Numina-Lean-Agent: An Open and General Agentic Reasoning System for Formal Mathematics

2026-01-20

AI Summary

Existing formal mathematical reasoning systems rely on task-specific pipelines and specialized models, limiting their generality and reproducibility. This work proposes the first approach that directly leverages general-purpose code agents for formal mathematical reasoning, enabling performance improvements through base model substitution without additional training. Built upon Claude Opus 4.5 and integrated with the Lean theorem prover via an MCP architecture, the system autonomously performs interactive theorem proving, lemma retrieval, and auxiliary reasoning. It achieves a perfect score on all 12 problems of the Putnam 2025 competition and successfully assists in the formalization of the Brascamp–Lieb inequality. The implementation and solutions are publicly released.

Technology Category

• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Multiagent Systems: Adversarial Agents
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Search and Retrieval-Augmented AI: Agentic search

Abstract

Agentic systems have recently become the dominant paradigm for formal theorem proving, achieving strong performance by coordinating multiple models and tools. However, existing approaches often rely on task-specific pipelines and trained formal provers, limiting their flexibility and reproducibility. In this paper, we propose the paradigm that directly uses a general coding agent as a formal math reasoner. This paradigm is motivated by (1) A general coding agent provides a natural interface for diverse reasoning tasks beyond proving, (2) Performance can be improved by simply replacing the underlying base model, without training, and (3) MCP enables flexible extension and autonomous calling of specialized tools, avoiding complex design. Based on this paradigm, we introduce Numina-Lean-Agent, which combines Claude Code with Numina-Lean-MCP to enable autonomous interaction with Lean, retrieval of relevant theorems, informal proving and auxiliary reasoning tools. Using Claude Opus 4.5 as the base model, Numina-Lean-Agent solves all problems in Putnam 2025 (12 / 12), matching the best closed-source system. Beyond benchmark evaluation, we further demonstrate its generality by interacting with mathematicians to successfully formalize the Brascamp-Lieb theorem. We release Numina-Lean-Agent and all solutions at https://github.com/project-numina/numina-lean-agent.

Problem

• formal theorem proving
• agentic reasoning
• flexibility
• reproducibility
• general coding agent

Innovation

• agentic reasoning
• formal mathematics
• general coding agent
• MCP
• Lean