Machine Learning

LEAP: Supercharging LLMs for Formal Mathematics with Agentic Frameworks

Po-Nien Kung, Linfeng Song, Dawsen Hwang, Jinsung Yoon, Chun-Liang Li, Simone Severini, Mirek Olšák, Tomas Pfister, Nanyun Peng

Featured June 25, 2026

Original Paper

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Simply

A new AI system called LEAP helps smart computer programs (LLMs) write perfect, step-by-step math proofs by breaking big problems into small parts and checking each step with a special math checker, making them much better at formal theorem proving.

In depth

The paper introduces LEAP, an agentic framework that enables general-purpose Large Language Models (LLMs) to achieve state-of-the-art performance in automated formal theorem proving. It leverages LLMs' informal reasoning and self-refinement by decomposing complex problems into smaller units, bridging informal blueprints with formal proof construction through continuous interaction with a Lean compiler. This iterative, verification-guided search within a DAG-based hierarchical memoization structure allows LLMs to generate mechanically verifiable proofs, challenging the need for specialized models.

Key Takeaways

1
LEAP is an agentic framework that enables general-purpose LLMs to perform state-of-the-art formal theorem proving in Lean.
2
It uses a blueprint-driven approach with hierarchical decomposition and iterative self-correction guided by Lean compiler feedback.
3
The framework achieves a 100% solve rate on Putnam 2025 and significantly boosts performance on the new Lean-IMO-Bench, surpassing specialized provers.

Conceptual Flow

HIGH LEVEL

Methodology (The 'Logic')

The system breaks down hard math problems into smaller steps, plans how to solve them like a human, and then checks its work with a computer math checker, fixing mistakes along the way.

Hard Math Problem

Break Down & Plan

Small Steps

Checked Proof

Results (The 'Impact')

This new method helped the computer solve all the hard math problems from a big competition and did much better than other smart computer programs on a new, tough math test.

Old Way

New Way

Compare Performance

Solved Few Problems

Solved All Problems