Not evaluated
OpenAI claims the irrationality exponent of π is 2 (family 017)
The gist
In its release of October 6, 2026, OpenAI claims that the irrationality exponent of π, a measure of how closely fractions can approach it, is 2.
DiscoverIA status on October 11, 2026: not evaluated, meaning no third-party evaluation found.
Text written by an AI, reviewed by Antoine Olivier,
Cite this entry
A single status snapshot since Oct 11, 2026: a citation always points to a dated snapshot.
Cite snapshot 1, Oct 11, 2026
APA citation with the dated link
BibTeX @misc, key discoveria-oai-fam-017-irrationality-exponent-pi-r1
@misc{discoveria-oai-fam-017-irrationality-exponent-pi-r1,
author = {{DiscoverIA}},
title = {OpenAI claims the irrationality exponent of π is 2 (family 017)},
howpublished = {DiscoverIA registry, entry oai-fam-017-irrationality-exponent-pi},
note = {Status “Not evaluated”, snapshot 1, recorded on October 11, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-017-irrationality-exponent-pi#releve-1},
urldate = {2026-10-11}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
If the proof held, the exact value of this exponent for π would be known, settling the accuracy that fractions approximating π can reach relative to the size of their denominator.
What remains unclear
No independent assessment is recorded, and no Lean proof (checkable by computer) has been found for this result. The sources read do not say where the question stood before the announcement.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com
Step 1 of 4 on the scale: not evaluated. Next step: under review.
- Announced
- Recordednot evaluated
- nextTo follow
What this status means
Source reading : Source read word for word (level 3 of 3)
The result is declared neither right nor wrong.
To move to “Under review”: a public review under way. To “Peer reviewed”: a journal publication or a review by named experts.
Sources
- Main sourcegithub.compage read word for word
Method
OpenAI publishes a manuscript (preprint) and a summary of the model's reasoning for family 017. The Lean formalisation was looked for by title in the repository's list, so its absence remains an estimate. DiscoverIA status: not evaluated, meaning that no third-party evaluation has been found in the sources read. Set on October 11, 2026 from github.com (page read, quotation checked word for word: “The irrationality exponent of <i>π</i> is 2.”).
Limits
DiscoverIA has not checked this result itself.
Key facts
- Claimed by
- OpenAI
announced on Oct 6, 2026 - Nature
- new result
- Field
- Mathematics (number theory)
- Checked by
- no verifier identified
- Sources
- 1 : 1 read word for word
- This entry
- Reviewed by Antoine Olivier, Oct 13, 2026
Status history
Only one observation so far.
An observation is added; none is ever erased.
In the same set
openai/math: 719 manuscripts in 372 families from an unreleased internal model · entry 17 of 372, by family number
- Not evaluated : Restricted geometric Langlands, generic Ramanujan and Arthur parameters (family 014)
- Not evaluated : Torus-packet equidistribution in prime, quartic, and sextic degrees (family 015)
- Not evaluated : Zilber–Pink in abelian varieties and the Siegel threefold (family 016)
- Not evaluated : OpenAI claims the irrationality exponent of π is 2 (family 017)
- Not evaluated : The Margulis–Platonov conjecture over global fields (family 018)
- Not evaluated : The p-adic section conjecture (family 019)
- Not evaluated : Squarefree quartics and power-free polynomial values (family 020)
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