# Learning to Reason with Insight for Informal Theorem Proving

arXiv: https://arxiv.org/abs/2604.16278 · HTML: https://mlsanity.com/paper/2604.16278/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 16 of its 29 references that are in the map.
- First posted on arXiv 17 Apr 2026.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

## Builds on (most cited first, 16 of 16)

- [Least-to-Most Prompting Enables Complex Reasoning in Large Language Models](https://mlsanity.com/paper/2205.10625/) (2022)
- [Plan-and-Solve Prompting: Improving Zero-Shot Chain-of-Thought Reasoning by Large Language Models](https://mlsanity.com/paper/2305.04091/) (2023)
- [MiniF2F: a cross-system benchmark for formal Olympiad-level mathematics](https://mlsanity.com/paper/2109.00110/) (2021)
- [Hierarchical Reasoning Model](https://mlsanity.com/paper/2506.21734/) (2025)
- [Self-Discover: Large Language Models Self-Compose Reasoning Structures](https://mlsanity.com/paper/2402.03620/) (2024)
- [Lean-STaR: Learning to Interleave Thinking and Proving](https://mlsanity.com/paper/2407.10040/) (2024)
- [ReasonFlux: Hierarchical LLM Reasoning via Scaling Thought Templates](https://mlsanity.com/paper/2502.06772/) (2025)
- [Hierarchical Memory for High-Efficiency Long-Term Reasoning in LLM Agents](https://mlsanity.com/paper/2507.22925/) (2025)
- [FIMO: A Challenge Formal Dataset for Automated Theorem Proving](https://mlsanity.com/paper/2309.04295/) (2023)
- [Learning Formal Mathematics From Intrinsic Motivation](https://mlsanity.com/paper/2407.00695/) (2024)
- [miniCTX: Neural Theorem Proving with (Long-)Contexts](https://mlsanity.com/paper/2408.03350/) (2024)
- [DeepTheorem: Advancing LLM Reasoning for Theorem Proving Through Natural Language and Reinforcement Learning](https://mlsanity.com/paper/2505.23754/) (2025)
- [Formal Theorem Proving by Rewarding LLMs to Decompose Proofs Hierarchically](https://mlsanity.com/paper/2411.01829/) (2024)
- [Solving Inequality Proofs with Large Language Models](https://mlsanity.com/paper/2506.07927/) (2025)
- [HyperTree Planning: Enhancing LLM Reasoning via Hierarchical Thinking](https://mlsanity.com/paper/2505.02322/) (2025)
- [Beyond Fast and Slow: Cognitive-Inspired Elastic Reasoning for Large Language Models](https://mlsanity.com/paper/2512.15089/) (2025)

## Built on by (most cited first, 2 of 2)

- [The Missing Primitive: Diagnosing and Repairing Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2610.02191/) (2026)
- [Learning to Plan by Looking Back: Hindsight Hierarchies for Training Reasoning Models](https://mlsanity.com/paper/2610.12168/) (2026)

## Abstract (arXiv)

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 textttDeepInsight, a unified training framework designed to cultivate this essential reasoning skill and enable LLMs to perform insightful reasoning. Our framework consists of three components: (1) textttDeepInsightTheorem, a hierarchical dataset that structures informal proofs by explicitly extracting core techniques and proof sketches alongside the final proof; (2) a Progressive Multi-Stage SFT strategy that mimics the human learning process, teaching the model proof writing, planning, and insight identification; and (3) textttInsightPO, a policy optimization method that assigns structured rewards over this insight hierarchy. 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.