AI Discovers Theorems Autonomously Without Human Priors

This research introduces an AI agent capable of autonomously discovering mathematical theorems within a formal axiomatic system. Unlike many existing AI approaches that leverage human mathematical knowledge, this agent starts solely with axioms and inference rules. It employs a self-supervised algorithm that iteratively performs proof searches and extracts useful theorems, building a library that then serves as lemmas for subsequent searches. Experiments demonstrate the agent's ability to uncover thousands of theorems and solve human-written benchmark problems, indicating the mathematical significance of its findings. Furthermore, these machine-discovered theorems can enhance the performance of large language models in proof generation when provided as external knowledge. This work suggests a novel pathway for developing self-evolving AI systems in mathematics, where discoveries are formally verifiable.