No LLM Solved Yu Tsumura's 554th Problem

Simon Frieder; William Hart

REVIEW 3 major objections 3 minor 9 references

No LLM Solved Yu Tsumura's 554th Problem

T0 review · 3 major / 3 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Yu Tsumura's 554th problem is an olympiad-scope, non-combinatorial problem with a public solution that no off-the-shelf LLM can readily solve.

desk verdict A possibly useful LLM-evaluation counterexample, but the submitted full text is a different paper, so there is nothing reviewable here yet. read the letter →

arxiv 2508.03685 v1 pith:B4W64KTN submitted 2025-08-05 cs.LG

Simon Frieder , William Hart This is my paper

classification cs.LG

keywords largelanguagemodelsmathematicalreasoningolympiadproblemsInternationalYuTsumura's554thproblemLLMsolvingnegativeresultbenchmarkcounterexample

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper sets out to demonstrate a single negative result: Yu Tsumura's 554th problem is an olympiad-scope problem that no off-the-shelf large language model, commercial or open-source, can readily solve, even though it is comparatively light on proof machinery and has a publicly available solution that is likely already in the models' training data. The authors argue that the problem is within the proof-sophistication scope of an International Mathematical Olympiad (IMO) problem, is not a combinatorics problem, and requires fewer proof techniques than typical hard IMO problems. If the claim holds, it undercuts the optimism fueled by recent gold-medal results on olympiad-style problems: a public, in-scope problem exists that separates current off-the-shelf LLMs from human solvers. The paper's contribution is the identification of a specific counterexample to the idea that recent LLM successes on olympiad problems generalize broadly.

What carries the argument

The central object is Yu Tsumura's 554th problem itself, used as a probe of LLM mathematical reasoning. The load-bearing properties are the five criteria stated in the abstract: olympiad-level proof sophistication, non-combinatorial content, low proof-technique demand, a public solution that is likely in training data, and failure across tested off-the-shelf models. The mechanism of the argument is selection: by choosing a problem that is easy on the dimensions that should favor LLMs — public solution, low proof complexity, and no combinatorics — the authors make a reported failure carry more weight than a failure on a hard, obscure, or combinatorial problem would. The problem functions as a controlled test instance for separating current off-the-shelf LLM capability from human-level olympiad solving.

What would settle it

Run Yu Tsumura's 554th problem against a broad panel of current off-the-shelf LLMs, using standard prompting and an explicit rule for what counts as a correct solution; if any model produces a correct accepted solution, criterion (e) is false. A second check is to verify that the solution is genuinely public and likely in training data, since criterion (d) is also load-bearing.

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Extended reading notes

Core claim

In the paper's own terms, the discovery is that Yu Tsumura's 554th problem satisfies five criteria simultaneously. It is within the proof-sophistication scope of an IMO problem. It is not a combinatorics problem, so the failure cannot be blamed on the genre that has historically caused LLMs difficulty. It requires fewer proof techniques than typical hard IMO problems. Its solution is publicly available and likely in the training data of the models. And yet, the paper asserts, no existing off-the-shelf LLM — commercial or open-source — can readily solve it. The problem thus stands as a counterexample to the claim that LLMs with olympiad-level medal results can handle the full range of olympiad-scope mathematics.

Load-bearing premise

The claim that no existing off-the-shelf LLM can readily solve the problem depends on the assumption that the models, prompts, sampling budget, and answer-verification method used in the tests fairly represent all off-the-shelf LLMs; the abstract reports none of these details, and the accompanying full text is a different manuscript.

Editorial extensions

If this is right

If the claim holds, a public solution in the training data is not enough for an off-the-shelf LLM to reproduce or apply that solution on demand.
If the claim holds, olympiad medal results by LLMs cannot be read as evidence that the models can solve olympiad-scope problems generally, because a deliberately easy, non-combinatorial, public-solution problem remains unsolved.
If the claim holds, the problem becomes a concrete benchmark item: any off-the-shelf LLM that solves it under standard prompting would refute criterion (e).
If the claim holds, failure is not confined to combinatorics, so explanations of LLM olympiad failure that point only at combinatorial reasoning are incomplete.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The full text supplied with the abstract is a different manuscript, so the models, prompts, sampling budgets, and answer-checking behind the failure claim are not visible in the provided material; the sweeping claim about all off-the-shelf LLMs therefore cannot be checked from what is supplied.
A natural testable extension is to run neighboring problems from the same source as Yu Tsumura's 554th problem, if such a numbered list exists, to see whether the failure is specific to this problem or common across the collection.
Another extension is to give models more sampling or stronger prompting while keeping them off-the-shelf; success under those conditions would not refute the paper's claim but would show how close current models are to solving it.
If the result replicates, it suggests that obscure olympiad-scope problems with public solutions may be a more realistic measure of LLM mathematical reasoning than high-profile medal benchmarks.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Short version: this submission is an abstract for a potentially interesting LLM evaluation claim, but the full text attached is a different paper (FairLangProc, arXiv:2508.03677). So there is no way to review the actual work. The abstract says Yu Tsumura's 554th problem is IMO-scope, non-combinatorial, proof-light, with a public solution, and that no off-the-shelf LLM can solve it. If the full paper documents a broad, careful evaluation, that would be a useful counterexample to IMO-medal hype and a sharper probe for math benchmarks. Credit for picking a concrete problem with a public solution and stating criteria explicitly.

The soft spots are severe. The universal negative "cannot be readily solved by any existing off-the-shelf LLM" is only as strong as the model set, prompts, sampling budget, and answer verification. The abstract gives none of these. LLM math performance is brittle to prompt phrasing and sampling; a narrow failure set would not justify the universal quantifier. Terms like "readily solved," "proof sophistication," and "fewer proof techniques" are undefined and hard to falsify. And the mismatch between abstract and full text means the submitted manuscript is not the paper. That alone is a desk-reject condition unless the authors uploaded the wrong file.

Who is this for? LLM evaluation researchers tracking IMO-level reasoning; they would read a properly supported version of this paper. But as submitted, this is an abstract, not a reviewable article. The citation pattern is not assessable, and the data are absent. I would not spend referee time on it until the correct full text is provided with the evaluation protocol.

Recommendation: return the submission to the authors to correct the file and to report models, prompts, compute budget, and verification. If those are present and the evaluation is robust, the paper deserves peer review.

Referee Report

3 major / 3 minor

Summary. The abstract announces a negative empirical claim about large language models: Yu Tsumura's 554th problem allegedly satisfies five criteria (a) through (e), most importantly that it cannot be readily solved by any existing off-the-shelf LLM, and the paper suggests this contradicts optimism fueled by recent IMO gold medals. The submitted full text, however, is a completely different manuscript, "FairLangProc: A Python package for fairness in NLP" (arXiv:2508.03677v1), which contains no experimental protocol, results, or analysis concerning Tsumura's problem or LLM mathematical reasoning. Consequently, the submission as provided contains no evidence for its central claim.

Significance. If established through a broad, carefully controlled evaluation, the claimed existence of an IMO-scope problem with a public solution that no off-the-shelf LLM can readily solve would be a substantive negative result for the LLM reasoning literature, and criteria (a) through (d) could serve as a useful benchmark-selection checklist. However, because the submission contains none of the experimental apparatus, including model identities, prompts, sampling budget, verification protocol, or even the problem statement, the claim is not assessable in its current form. The universal quantifier over "any existing off-the-shelf LLM" in particular demands a sampling and protocol justification that is entirely absent. The paper's potential significance is real, but the submitted manuscript does not realize it.

major comments (3)

[Full Text] The manuscript body (pp. 1-40) is arXiv:2508.03677v1, "FairLangProc: A Python package for fairness in NLP," which is unrelated to the abstract. No definition of Yu Tsumura's 554th problem, no evaluation protocol, no model list, and no results appear in the submission. The central claim in the abstract is therefore completely unsupported by the submitted materials.
[Abstract, criterion (e)] The universal negative claim that the problem "cannot be readily solved by any existing off-the-shelf LLM (commercial or open-source)" requires a specification of the tested models, prompts, sampling temperature and budget, few-shot exemplars, and answer-verification method. None of these are reported in the abstract or body, so the claim is unfalsifiable from the submission. Furthermore, "readily solved" is undefined; without a threshold for success or effort, the criterion cannot be tested.
[Abstract, criteria (a) and (c)] The comparative assessments that the problem is "within the scope of an IMO problem in terms of proof sophistication" and "requires fewer proof techniques than typical hard IMO problems" are not operationalized. No rubric, baseline set of IMO problems, or definition of "proof techniques" is given, making criteria (a) and (c) impossible to verify or contest.

minor comments (3)

[Full Text, header] The full text is labeled arXiv:2508.03677v1 [cs.CL], while the abstract is drawn from arXiv:2508.03685; the identifiers do not match, compounding the difficulty of verifying the submission's provenance.
[Abstract, criterion (e)] Even the set of "off-the-shelf" LLMs is not defined; it is unclear whether this includes models available via API only, open-weight models, or both, and at what cutoff date.
[FairLangProc full text] If the unrelated full text is included by accident, its numerous typos and formatting issues (e.g., "developement," "progessively," "refered") should not be counted against the actual paper; however, the mismatch itself must be corrected before review can proceed.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular structure is detectable: the submission's full text is an unrelated paper, and the abstract alone describes no derivation, fitted parameters, or self-citation chain to reduce.

full rationale

The claimed paper, arXiv:2508.03685, is represented only by an abstract asserting that Yu Tsumura's 554th problem is within IMO proof-sophistication scope, is not combinatorics, requires fewer proof techniques, has a public solution, and cannot be readily solved by off-the-shelf LLMs. The supplied full text, however, is arXiv:2508.03677 (FairLangProc), a Python package paper on NLP fairness with no connection to the claimed problem or LLM evaluation. Consequently, there is no derivation chain, set of equations, fitted parameter, or argument-by-citation present to audit for circularity. The abstract makes an empirical universal negative claim whose strength depends on unstated evaluation details (model set, prompts, sampling budget, verification), but that is an evidentiary or selection-bias concern, not a circularity concern. No quoted reduction can be exhibited because none exists in the provided material. Under the hard rule that circularity may be claimed only when a specific reduction can be quoted, the correct finding is no significant circularity.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

The central claim rests on the problem having the properties in criteria (a)-(d) and on the evaluation being fair and representative. None of these are quantified in the abstract. No fitted numbers or invented entities appear; the assumptions are domain assumptions about problem scope, availability of the solution in training data, and adequacy of the model sample and judging protocol.

assumptions (4)

domain assumption The problem is within the scope of an IMO problem in terms of proof sophistication.
Asserted in abstract criterion (a); no formal definition of IMO scope or proof sophistication is given, and the supplied full text does not address it.
domain assumption A publicly available solution to the problem exists and is likely in the training data of LLMs.
Asserted in abstract criterion (d); this supports the claim that failure is not due to the answer being absent from training data, but no citation or evidence of training-data inclusion is given.
domain assumption The set of evaluated off-the-shelf LLMs and the evaluation protocol are representative enough to support the universal negative over all off-the-shelf LLMs.
Required for the claim in abstract criterion (e); the abstract gives no model list, prompts, sampling budget, or verification method.
domain assumption Model attempts can be reliably judged as solved or unsolved.
Needed to assert that no LLM solved the problem; the abstract does not state how correctness was assessed (human judges, exact-answer matching, proof checking).

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Cite this review

Pith. "Pith review of No LLM Solved Yu Tsumura's 554th Problem." pith.science (2026). https://pith.science/paper/B4W64KTN

@misc{pith2026250803685,
  author       = {Pith},
  title        = {Pith review of: No LLM Solved Yu Tsumura's 554th Problem},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/B4W64KTN}},
  note         = {Machine review of arXiv:2508.03685}
}

read the original abstract

We show, contrary to the optimism about LLM's problem-solving abilities, fueled by the recent gold medals that were attained, that a problem exists -- Yu Tsumura's 554th problem -- that a) is within the scope of an IMO problem in terms of proof sophistication, b) is not a combinatorics problem which has caused issues for LLMs, c) requires fewer proof techniques than typical hard IMO problems, d) has a publicly available solution (likely in the training data of LLMs), and e) that cannot be readily solved by any existing off-the-shelf LLM (commercial or open-source).

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Reference graph

Works this paper leans on

9 extracted references · 1 canonical work pages

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

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Mitigating Language-Dependent Ethnic Bias in BERT

33 Ahn J, Oh A (2021). “Mitigating Language-Dependent Ethnic Bias in BERT.” In MF Moens, X Huang, L Specia, SWt Yih (eds.),Proceedings of the 2021 Conference on Empirical Meth- ods in Natural Language Processing, pp. 533–549. Association for Computational Linguis- tics, Online and Punta Cana, Dominican Republic.doi:10.18653/v1/2021.emnlp-main

doi:10.18653/v1/2021.emnlp-main 2021

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Collecting a Large-Scale Gender Bias Dataset for Coreference Resolution and Machine Translation

Levy S, et al. (2021). “Collecting a Large-Scale Gender Bias Dataset for Coreference Resolution and Machine Translation.” In MF Moens, X Huang, L Specia, SWt Yih (eds.), Findings of the Association for Computational Linguistics: EMNLP 2021 , pp. 2470–2480. Association for Computational Linguistics, Punta Cana, Dominican Repub- lic. doi:10.18653/v1/2021.fi...

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Intra-Processing Methods for Debiasing Neural Networks

Rajpurkar P, et al. (2016). “SQuAD: 100,000+ Questions for Machine Comprehension of Text.” In J Su, K Duh, X Carreras (eds.),Proceedings of the 2016 Conference on Empirical Methods in Natural Language Processing, pp. 2383–2392. Association for Computational Linguistics, Austin, Texas. doi:10.18653/v1/D16-1264. URL https://aclanthology. org/D16-1264/. Rana...

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Announcing Microsoft Copilot, your every- day AI companion

Microsoft (Accessed 27/05/2025). “Announcing Microsoft Copilot, your every- day AI companion.” URL https://blogs.microsoft.com/blog/2023/09/21/ announcing-microsoft-copilot-your-everyday-ai-companion/ . Nadeem M, et al. (2021). “StereoSet: Measuring stereotypical bias in pretrained language models.” InCZong, FXia, WLi, RNavigli(eds.), Proceedings of the 5...

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Language models are few-shot learners

Brown T,et al.(2020). “Language models are few-shot learners.”Advances in neural infor- mation processing systems, 33, 1877–1901. Caliskan A, Bryson JJ, Narayanan A (2017). “Semantics derived automatically from language corpora contain human-like biases.”Science, 356(6334), 183–186. Cer D, et al. (2017). “SemEval-2017 Task 1: Semantic Textual Similarity M...

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GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding

Wang A,et al.(2018). “GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding.” In T Linzen, G Chrupała, A Alishahi (eds.), Proceedings of the 2018 EMNLP Workshop BlackboxNLP: Analyzing and Interpreting Neural Networks for NLP, pp. 353–355. Association for Computational Linguistics, Brussels, Belgium.doi: 10.18653/v1/W18-5446...

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Neural network acceptability judgments

Warstadt A,et al. (2019). “Neural network acceptability judgments.” Transactions of the Association for Computational Linguistics, 7, 625–641. Webster K, et al. (2018). “Mind the GAP: A Balanced Corpus of Gendered Ambiguous Pronouns.” Transactions of the Association for Computational Linguistics, 6, 605–617. doi:10.1162/tacl_a_00240. URL https://aclanthol...

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Entropy-based Attention Regularization Frees Unintended Bias Mitigation from Lists

URL https://aclanthology.org/2021.emnlp-main.42/. Attanasio G,et al.(2022). “Entropy-based Attention Regularization Frees Unintended Bias Mitigation from Lists.” In S Muresan, P Nakov, A Villavicencio (eds.),Findings of the As- sociation for Computational Linguistics: ACL 2022, pp. 1105–1119. Association for Com- putational Linguistics, Dublin, Ireland.do...

arXiv 2022