DeepSeek V4 does mathematical proof: Princeton breaks record with 500 times cost advantage

The field of mathematics is being profoundly impacted by AI. In May 2026, OpenAI overturned the 80-year-old "unit distance conjecture". Fields Medal winner Gowers called it an "epoch-making milestone". Terence Tao announced that he would give up following up on all new proofs in real time: "Mathematics is moving from an era of proof scarcity to an era of proof excess."

Against this background, the Princeton University PLI team (Sanjeev Arora + Chen Danqi) used DeepSeek V4 Flash to build the Goedel-Architect agent framework and complete all 672 PutnamBench questions for $294 - the previous Hilbert system driven by Google Gemini 2.5 Pro required $170,000. The pass rate is 75.6% vs 70.0%, and the cost advantage is about 500 times. MiniF2F-test reached 99.2%, becoming the first system to clear all 244 questions.

Core Innovations of Goedel-Architect

The concept of "Blueprint" is a key breakthrough of Goedel-Architect - a directed acyclic graph is generated before proving, including all definitions and dependencies of the lemma, and then distributed to the Lean prover for parallel processing. Failure is not an end but a diagnostic signal: the system automatically corrects incorrect propositions and breaks down difficult-to-prove lemmas through "blueprint refinement." Experiments with controlled variables prove that the key to the 500x cost advantage lies in pipeline design rather than better models.

Core R&D Team

PLI's founding director Sanjeev Arora (winner of the ACM Computing Award) and Chen Danqi (90,000+ Google Scholar citations, Tsinghua undergraduate/Stanford PhD) are co-led. The team has previously released the Goedel-Prover series, which improves MiniF2F from 60% to 90%.

Benchmark results

• PutnamBench: 75.6% pass@1 (Hilbert 70.0%), 88.8% after natural language assistance
• MiniF2F-test: 99.2% (the first to clear all 244 questions)
• IMO 2025: 4/6 questions
• Putnam 2025: 11/12 questions
• USAMO 2026: 3/6 questions (contamination immunity test)

The 500-fold cost advantage comes from the dual innovation of DeepSeek’s ultimate cost-effectiveness and blueprint refinement framework. Formal theorem proving is an important direction for AI alignment and trustworthiness—Lean compilers provide certainty that is more reliable than any peer review. What is more symbolic is that a top Princeton team chose the Chinese open source model instead of the American closed source model to complete this breakthrough work, which has a profound impact on the global AI research ecosystem.

Worth following up on:

1. Open source diffusion: Can the Goedel-Architect framework be used by other models (Doubao/GLM) to reproduce similar effects?
2. Research Ecological Signal: The impact of Princeton’s decision to use China’s open source model on the global AI academic community
3. Industrialization of formal verification: Application prospects in key software verification, smart contract auditing and other scenarios