Learning to Reason with Insight for Informal Theorem Proving: Introducing DeepInsightTheorem

Forum topic · 小凯 · 2026-04-21

Summary

This paper addresses a key bottleneck in informal theorem proving with large language models (LLMs): a lack of insight, i.e., the difficulty of recognizing the core techniques needed to solve complex mathematical problems. The authors propose DeepInsightTheorem, a hierarchical dataset that structures informal proofs by explicitly extracting core techniques and proof sketches alongside the final proof. To exploit this data, they design a Progressive Multi-Stage SFT (supervised fine-tuning) strategy that mimics human learning, guiding models from basic proof writing toward insightful reasoning. Experiments on challenging mathematical benchmarks show that this insight-aware generation strategy significantly outperforms baselines, demonstrating that teaching models to identify and apply core techniques can substantially improve their mathematical reasoning and informal theorem-proving capabilities. Paper: arXiv 2604.16278.

Paper Overview

Field: NLP / Mathematical Reasoning
Authors: Yunhe Li, Hao Shi, Bowen Deng, Wei Wang, Mengzhe Ruan, Hanxu Hou, Zhongxiang Dai, Siyang Gao, Chao Wang, Shuang Qiu, Linqi Song
arXiv: 2604.16278

Abstract

Although most of the automated theorem-proving approaches depend on formal proof systems, informal theorem proving can align better with large language models' (LLMs) strength in natural language processing. In this work, we identify a primary bottleneck in informal theorem proving as a lack of insight, namely the difficulty of recognizing the core techniques required to solve complex problems. To address this, we propose a novel framework designed to cultivate this essential reasoning skill and enable LLMs to perform insightful reasoning.

We propose $\mathtt{DeepInsightTheorem}$ , a hierarchical dataset that structures informal proofs by explicitly extracting core techniques and proof sketches alongside the final proof. To fully exploit this dataset, we design a Progressive Multi-Stage SFT strategy that mimics the human learning process, guiding models from basic proof writing to insightful thinking. Experiments on challenging mathematical benchmarks show that this insight-aware generation strategy significantly outperforms baselines. These results indicate that teaching models to identify and apply core techniques can substantially improve their mathematical reasoning capabilities.

Key Contributions

Identifies lack of insight (recognizing core techniques) as the main bottleneck in informal theorem proving with LLMs.
Introduces DeepInsightTheorem, a hierarchical dataset structuring proofs into core techniques, proof sketches, and final proofs.
Proposes a Progressive Multi-Stage SFT strategy modeled on human learning, moving from basic proof writing to insightful reasoning.
Empirically shows significant gains over baselines on challenging mathematical benchmarks.

--- *Auto-collected on 2026-04-21.*