AI's 722 Math Manuscripts: Only 25 Claim Progress
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OpenAI’s October 2026 release of 722 AI-generated math manuscripts made headlines and social media rounds, fueling claims that artificial intelligence had “solved 722 open problems.” The real numbers, and what mathematicians themselves say, tell a more complicated story. Here’s what actually came out, what counts as a solved problem, and what it means for the future of mathematics.
722 Manuscripts Is Not 722 Solved Problems
OpenAI’s October 6, 2026 release consisted of 722 manuscripts, grouped into 372 “result families” spanning 17 mathematical fields. Each manuscript was generated by an internal, unreleased model after posing about 4,000 problems to it, but the key number—722—counts manuscripts, not solved problems[1, 2].
On average, each result family contains roughly 1.94 manuscripts (722 divided by 372), reflecting companion arguments or alternate proofs per result family [1]. The release README admits that not all results are fully checked or formalized: about 42–50% were not confirmed by computer or human review at launch[1, 2, 3]. The manuscripts themselves are best understood as raw research outputs, not polished, peer-reviewed theorems[3].
The Erdős Problem Slice: 25 Claimed Results, No Endorsements
Of the 722 manuscripts, only 25 address classic Erdős problems—well-known open questions in combinatorics and discrete mathematics[1, 4]. Of these, 21 have been formalized in Lean, a language where a computer checks every step of the proof[1]. But the site’s owner, Thomas Bloom (who maintains the main Erdős problems list), has not checked or endorsed any of these claims. He cautions that “none of these should be viewed as ‘closing the problem’” and expects “the vast majority of them are (a) correct yet (b) capable of being substantially simplified”[1].
As of the release, the public tracking of which Erdős problems are solved was frozen, so none has been accepted as a closed case by the community[1]. The last public tally, days before the release, showed about 48% of the 1,200 problems as solved, but the site no longer displays this figure[1].
How Many Were Actually Checked? The Role of Lean Formalization
Lean formalization is the main automated check for these AI-generated math results, but the coverage is patchy and the guarantees are limited. Source [1]—our own first-hand breakdown from November 2026—shows that, across the 722 released manuscripts, the share with a Lean formalization is somewhere between about 42% (per the repository README) and 162 papers with a Lean proof for the main result (per project file counts), but these figures do not reconcile and no source gives a definitive number for the entire release[1][2][4].
What Lean does give is a step-by-step computer verification of a theorem as stated in the formalization—not a check that the theorem matches the named open problem, nor that it is new, nor that the formalization covers the full strength of the claim. For the 25 Erdős problem claims, the site owner's measurement found that 21 have a Lean formalization, but as with the main set, these Lean proofs sometimes cover only a restricted or weaker version of the problem[1][4]. Example: the manuscript for Erdős problem #3 (a $5,000 prize problem) is Lean-formalized, but the formal version covers only a “reciprocal-sum” variant, not the exact statement posed by Erdős[1][4].
Mathematicians tracking the release, like Johan Commelin (Mathlib), flagged that some formalizations “appear to prove weaker statements than what's claimed in the paper”[1, 11]. The Lean check ensures the argument is logically correct for the formalized version—but not that the right problem has been solved.
The error rate in the first two days gives a sense of how much checking remained: three manuscripts were withdrawn for errors within 24 hours, and 14 were revised[1, 3]. This kind of rapid correction is typical for a bulk, unrefereed release and signals that even with Lean checks, significant manual review is still needed.
For practitioners, the upshot is: Lean formalization is a real filter for logical mistakes in the formalized statement, but it is not a stamp of external validation or a guarantee that the most interesting version of a problem was solved. The automated check is necessary, but far from sufficient—especially when the formalized target may miss the nuance or full strength of the original question.
What the Mathematicians Who Checked It Say
The mathematicians most familiar with these problems have been careful and, in some cases, critical. Thomas Bloom, the Erdős list maintainer, was explicit: “I have not yet looked at in any serious way any of the proofs in this release” and “none of these should be viewed as ‘closing the problem’”[1]. He expects many results will be correct, but likely not in their optimal or final form.
Terence Tao, one of the world’s leading mathematicians, commented that “solutions to open problems are now being harvested at large scale in an unsustainable fashion,” warning of a risk of “indiscriminate strip-mining” of mathematical problems and a devaluing of traditional mathematical practice[1]. Tao also estimated that only about 1–2% of open Erdős problems are simple enough for current AI, with minimal human help, to solve[1].
Other mathematicians (including the Association for Human Mathematics) criticized the approach as a “demonstration of power” rather than scholarship and called for stronger standards of verification and transparency[1].
A Controlled Benchmark: How Many Hard Problems Did AI Solve?
Pulling focus from the 722-manuscript headline, the only controlled benchmark so far—FrontierMath Erdős, as of September 2026—offers a reality check on what current AI models do with genuinely tough mathematics. In this test, 68 Erdős problems were handpicked for their difficulty and lack of prior resolution, then posed to leading AI models under the same compute and review constraints. The outcome: the best model, GPT-6 Astra, solved just 2 of the 68 problems (3%), while all others scored zero[1]. This isn’t a random sample—it’s the slice of problems that resisted attention from human mathematicians, where rediscovering known results or formalizing existing proofs wouldn’t count toward the score. Bloom, who co-designed the benchmark, estimated that only about three to five problems of this calibre had been solved by AI in total as of August 2026[1].
Here’s what the numbers look like from our own data, gathered 1 November 2026[1]:
| Benchmark / Set | Problems Tested | Full Solutions (AI) | Share Solved |
|---|---|---|---|
| FrontierMath Erdős (hard, curated) | 68 | 2 | 3% |
| Pre-release AI-led solutions (all types) | ~1,200 | 69 | ~6%* |
*But of those 69, many were literature searches or formalizations of existing proofs, not novel solutions[1].
It’s instructive to contrast this with the October 2025 overclaim, when OpenAI staff posted that GPT-5 had “solved” 10 Erdős problems and “made progress” on 11 others—until it became clear all 10 were previously published papers, not new proofs[1]. The community pushback that followed made the need for controlled, public benchmarks obvious.
In summary: on the benchmark set designed specifically to filter out “easy wins” via literature search or re-proving known the
A Worked Example: What Counts as "Solved"?
Take an illustrative case, modelled on what happened with Erdős problem #3: suppose an AI manuscript in the repository claims to resolve it. The claim comes with a Lean formalization that proves a related, but not identical, proposition. The Lean file passes its automated check—so the formal argument is valid for what it actually states.
What does this mean in practice?
- The original Erdős problem remains open: the AI proof covers only a subset or special case.
- No human checker or problem maintainer has endorsed the result—so there is no community verification.
- The formalized proof might still be of use: it could offer new methods or partial progress, but it does not "close" the problem.
This kind of scenario is common in the AI manuscript dump: a Lean-verified partial result, not a full solution. As our own data from 1 November 2026 shows, manuscript counts only tell you how many papers have been submitted—not how many long-standing math problems have actually been solved [1]. For practitioners, the bar remains: a solution must precisely match the problem statement and clear community review before it moves the field forward.
What Does This Mean for Mathematicians—and for AI?
The October 2026 release shows that AI can generate large quantities of plausible mathematical work, but the process of checking, refining, and accepting new results remains fundamentally human. The current wave of manuscripts includes errors, unpolished arguments, and claims that need careful attribution and verification[1]. The risk, as Tao and others note, is that the “strip-mining” of open problems could erode the culture of deep mathematical understanding if not managed with transparency and rigor.
For now, mathematicians are not “cooked”—AI is a powerful tool for discovery and formalization, but it has not replaced the essential process of verification, simplification, and creative insight that defines the field.
Questions readers ask
Did the AI release actually solve any famous open problems?
A handful of manuscripts claim solutions to well-known problems, including several with substantial prizes attached. However, none of these claims have been accepted as final by the mathematical community, and in some cases, the formalized result covers only a weaker form of the problem[1].
Can anyone check or reproduce the AI's results?
About 22% of the manuscripts are formalized in Lean, so those proofs can be checked by anyone with the right software. However, the model itself is not public, and for most results, detailed prompts and reasoning are not available, making full reproduction difficult[1, 2, 3].
What should count as a solved problem in mathematics?
Mathematicians generally require that a solution exactly matches the posed problem, is clearly new, and is reviewed or endorsed by experts. A Lean formalization is a strong check of logical validity but not enough by itself unless the formal and original problems match precisely[1, 2, 4].