OpenAI claims the irrationality exponent of π is 2 (family 017)
Status
Not evaluated
Recorded on · raw.githubusercontent.com
- Announced
- Recordednot evaluated
- nextTo follow
What this status means
Source reading : Source read word for word (level 3 of 3)
No DiscoverIA status yet; this does not mean nobody has checked it.
To move to “Under review”: a public review under way. To “Peer reviewed”: a journal publication or a review by named experts.
The gist
In its release of 6 October 2026, OpenAI claims that the irrationality exponent of π, a measure of how closely fractions can approach it, is 2.
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/en/fiche/oai-fam-017-irrationality-exponent-pi/#releve-1},
urldate = {2026-10-11}
}Dated link opens this snapshot in the history
Text written by an AI (DiscoverIA pipeline), on Reviewed by: Antoine Olivier, Oct 13, 2026Report an error
What has not been reviewed?
The status and its sources come from the registry; the explanatory text has been reviewed by a human.
The status and its sources come from the registry; the explanatory text has been reviewed by a human.
Key facts
- Claimed by
- OpenAI
announced on Oct 6, 2026 - Nature
- new result
- Field
- Mathematics (number theory)
- Checked by
- no verifier identified
- Sources (domains)
- 1 : 1 links only
- This entry
- Reviewed by Antoine Olivier, Oct 13, 2026
To understand
Analogy
Like darts aimed at a bullseye, fractions get close to an irrational number without ever hitting it. The irrationality exponent says how accurate infinitely many fractions can be, given their denominator, the number below the fraction bar.
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.
1 source.
For experts
Sources(domains)
- primairegithub.comlink only, reading not recorded
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. Status “not evaluated” recorded on 11 October 2026 from github.com (page read, quotation checked word for word).
Limits
DiscoverIA has recorded no independent evaluation as of this date.
Like darts aimed at a bullseye, fractions get close to an irrational number without ever hitting it.
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 : Not all have accompanying Lean formalizations.
- Not evaluated : describes the scope of the Lean formalization
- Not evaluated : Not all have accompanying Lean formalizations.
- Not evaluated : OpenAI claims the irrationality exponent of π is 2 (family 017)
- Not evaluated : Not all have accompanying Lean formalizations.
- Not evaluated : Not all have accompanying Lean formalizations.
- Not evaluated : describes the scope of the Lean formalization
Status history
Only one observation so far.
An observation is added; none is ever erased.
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