Evaluating Large Language Models in Mathematical Reasoning

The field of mathematical reasoning is experiencing significant developments with the introduction of large language models (LLMs). Current research is focused on evaluating the capabilities and limitations of LLMs in solving complex mathematical problems, highlighting the need for substantial improvements in reasoning and proof generation capabilities. Studies have shown that while LLMs achieve impressive performance on certain mathematical benchmarks, they often struggle with rigorous mathematical reasoning tasks and fail to distinguish correct mathematical reasoning from flawed solutions. The development of new evaluation benchmarks and methods is crucial to assess the true capabilities of LLMs in mathematical reasoning. Noteworthy papers in this area include: Proof or Bluff, which introduces a comprehensive evaluation of full-solution reasoning for challenging mathematical problems, revealing significant shortcomings in current LLMs. Large Language Models in Numberland, which evaluates the numerical reasoning abilities of LLM-based agents, highlighting their fragile number sense. Brains vs. Bytes, which conducts human evaluations of proofs generated by LLMs, underscoring the substantial gap between LLM performance and human expertise in advanced mathematical reasoning.

Sources

Proof or Bluff? Evaluating LLMs on 2025 USA Math Olympiad

Large Language Models in Numberland: A Quick Test of Their Numerical Reasoning Abilities

Investigating Large Language Models in Diagnosing Students' Cognitive Skills in Math Problem-solving

Brains vs. Bytes: Evaluating LLM Proficiency in Olympiad Mathematics

LLM for Complex Reasoning Task: An Exploratory Study in Fermi Problems

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