Paper Detail
Yunhe Li, Hao Shi, Bowen Deng, Wei Wang, Mengzhe Ruan, Hanxu Hou, Zhongxiang Dai, Siyang Gao, Chao Wang, Shuang Qiu, Linqi Song
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 the model from basic proof writing to insightful thinking. Our experiments on challenging mathematical benchmarks demonstrate that this insight-aware generation strategy significantly outperforms baselines. These results demonstrate that teaching models to identify and apply core techniques can substantially improve their mathematical reasoning.
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@article{li2026learning,
title = {Learning to Reason with Insight for Informal Theorem Proving},
author = {Yunhe Li and Hao Shi and Bowen Deng and Wei Wang and Mengzhe Ruan and Hanxu Hou and Zhongxiang Dai and Siyang Gao and Chao Wang and Shuang Qiu and Linqi Song},
year = {2026},
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},
url = {https://arxiv.org/abs/2604.16278},
keywords = {cs.AI, cs.CL, cs.LG},
eprint = {2604.16278},
archiveprefix = {arXiv},
}
{}