Another great paper from Google.

Shows general LLMs can solve formal math by planning proofs and checking each step. Raised general LLM performance from under 10% to 70%.

A general LLM failed badly when asked to write full formal proofs in 1 try, but became much stronger when it planned, split the work into smaller claims, reused past claims, and learned from Lean’s feedback.

The paper shows the weakness was not just the model’s math ability, but the way it was being used - the absence of structured interaction with a verifier.

The key idea is that the model does not try to write one giant perfect proof at once, because that usually fails on long and tricky problems.

Instead, LEAP stores the proof as a graph of goals and subgoals, so useful lemmas can be reused instead of rediscovered every time.

The authors tested LEAP on Putnam 2025 and a new Lean benchmark built from 60 IMO-style problems, where ordinary one-shot proof writing did very poorly.

LEAP solved all 12 Putnam 2025 problems and raised general LLM performance on the Lean IMO benchmark from under 10% to 70%.

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Link – arxiv. org/abs/2606.03303

Title: "LEAP: Supercharging LLMs for Formal Mathematics with Agentic Frameworks"