Large Language Models for Mathematical Analysis

TL;DR

This paper introduces a new dataset and framework to improve large language models' ability to solve mathematical analysis problems involving proofs and formal reasoning, addressing a key gap in AI mathematical capabilities.

Contribution

The paper presents DEMI-MathAnalysis, a novel dataset for proof-based mathematical analysis problems, and a framework that significantly enhances LLMs' reasoning and proof generation abilities.

Findings

LLMs fine-tuned on DEMI-MathAnalysis produce more rigorous proofs

Framework improves logical consistency and completeness in solutions

Enhanced models demonstrate better handling of formal mathematical language

Abstract

Mathematical problem-solving is a key field in artificial intelligence (AI) and a critical benchmark for evaluating the capabilities of large language models (LLMs). While extensive research has focused on mathematical problem-solving, most existing work and datasets concentrate on computational tasks, leaving gaps in areas like mathematical analysis, which demands rigorous proofs and formal reasoning. We developed the DEMI-MathAnalysis dataset, comprising proof-based problems from mathematical analysis topics such as Sequences and Limits, Infinite Series, and Convex Functions. We also designed a guiding framework to rigorously enhance LLMs' ability to solve these problems. Through fine-tuning LLMs on this dataset and employing our framework, we observed significant improvements in their capability to generate logical, complete, and elegant proofs. This work addresses critical gaps in mathematical reasoning and contributes to advancing trustworthy AI capable of handling formalized mathematical language. The code is publicly accessible at LLMs for Mathematical Analysis.