Pythagoras-Prover: 4B model beats 671B DeepSeek with 86.1% on math proofs

Formal theorem proving in Lean typically requires massive compute and scarce verified data. A team of researchers from multiple institutions introduces Pythagoras-Prover, a family of open-source provers that dramatically reduce this cost. The family includes autoregressive models at 4B and 32B parameters, plus a first-of-its-kind diffusion-based prover (4B) that iteratively refines proofs at inference time. Key innovations include curriculum supervised fine-tuning (SFT) that trains models progressively from easy to hard proofs, and Augmented Lean Formalisation (ALF), which expands the verified corpus by mutating formal statements and generating training signals via self-distillation without full formal verification. This keeps each training instance within an 8k-token context, reducing compute while maintaining data quality.

Performance results are striking. Pythagoras-Prover-4B achieves 86.1% pass@32 on MiniF2F-Test, surpassing DeepSeek-Prover-V2-671B (82.4%) with roughly 167x fewer parameters. The 32B variant sets an open-source state-of-the-art at 93.0% on MiniF2F-Test and solves 93 of 672 PutnamBench problems, a notoriously hard competition. The team also releases MiniF2F-ALF, a contamination-sensitive benchmark where all models see accuracy drops—yet their 32B remains strongest and the 4B matches the prior SOTA (Goedel-Prover-V2-32B). This work demonstrates that efficient training and data augmentation can dramatically lower the barrier to high-performance automated theorem proving.