Goedel-Architect: Blueprint-Based AI Hits 99.2% on MiniF2F and Solves 4/6 IMO 2025 Problems

Forum topic · 小凯 · 2026-06-07

Summary

Goedel-Architect is a formal theorem proving system built on the open-weight DeepSeek-V4-Flash model that replaces traditional recursive lemma decomposition with a blueprint-driven approach. The system first generates a dependency graph (blueprint) of definitions and lemmas, optionally seeded by a natural-language proof sketch, then proves all sub-goals in parallel and refines the blueprint globally whenever a proof fails. Reported results include 99.2% pass@1 on MiniF2F-test (100% with natural-language seeding), 75.6% on PutnamBench (88.8% with seeding), 4/6 problems on IMO 2025, 11/12 on Putnam 2025, and 3/6 on USAMO 2026, at roughly 500x lower cost than comparable closed-source systems. The post analyzes why the blueprint method works through cognitive science, complexity science, and philosophy-of-mathematics lenses, and discusses implications for mathematical research, education, software verification, and AI safety. Paper: arXiv:2606.015xx by Jui-Hui Chung, Ziyang Cai, and Zihao Li.

Paper: Goedel-Architect: Streamlining Formal Theorem Proving with Blueprint Generation and Refinement Authors: Jui-Hui Chung, Ziyang Cai, Zihao Li arXiv: 2606.015xx Category: cs.AI | Posted: 2026-06-07

This forum post introduces Goedel-Architect, an AI system for formal theorem proving in Lean 4 that achieves striking competition-level results. Below is a structured English rendering of the original discussion.

Key points

Benchmark results:
MiniF2F-test: 99.2% pass@1 (243/244); 100% (244/244) with natural-language proof seeding
PutnamBench: 75.6% pass@1 (508/672); 88.8% (597/672) with seeding
IMO 2025: 4/6 problems solved (~silver-medal level, 28/42 points)
Putnam 2025: 11/12 solved; USAMO 2026: 3/6 solved
Cost advantage: Built on the open-weight DeepSeek-V4-Flash model (284B parameters, 13B activated), reportedly ~500x cheaper than comparable closed-source-model systems.

The core idea: blueprints instead of recursive decomposition

Prior formal-proving pipelines rely on recursive lemma decomposition: prove theorem A, discover it needs lemma B, prove B, discover B needs C, and so on. This is serial, prone to circular dependencies and dead ends, and lacks a global view of the proof.

Goedel-Architect instead works like an architect:

1. Blueprint generation: An LLM produces a dependency graph of formalized definitions and lemma statements, rooted at the target theorem. 2. Natural-language seeding: An informal proof sketch (human-written or LLM-generated) provides high-level intuition; the blueprint generator converts it into a structured dependency graph. 3. Parallel proving: All lemmas in the blueprint are proved concurrently rather than serially. 4. Failure-driven refinement: If a lemma proof fails, the system analyzes why (imprecise definitions, missing preconditions, wrong dependencies) and updates the *global* blueprint, then retries — analogous to revising an architectural blueprint rather than building on a flawed wall.

The post contrasts the two paradigms: recursive decomposition searches an exploration tree with local backtracking, while the blueprint method optimizes over a constructed graph with global visibility.

Background: why formal proving is hard

Lean 4 treats theorems as types and proofs as programs; a proof is correct iff it type-checks. This gives absolute rigor but a steep learning curve: a 5-line paper proof may require ~50 lines of formal code, and geometric intuition does not translate directly into formal steps.
The analogy used: rebuilding a cathedral out of individually numbered Lego bricks, following strict instructions.

Analysis offered in the post

Cognitive science (Global Workspace Theory): The blueprint acts as a global workspace where proof modules broadcast failures and other modules adapt — avoiding information silos.
Complexity science: Simple per-node rules plus self-organization yield emergent collective problem-solving capability, like an ant colony.
Philosophy of mathematics: The pipeline bridges intuition (natural-language seed), form (blueprint), and rigor (verified proof), suggesting intuition and formalism are complementary rather than opposed.

Implications discussed

Math research: Compressing months of failed proof attempts into hours of AI-guided exploration; humans shift from proof executors to problem posers, blueprint designers, and interpreters.
Education: Personalized proof tutoring, step-level logical feedback, and visualizable proof blueprints.
Software verification: Lowering the cost of formal verification so critical software could routinely be proven bug-free.
Safety and ethics: Automated theorem proving could expose cryptographic vulnerabilities; heavy student reliance on AI may erode mathematical intuition; success rates near human-elite levels force a rethink of what "creativity" means.

Closing thought

The post ends by echoing Gödel's incompleteness theorems: while unprovable truths exist, most practically important mathematical questions are provable — and AI systems like Goedel-Architect are learning to find those proofs. Gödel showed mathematics' boundary; Goedel-Architect shows how far we can build within it.

Reference: Chung, J.H., Cai, Z., Li, Z., et al. "Goedel-Architect: Streamlining Formal Theorem Proving with Blueprint Generation and Refinement." arXiv:2606.015xx (2026).