No LLM Solved Yu Tsumura's 554th Problem

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Conflicts of Interest

Identified Weaknesses

Rating Explanation

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Paper Summary

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AI Still Can't Do ALL the Math: Popular LLMs Flunk a Known Group Theory Challenge

This paper challenges recent optimism about large language models' (LLMs) mathematical reasoning, demonstrating that leading commercial and open-source LLMs failed to solve Yu Tsumura's 554th problem. Despite being within the International Mathematical Olympiad's scope and having a publicly available solution pre-dating LLMs, models struggled with the intricate symbolic manipulation required, suggesting fundamental limitations in deep search and algebraic error prevention.

Possible Conflicts of Interest

None identified

Identified Weaknesses

Susceptibility to Goodhart's Law

The paper acknowledges that once this specific problem is publicized, LLM developers might optimize models directly for it, potentially leading to a solution without genuinely improving general mathematical reasoning, thus undermining the long-term impact of this finding.

One-Shot Evaluation Protocol

The study evaluated models based on a single attempt. Commercial LLMs might employ internal "repeated evaluation" or "majority voting" strategies, which could potentially yield correct solutions if given multiple tries, suggesting the end-user experience might sometimes differ.

Limited Scope of Models Examined

The analysis focused on publicly available and widely deployed LLMs. The authors cannot definitively rule out that specialized "boutique models" or those not yet publicly released could reliably solve the problem.

Exclusion of External Tools/RAG

To specifically assess reasoning, the study intentionally prohibited web searches (RAG) and access to symbolic solvers. Allowing such tools might enable an LLM to find the existing solution or derive it, though this would test tool-integration rather than raw reasoning.

Rating Explanation

The paper presents a robust and timely counter-argument to exaggerated claims of LLM mathematical prowess, using a clearly defined and publicly verifiable problem. Its methodology for evaluating "off-the-shelf" LLMs is sound for its stated purpose, and the authors transparently discuss the study's limitations, adding significant value to the ongoing discourse on AI capabilities.

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