"A long-standing goal of artificial intelligence is to build systems capable of complex reasoning in vast domains, a task epitomized by mathematics with its boundless concepts and demand for rigorous proof. Recent AI systems, often reliant on human data, typically lack the formal verification necessary to guarantee correctness. By contrast, formal languages such as Lean1 offer an interactive environment that grounds reasoning, and reinforcement learning (RL) provides a mechanism for learning in such environments."
"We are providing an unedited version of this manuscript to give early access to its findings. Before final publication, the manuscript will undergo further editing. Please note there may be errors present which affect the content, and all legal disclaimers apply. Computational science Computer science A long-standing goal of artificial intelligence is to build systems capable of complex reasoning in vast domains, a task epitomized by mathematics with its boundless concepts and demand for rigorous proof."
Mathematics exemplifies a domain requiring complex, rigorous reasoning and formal proof. Many current AI systems depend heavily on human-generated data and lack guarantees of formal correctness. Formal proof assistants such as Lean provide an interactive environment that grounds symbolic reasoning and enforces formal verification. Reinforcement learning provides a mechanism to learn within these environments and discover proof strategies. AlphaProof is an AlphaZero-inspired reinforcement-learning agent designed to operate inside Lean to learn automated proof construction and verified reasoning. The approach aims to combine empirical learning with formal guarantees to produce provably correct mathematical solutions.
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