Otto365 AI Brief #013
OpenAI: AI maths proofs looked finished, some were wrong
What happened
OpenAI's AI maths proofs looked finished, and some were wrong. This updates our earlier Brief. OpenAI announced on the 7th of October 2026 it had withdrawn three AI-produced maths manuscripts over a sign error. They were among 722 preprints posted under 24 hours earlier, Retraction Watch reported.123
Three things to know
- Wrong sign, three out First, one wrong sign invalidated one paper's argument and a construction two dependent papers used; all three were withdrawn. Each carries a notice explaining the gap and linking the archived copy.12
- 14 repaired, 13 updated Second, OpenAI revised 14 other manuscripts with proof repairs and updated 13 more to cite them. As Retraction Watch reported, OpenAI says it found the errors in an audit and will withdraw papers it cannot fix.12
- Lean checks 300 of 719 Third, OpenAI added 6 formalisations: 300 of 719 top-line results, about 42 percent, are now formalised in Lean, a language that lets a computer check a proof. The rest are not yet.13
Why it matters to you
Otto365's take (opinion)
So, my take. AI output can look finished and still be wrong; even OpenAI withdrew some. For UK small businesses, a quote, contract clause or spreadsheet formula built on an AI answer inherits its mistakes.123
Do this week
Try this: check one AI answer at source before building on it.
Sources
- OpenAI: math/history.md at main · openai/math · GitHub (opens in a new tab) Primary source, accessed 9 Oct 2026
- Retraction Watch: OpenAI withdraws three preprints a day after releasing 722 manuscripts on unsolved math problems (opens in a new tab) News report, accessed 9 Oct 2026
- OpenAI: Sharing AI progress in mathematics (opens in a new tab) Primary source, accessed 7 Oct 2026
The quotes we checked (15)
In “Algebraicity of Weil classes on split abelian eightfolds” a sign error invalidates a stabilization-trace cancellation argument and the construction used by two dependent papers. As a result, we have withdrawn the following three manuscripts:
OpenAI · source 1
The error invalidated an argument in one manuscript and the construction used by two dependent papers, according to the announcement.
Retraction Watch · source 2
October 7, 2026 Withdrawals In “Algebraicity of Weil classes on split abelian eightfolds” a sign error
OpenAI · source 1
But on Oct. 7, OpenAI announced the withdrawal of three manuscripts because of a sign error.
Retraction Watch · source 2
The withdrawn papers now carry notices explaining the gap and linking to the archived manuscripts.
OpenAI · source 1
For any withdrawn papers, their README files explain the gap and link to the retracted manuscript.
OpenAI · source 1
We have revised 14 other manuscripts with proof repairs, corrected statements, clearer hypotheses and dependencies, and one correction to an obsolete citation.
OpenAI · source 1
we updated 13 additional manuscripts to cite the revised editions of companion papers. These changes update references and version dates.
OpenAI · source 1
A spokesperson for OpenAI told us the company identified the errors during an audit.
Retraction Watch · source 2
Where errors are identified, we will work to correct them promptly and withdraw papers if no fixes can be found.
Retraction Watch · source 2
We have added an additional 6 formalizations and 5 other additions covering supporting results. This brings the total percentage of top-line results formalized to 300 / 719 = ~42%.
OpenAI · source 1
we are sharing formalizations of many of the proofs in Lean, a programming language that allows mathematical proofs to be checked by a computer.
OpenAI · source 3
On Oct. 6, OpenAI published 722 preprints in a GitHub repository about purported progress in solving 372 math problems in geometry, computer science, algebra and other subjects.
Retraction Watch · source 2
Less than 24 hours after OpenAI posted over 700 preprints describing major math results by an internal AI model, the company has withdrawn three of the manuscripts for errors.
Retraction Watch · source 2
We’re releasing a broad range of new mathematical results produced by an internal frontier model.
OpenAI · source 3
Transcript
Full transcript
OpenAI's AI maths proofs looked finished, and some were wrong. This updates our earlier Brief.
Play from 0:07 OpenAI announced on the 7th of October 2026 it had withdrawn three AI-produced maths manuscripts over a sign error. They were among 722 preprints posted under 24 hours earlier, Retraction Watch reported.
Play from 0:21 First, one wrong sign invalidated one paper's argument and a construction two dependent papers used; all three were withdrawn. Each carries a notice explaining the gap and linking the archived copy.
Play from 0:34 Second, OpenAI revised 14 other manuscripts with proof repairs and updated 13 more to cite them. As Retraction Watch reported, OpenAI says it found the errors in an audit and will withdraw papers it cannot fix.
Play from 0:49 Third, OpenAI added 6 formalisations: 300 of 719 top-line results, about 42 percent, are now formalised in Lean, a language that lets a computer check a proof. The rest are not yet.
Play from 1:04 So, my take. AI output can look finished and still be wrong; even OpenAI withdrew some. For UK small businesses, a quote, contract clause or spreadsheet formula built on an AI answer inherits its mistakes.
Play from 1:19 Try this: check one AI answer at source before building on it.
I'm Otto365.
Follow the Brief.
On screen
- Play from 0:00
- Otto365 AI Brief #013, OpenAI, 7 Oct 2026
- AI proofs looked finished Some were wrong
- Three proofs withdrawn
- Play from 0:07
- OpenAI pulls three proofs
- Announced 7 Oct 2026
- 722 preprints
- Sign error found
- Three withdrawn
- 14 repaired
- Source: OpenAI, 7 Oct 2026
- Play from 0:21
- Wrong sign, three out
- Wrong sign
- Argument fails
- Two papers fall
- Three withdrawn
- Notice explains the gap
- Archived copy linked
- Play from 0:34
- 14 repaired, 13 updated
- 14 revised: Proof repairs, Clearer hypotheses
- 13 updated: 13 cite revisions, Version dates
- OpenAI audit
- Errors found
- Fix promptly
- Or withdraw
- Play from 0:49
- Lean checks 300 of 719
- Proof
- Written in Lean
- Computer checks
- 300 of 719
- 42% Top-line results in Lean
- Play from 1:04
- Check the foundation
- Looks finished: 722 preprints, Proofs written up
- Still wrong: Three withdrawn, 14 repaired
- AI answer
- Quote or clause
- Inherits mistakes
- Play from 1:19
- Check an AI answer at source
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