Why Agentic Theorem Prover Works: A Statistical Provability Theory of Mathematical Reasoning Models
arXiv:2602.10538v3 Announce Type: replace-cross Abstract: Agentic theorem provers combine a reasoning model, retrieval, search, and a proof assistant verifier, yet it remains unclear which components actually improve finite-budget proof success and why they help on real mathematical workloads. We study this question through statistical provability: the probability of reaching a verified proof within a budget on a specified stream of theorem instances. We model formal proof search as a finite-horizon reachability MDP with deterministic verifier dynamics, and show that under a faithful state abs
The rapid advancement of large language models and agentic AI systems has created a need to understand the underlying mechanisms of their success in complex reasoning tasks like theorem proving.
This research provides a theoretical framework 'Why Agentic Theorem Prover Works,' for understanding the efficacy of agentic AI in mathematical reasoning, which is a critical step towards more reliable and robust autonomous AI systems.
The understanding of agentic AI's capabilities and mechanisms for theorem proving shifts from empirical observation to a more formalized statistical provability theory.
- · AI research institutions
- · Theorem proving developers
- · AI agent developers
- · Formal verification specialists
- · Heuristic-only AI approaches
- · Traditional symbolic AI without integrative search
The theoretical understanding will guide the development of more efficient and powerful agentic AI systems for complex problem-solving.
Improved agentic theorem provers could accelerate scientific discovery and software verification, leading to new technological breakthroughs and more secure systems.
A robust theory of statistical provability might generalize to other complex reasoning domains, making AI agents more capable of autonomous decision-making in diverse fields.
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Read at arXiv cs.LG