Key Takeaways
- OpenAI's public repository lists 719 mathematical manuscripts, released on October 6, 2026.
- Only 300 of the 719 manuscripts, or 41.7 percent, have Lean formalizations, meaning formal proofs in the Lean system.
- The repository lists 719 manuscripts, three fewer than the 722 Decrypt reported, a gap that matches three withdrawals on October 7.
- The repository contains no manuscript on cryptography, ECDSA or post-quantum signatures, based on a search of its index.
OpenAI published its mathematical results on Tuesday, October 6, 2026, according to Decrypt. Its public repository lists 719 manuscripts. The README says the model was posed approximately 4,000 problems, and the manuscripts come from an internal OpenAI model.
What the 719-manuscript repository contains
The repository groups the 719 manuscripts into 372 result families. Its index lists work in number theory, algebraic geometry, probability and statistical physics. The README says the average result used about three hours of ChatGPT Pro thinking compute. It also says the 719 manuscripts are results that reached "an appropriate level of significance," and it does not say how many attempts failed.
- Lean formalizations: 300 of 719 manuscripts, or 41.7 percent (300 divided by 719). That leaves 419, or 58.3 percent, without a machine check.
- Count change: 722 results reported by Decrypt minus three withdrawn manuscripts equals 719. This is an inference from the two counts, not a figure the repository states.
The README is direct about the gap. It states: "This collection includes results at different stages of verification. Not all have accompanying Lean formalizations." It also warns that some unformalized results could have issues.
Three withdrawals on the second day
On October 7, OpenAI withdrew three manuscripts after a sign error in a stabilization-trace cancellation argument invalidated the construction used by two dependent papers. The withdrawn papers are Algebraicity of Weil classes on split abelian eightfolds, Algebraicity of Kuga–Satake Correspondences for K3 Surfaces, and The rational Hodge conjecture for products of K3 surfaces. OpenAI also revised 14 other manuscripts. The current Lean catalogue has no entry for any of the three withdrawn papers. The repository does not say whether they had a formal check before release.
What the release does not show about crypto signatures
The warnings from Ethereum researcher Justin Drake and Ethereum co-founder Vitalik Buterin rest on a forecast, not on a result in this repository. ECDSA is the signature scheme behind Bitcoin and Ethereum, according to Decrypt. A search of the manuscript index found no entry that mentions cryptography, ECDSA or post-quantum signatures. The lattice results concern geometry, and the elliptic-curve results concern curves over the rational numbers, not the curves Bitcoin and Ethereum use.
Buterin has argued that AI could help prove software secure. In September he wrote: "If AI can prove Navier-Stokes and FLT, then AI can prove the statement 'this program is secure' as a mathematical theorem," he wrote. That is a hypothetical, and this release does not test it. WYDE's September report on a separate OpenAI claim about Navier-Stokes concerns a separate claim, and that result does not appear in this repository.
The stakes for crypto holders are not abstract. The Giving Block reports more than $1 billion in crypto donated to charitable causes in 2024, and WYDE's companion report examines the donation side of the same warnings. The release does not change any of those wallets. A machine-checked attack on ECDSA or on a lattice signature scheme would. The repository contains neither.
People Also Ask
How many math manuscripts did OpenAI release?
OpenAI's public openai/math repository lists 719 mathematical manuscripts, grouped into 372 result families. The repository was created on October 6, 2026, and is licensed under Apache 2.0, according to its GitHub record.
How many OpenAI math results have Lean formalizations?
300 of the 719 manuscripts, or 41.7 percent, have Lean formalizations, according to the October 7 update in the repository's history file. The other 419 do not yet have a machine check.
Did OpenAI's math results break Bitcoin or Ethereum signatures?
No. The repository contains no manuscript on cryptography, ECDSA or post-quantum signatures, based on a search of its index. Warnings about signature security come from Justin Drake and Vitalik Buterin, and they forecast risk rather than report a break.
Sources: openai/math on GitHub, including its README and manuscript index, and its history file. Decrypt on Justin Drake reported the 722 count, and Decrypt on Vitalik Buterin covered his remarks on AI and security.