprint, or even a formal proof certificate, as this devolves to a race to who can prompt their AI the fastest", but to "the first author(s) who can present the results clearly". In follow-up posts he split a proof into "a generation artifact (e.g., AI chat logs), a verification artifact (e.g., Lean code), an exposition artifact (e.g., a recorded talk), and a publication artifact", and imagined researchers keeping "a private repository containing partial progress … with timestamps recording the date each step of partial progress was achieved", made public once the work is ready. He also floated announcing work in progress with "encrypted hashes", adding: "I am not sure whether this would be a desirable development".

How to read the next "AI solved an Erdős problem" headline#

Six questions, drawn from the cases above. For claims on bigger problems, see Has AI solved a Millennium Prize Problem?

1. Which number, which part? Many problems have parts and variants: AlphaProof Nexus's nine include two parts of #12, two of #741 and a variant of #26 "not posed by Erdős himself".
2. Was it already known? Check the problem's page and references. Literature search turned up the answers to many problems listed as open, and #333 was in a 1977 paper by Erdős.
3. Who wrote the Lean statement? A Lean proof is only as good as the statement it proves. The wiki's advice: "it is best if the statement of the result is formalized by a human or a third party rather than by the AI doing the proof".
4. Is there a proof a person can follow? Bloom says he will try to link correct Lean formalizations verified on Palomar, but proofs "poorly explained, and not accompanied by a formalisation" he is "unlikely to update the site with".
5. What did the people do? Choosing problems, prompting, fixing statements and writing the proof up all count; in AlphaProof Nexus, team members wrote the ordinary-language proofs, helped by the agent's drafts.
6. Who outside the lab has checked it? Compare the unit distance result, digested by nine named mathematicians in a joint paper, with the October release, which Bloom lists as claims.

Where Papex fits#

Papex does not count Erdős problems, does not check proofs and does not run Lean.

Its catalogue of open problems includes some that Erdős posed: the Erdős–Straus conjecture (#242 on erdosproblems.com), the sunflower conjecture of Erdős and Rado (#20) and the Hadwiger–Nelson problem (#508). The Hadwiger–Nelson page has an "AI-assisted claims" block that quotes OpenAI's five-colour claim as its source states it, with Bill Gasarch's published response. The block's note says what it is: "Claims as their sources state them. Papex has not checked them; the status stays the source’s."

For researchers, Papex keeps a record of the work, and parts of the picture in Tao's posts resemble how it works. An AI app connected to Papex (see Papex in AI apps) can prepare a private draft and take private session checkpoints, short summaries of a working session that only the owner sees. The person, not the app, signs the exact version, with the AI tools they used declared beside their name; an AI app is never listed as an author. Each signed version is timestamped with OpenTimestamps and anchored in Bitcoin, with no wallet needed, and later edits become new versions, so the history stays visible. A public record can be linked to a problem and is listed on its page.

A Papex record is not a priority ruling. It does not show that a proof is correct, original or first, and it is not peer review. It shows which version a named person signed, when, and what they said the AI did. Model names are as the person declares them.

Sources#

• erdosproblems.com home page, checked 21 October 2026; earlier counts from Internet Archive copies of 10 October 2025, 2 January 2026, 1 July 2026, 5 August 2026 and 5 October 2026
• Changes (Thomas Bloom, erdosproblems.com, 6 October 2026), checked 21 October 2026
• Erdős problems in the OpenAI proofs (Thomas Bloom, erdosproblems.com, 8 October 2026), checked 21 October 2026
• A new blog and a site retrospective (Thomas Bloom, erdosproblems.com, 19 January 2026), checked 21 October 2026
• erdosproblems.com problem pages #12, #90, #152 and its forum thread, #508, #728, #741, #846, the #90 forum thread and the AI Contributions 2 thread, checked 21 October 2026; the May wording of #90 from an Internet Archive copy of 24 May 2026
• teorth/erdosproblems, STATISTICS.md and CONTRIBUTING.md (GitHub, 20 October 2026), checked 21 October 2026
• AI contributions to Erdős problems (GitHub wiki, frozen 30 June 2026), with its Disclaimers and caveats, section placement and advice to AI users pages, checked 21 October 2026; counts made by us from the page's markdown at the wiki's last commit
• Erdős Problems, About (erdosproblems.ai, Plasma AI) and its home page, checked 21 October 2026
• Tsoukalas et al., Advancing mathematics research with AI-driven formal proof search (Science 394, 234–239, 8 October 2026), abstract checked 21 October 2026; arXiv preprint 2605.22763, version 2 of 8 June 2026, checked 21 October 2026; results repository, checked 21 October 2026
• Avigad and Ballard, AI for research mathematics has arrived (Science 394, 166–167, 8 October 2026), title checked 21 October 2026
• Hulick, column on mathematics in the AI age (Science News, 14 October 2026), checked 21 October 2026
• An OpenAI model has disproved a central conjecture in discrete geometry (OpenAI, 20 May 2026), checked 21 October 2026 (Internet Archive copies of 20 May and 19 October 2026; the live page blocked automated access)
• Alon et al., Remarks on the disproof of the unit distance conjecture (arXiv 2605.20695, 20 May 2026) and Sawin, An explicit lower bound for the unit distance problem (arXiv 2605.20579, 20 May 2026), checked 21 October 2026
• Howlett, AI just solved an 80-year-old Erdős problem (Scientific American, 21 May 2026) and Amateur armed with ChatGPT … (Scientific American, 24 April 2026), checked 21 October 2026
• Levent Alpöge on X (26 May 2026) and the write-up on Anthropic's site, checked 21 October 2026
• Kevin Weil on X (17 October 2025, deleted), from the Internet Archive copy of 17 October 2025; replies by Thomas Bloom, Demis Hassabis and Sébastien Bubeck, checked 21 October 2026
• Terence Tao on Mathstodon: 16 October 2025, 26 December 2025, 6 August 2026 with follow-ups 117048872440592361, 117049010143179551 and 117049082185697696, checked 21 October 2026
• Feng et al., Semi-Autonomous Mathematics Discovery with Gemini: A Case Study on the Erdős Problems (arXiv 2601.22401, January 2026), checked 21 October 2026
• Kakaes, Why the Legendary Erdős Problems Are Falling to AI (Quanta Magazine, 3 August 2026), checked 21 October 2026
• Sothanaphan, Resolution of Erdős Problem #728 (arXiv 2601.07421, January 2026) and Alexeev et al., Primitive sets and von Mangoldt chains: Erdős Problem #1196 and beyond (arXiv 2605.00301, 1 May 2026), checked 21 October 2026
• Ten advances in mathematics (OpenAI, 1 August 2026), checked 21 October 2026 (Internet Archive copy of 11 October 2026)
• openai/math, README and history (GitHub), checked 21 October 2026
• Simons Foundation Launches $15M Effort To Help Mathematicians Navigate AI Era (Simons Foundation, 15 October 2026) and Targeted Grants to Math+AI Institutes – 2027, checked 21 October 2026; OpenAI's $5 million from the 15 October update to Sharing AI progress in mathematics (Internet Archive copy of 16 October 2026) and Anthropic's from its post on X
• Leiden Declaration on Artificial Intelligence and Mathematics (June 2026), checked 21 October 2026
• Tao, Palomar: a registry of Lean-verified mathematics (18 August 2026) and the formalization.yaml template, checked 21 October 2026