Disputed claim that Catalan's constant is irrational
A preprint claims a proof that Catalan's constant is irrational, using weighted tails in the Calegari-Dimitrov-Tang framework; a specific technical objection to the argument has been raised publicly and is unresolved.
- Model
- ChatGPT 5.6 Solar, named in the paper as the verifier; the model consulted during the work is named only as AI
- Field
- Mathematics
- Date
- 2026-09-03
- Human collaborators
- Zhi-Wei Sun
Sources
Original work
Challenge
What was found
The irrationality of Catalan's constant is a long-standing open problem. The preprint adapts the method Calegari, Dimitrov and Tang used for the linear independence of 1, zeta(2) and L(2, chi_-3), replacing part of the arithmetic input with a construction of suitable weights and weighted tails. The acknowledgements set out an unusually specific division of labour: repeated attempts by the model failed, the author then supplied the weighting idea that made the approach work, and the model produced the numerical data. The paper states that 'the whole proof has passed the verification of Chatgpt 5.6 Solar', which is a machine reading rather than a human check.
Novelty check
The irrationality of Catalan's constant is a well-known open problem with no claimed resolution in the four registries before this preprint. The method is explicitly derivative of Calegari, Dimitrov and Tang's 2024 work, which the paper cites, and the claimed novelty is the weighting construction rather than the framework. No competing claim was found. The question of priority is not the issue here; the correctness of the argument is, and it is disputed.
Caveats and known objections
Graded disputed on a specific, unresolved technical objection rather than on general scepticism. The objection, raised publicly and cited here, is that the tail recurrence of equation 1.4 is inconsistent with the factor used in equation 2.12, so the zero count the argument needs in order to force the degree bound fails. The same critique notes that the paper replaces the arithmetic content of the model it follows with a combinatorial minimization plus numerics that no human has checked, and points to internal inconsistencies in the write-up. The preprint remains at version one with no revision or withdrawal at entry. Autonomy is graded ai-assisted, and the paper's own account is the reason: the model 'made many attempts but we failed again and again' until 'the author realized that we should use suitable weights', so the decisive idea is the author's. The only stated verification of the whole proof is by a language model, which is not an independent check by any human.
Nobody outside the lab has checked this yet.
Reading the primary source closely enough to say whether it supports the claim counts as a check, and you are credited on the entry.
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Entry history (1 event)
- AddedEntered the registry graded Disputed and AI-assisted.
Entries are never deleted. A grade that does not hold up is downgraded on the record, with the reason beside it.
Graded disputed for verification and ai-assisted for autonomy. What these mean.
Cite this entry
whataifound.org. (2026). Disputed claim that Catalan's constant is irrational. whataifound.org: A Registry of AI Scientific and Mathematical Discoveries. https://whataifound.org/finding/2026-09-03-catalan-constant-irrationalityBibTeX
@misc{whataifound-nanjinguniversity-2026-irrationality,
title = {Disputed claim that Catalan's constant is irrational},
author = {{whataifound.org}},
year = {2026},
howpublished = {whataifound.org: A Registry of AI Scientific and Mathematical Discoveries},
note = {Result by Nanjing University. Verification: Disputed. Autonomy: AI-assisted.},
url = {https://whataifound.org/finding/2026-09-03-catalan-constant-irrationality}
}