Max It or Miss It: Benchmarking LLM On Solving Extremal Problems

Binxin Gao; Jingjun Han

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arXiv · 2510.12997

Max It or Miss It: Benchmarking LLM On Solving Extremal Problems

Binxin Gao·Jingjun Han

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Abstract

Test-time scaling has enabled Large Language Models (LLMs) with remarkable reasoning capabilities, particularly in mathematical domains, through intermediate chain-of-thought (CoT) reasoning before generating final answers. However, the specific sources and mechanisms underlying these reasoning capabilities remain insufficiently understood. Optimization reasoning, i.e. finding extrema under constraints, represents a fundamental abstraction that underpins critical applications in planning, control, resource allocation, and prompt search. To systematically evaluate this capability, we introduce ExtremBench, a benchmark dataset for solving mathematical extremal problems, curated from inequality exercises used for Chinese Mathematical Olympiad and transformed into $93$ standardized extrema-finding problems. We conduct extensive evaluations across various state-of-the-art open-source model families, including the Qwen3, GPT-OSS, and DeepSeek. Our results reveal that LLMs' extremal-solving reasoning capabilities do not always align with those of current mathematical benchmarks such as AIME25 and MATH-500, with some models showing strong general mathematical reasoning but poor extremal-solving skills, and vice versa. This discrepancy highlights a critical gap in current evaluation practices and suggests that existing benchmarks may not comprehensively capture the full spectrum of mathematical reasoning abilities.

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Binxin Gao, Jingjun Han. 2025-10-14. Max It or Miss It: Benchmarking LLM On Solving Extremal Problems. https://arxiv.org/abs/2510.12997

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