LeanConjecturer: Automatic Generation of Mathematical Conjectures for Theorem Proving
This addresses the data scarcity challenge for researchers and developers in automated theorem proving, though it is incremental as it builds on existing LLM and rule-based methods.
The authors tackled the data scarcity problem in formal theorem proving by developing LeanConjecturer, a pipeline that automatically generates university-level mathematical conjectures using LLMs, producing 12,289 conjectures with 3,776 identified as syntactically valid and non-trivial, and demonstrating utility in enhancing theorem proving through reinforcement learning.
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 \texttt{aesop} 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.