Goedel-Architect: Streamlining Formal Theorem Proving with Blueprint Generation and Refinement

Goedel-Architect is a new AI framework for formal theorem proving that uses blueprint generation and refinement to achieve state-of-the-art results on mathematical benchmarks. Built on DeepSeek-V4-Flash, it demonstrates significant improvements in solving complex mathematical problems while maintaining cost efficiency up to 500x lower than comparable solutions.

Goedel-Architect represents a meaningful advancement in AI-assisted formal mathematics by introducing a blueprint-based architecture that fundamentally differs from recursive decomposition approaches. The framework generates dependency graphs of definitions and lemmas that build toward a target theorem, then leverages parallel processing to close lemmas using relevant dependencies. Failed attempts trigger blueprint refinement rather than unproductive looping, suggesting more efficient problem-solving pathways. The achievement of 100% on MiniF2F-test, 88.8% on PutnamBench with natural language seeding, and notable results on IMO 2025 and Putnam 2025 problems demonstrates the approach's viability for increasingly difficult mathematical domains. The use of open-weight DeepSeek-V4-Flash as the backbone is particularly significant—it signals that high-performance AI mathematics doesn't require proprietary frontier models, democratizing access to formal theorem proving capabilities. This cost advantage (500x cheaper than comparable pipelines) matters substantially for academic research, which historically faced constraints in leveraging AI for mathematical verification. The framework's ability to integrate natural language proof guidance suggests a practical bridge between human mathematical intuition and formal verification systems. Looking ahead, such systems could accelerate mathematical research by automating verification bottlenecks and enabling broader exploration of proof spaces. The open-source nature creates potential spillover effects across academia and industry. Future developments to monitor include scaling beyond competition problems to open research questions and extending the approach to other formal verification domains beyond Lean 4.

• →Goedel-Architect achieves 100% on MiniF2F-test and 88.8% on PutnamBench using open-weight models at drastically lower cost than proprietary alternatives
• →Blueprint-based architecture with parallel lemma-solving outperforms traditional recursive decomposition by avoiding dead-end proof strategies
• →Integration of natural language proof guidance significantly improves performance on harder mathematical problems
• →Open-source pipeline democratizes access to AI-assisted formal mathematics, removing cost barriers for academic researchers
• →Success on IMO 2025, Putnam 2025, and USAMO 2026 problems demonstrates applicability to genuinely difficult unsolved mathematical challenges