Goedel-Prover v2: Open-Source AI Theorem Prover with Lean Formal Verification

In recent years, AI models have learned to solve increasingly complex mathematical problems — up to the level of the International Mathematical Olympiad (IMO). Yet one problem remained: verifying the correctness of such solutions still required a human expert.

This challenge stems from the nature of large language models as “black boxes.” They can produce a proof that looks perfectly reasonable, but there is no way to guarantee its actual correctness.

A New Generation of AI Theorem Provers

In July 2025, researchers from Princeton introduced Goedel-Prover v2 — an updated version of an open-source AI theorem prover built on the Lean formal verification language. Lean allows mathematical statements to be proved rigorously, with every step of the reasoning verified against strict mathematical rules.

Goedel-Prover v2 is capable of:

• generating mathematical proofs,
• verifying their rigor within Lean,
• automatically correcting errors in its own reasoning via a self-correction mode.

Benchmark Results: From 60% to 90% Accuracy

The model was evaluated across three benchmarks:

• PutnamBench — university-level competition problems,
• miniF2F — high-school-level mathematics,
• MathOlympiadBench — IMO-level problems.

Accuracy on miniF2F improved from 60% in the first version to 90% in v2. Notably, Goedel-Prover operates with a 32-billion-parameter model and runs on computational resources available in an academic setting — roughly 20 times less than those used by competing systems.

Scaffolded Learning: How the AI Theorem Prover Trains Itself

A distinctive feature of the system is its scaffolded learning regime. When the model cannot solve a given problem, it generates simpler variants, solves those, and incorporates them into its own training data. This allows the model to accumulate useful examples and improve without external intervention.

The core correctness guarantee comes from Lean itself: every proof is formalized and verified against mathematical axioms, eliminating the ambiguity inherent in natural language reasoning.

Toward a Closed-Loop AI for Formal Mathematics

This architecture has the potential to create a fully closed learning loop — where an AI theorem prover generates problems, constructs proofs, verifies them, and continuously expands its own mathematical repertoire without human oversight.

According to the authors, this represents one of the key steps toward building a genuine AI co-author in mathematics.