Can LLMs Reliably Grade Olympiad Proofs? A Study of Mathematical Verification with LLMs

Authors: Azim Ospanov , Zijin Feng , Ding Ding , Chengwu Liu , Haoli Bai , Jiacheng Sun , Lifeng Shang , Farzan Farnia

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Abstract: Large Language Models (LLMs) have made remarkable progress on solving competition-level mathematics, yet their ability to verify natural-language mathematical proofs remains relatively underexplored. This gap is especially pronounced for Olympiad-level proofs, which require meticulous assessment of each claim in a long reasoning chain. Current proof verification thus primarily relies on expert inspection, which is costly to scale. In this paper, we present a systematic study of LLM-based verification in this setting. Specifically, we introduce a human-curated dataset of USAMO 2025 candidate solutions with expert grading, and conduct a broad evaluation of existing LLM verifiers across frontier models. We also propose TROJAN, an iterative self-critique pipeline for generating high-fidelity adversarial proofs at scale. Our comprehensive evaluation covers 20 models spanning seven metrics, two prompt styles, three inference methods, and three prompt templates, showing that state-of-the-art models still leave considerable room for improvement. To narrow this gap, we propose MABGrader, a Multi-Armed Bandit framework that reframes grading as arm selection over the discrete score space. MABGrader outperforms the SOTA ProofGrader by 26.4% in Quadratic Weighted Kappa and reduces grading error by 14%. Code and dataset are available at this https URL .

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Artificial Intelligence (cs.AI)

Cite as:

arXiv:2610.36767 [cs.AI]

(or

arXiv:2610.36767v1 [cs.AI] for this version)

https://doi.org/10.48550/arXiv.2610.36767

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arXiv-issued DOI via DataCite (pending registration)

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From: Azim Ospanov [ view email ]

[v1]

Tue, 27 Oct 2026 07:28:08 UTC (20,980 KB)

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