# LeanConjecturer: Automatic Generation of Mathematical Conjectures for Theorem Proving

arXiv: https://arxiv.org/abs/2506.22005 · HTML: https://mlsanity.com/paper/2506.22005/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jun 2025.

## Built on by (most cited first, 8 of 8)

- [MathlibLemma: Folklore Lemma Generation and Benchmark for Formal Mathematics](https://mlsanity.com/paper/2602.02561/) (2026)
- [COMPOSE: Composing Future Theorems from Citations and Formal Structure](https://mlsanity.com/paper/2605.30333/) (2026)
- [The Problem Is the Problem: Towards Scalable Mathematical Discovery](https://mlsanity.com/paper/2608.16977/) (2026)
- [MathlibPR: Pull Request Merge-Readiness Benchmark for Formal Mathematical Libraries](https://mlsanity.com/paper/2605.07147/) (2026)
- [MECA: A Mechanism-Centered Agent for Constructing Well-Specified and Valuable Mathematical Conjectures](https://mlsanity.com/paper/2607.27709/) (2026)
- [LLM Framework for Discovering Major Mathematical Conjectures: AI's Quest for the Next Riemann Hypothesis](https://mlsanity.com/paper/2607.28632/) (2026)
- [Delta1 with LLM: symbolic and neural integration for credible and explainable reasoning](https://mlsanity.com/paper/2603.12953/) (2026)
- [LANTERN: Illuminating Hidden Mathematical Knowledge in Language Models](https://mlsanity.com/paper/2609.32264/) (2026)

## Abstract (arXiv)

We introduce LeanConjecturer, a pipeline for automatically generating university-level mathematical conjectures in Lean 4 using Large Language Models (LLMs). Our hybrid approach combines rule-based context extraction with LLM-based theorem statement generation, addressing the data scarcity challenge in formal theorem proving. Through iterative generation and evaluation, LeanConjecturer produced 12,289 conjectures from 40 Mathlib seed files, with 3,776 identified as syntactically valid and non-trivial, that is, cannot be proven by textttaesop tactic. We demonstrate the utility of these generated conjectures for reinforcement learning through Group Relative Policy Optimization (GRPO), showing that targeted training on domain-specific conjectures can enhance theorem proving capabilities. Our approach generates 103.25 novel conjectures per seed file on average, providing a scalable solution for creating training data for theorem proving systems. Our system successfully verified several non-trivial theorems in topology, including properties of semi-open, alpha-open, and pre-open sets, demonstrating its potential for mathematical discovery beyond simple variations of existing results.