An Open Recipe for IMO Gold: Training Nemotron for Olympiad Mathematics

NVIDIA presents an open, natural-language recipe for olympiad-level proof generation built on three Nemotron 3 Ultra 550B-A55B checkpoints: the general-availability model, a supervised-fine-tuned specialist, and a reinforcement-learned specialist. The system performs iterative generate-verify-refine search, using complementary prompts and independent verifier panels, then applies a separate high-compute selection stage; it uses no formal prover, external tools, or internet access. Supervised fine-tuning combines proof construction, refinement, verification, and meta-verification traces into a corpus of 414890 quality-filtered examples, while reinforcement learning trains on difficult problems with asynchronous sampling. On a 30-problem development set, the full ensemble reaches a 188-point end-to-end jury score, outperforming any single checkpoint; the key benefit comes from checkpoint diversity rather than simply doubling samples from one model. For verification, unanimous agreement between the RL and SFT panels reduces false accepts to 1.1%, although it increases false rejects, favoring safe continued search. At IMO 2026, the pipeline scored 30 out of 42 points, above the 29-point gold threshold, earning full credit on Problems 1, 2, 4, and 5. The release includes the post-trained checkpoints, code, training data, submitted proofs, and Nemotron-IMO-Bench, a benchmark of 200 novel olympiad-level problems. The work contrasts with formal systems such as AlphaGeometry and DeepSeekProver, while its model-based judging is evaluated alongside GPT-5.5, Gemini 3.1 Pro, and Claude Opus 4.8.