Advances in Mathematical Reasoning with Large Language Models

The field of mathematical reasoning with large language models is moving towards more rigorous evaluation frameworks and innovative applications. Recent developments have highlighted the potential of these models in solving complex mathematical problems, but also revealed their limitations in terms of numerical precision, logical consistency, and proof verification. Researchers are exploring new approaches to improve the reliability and effectiveness of large language models in mathematical reasoning, including the use of neural-guided equation discovery, generative adversarial policy optimization, and prompt engineering. Noteworthy papers in this area include: A Survey on Mathematical Reasoning and Optimization with Large Language Models, which provides a comprehensive review of the current landscape and future directions of mathematical reasoning and optimization with large language models. Beyond Final Answers: Evaluating Large Language Models for Math Tutoring, which evaluates the correctness and quality of large language models in math tutoring contexts and highlights their potential and limitations.

Sources

Beyond Final Answers: Evaluating Large Language Models for Math Tutoring

Neural-Guided Equation Discovery

A Survey on Mathematical Reasoning and Optimization with Large Language Models

GAPO: Learning Preferential Prompt through Generative Adversarial Policy Optimization

A Theoretical Framework for Prompt Engineering: Approximating Smooth Functions with Transformer Prompts

Challenging the Boundaries of Reasoning: An Olympiad-Level Math Benchmark for Large Language Models

Proof or Bluff? Evaluating LLMs on 2025 USA Math Olympiad

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