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

Summary

This study examines how post-training and test-time inference affect natural-language proof generation for difficult olympiad mathematics. Starting from Nemotron 3 Ultra, the authors train two specialist checkpoints with supervised fine-tuning and reinforcement learning, then study checkpoint selection, proof verification, and refinement. Their open-model pipeline uses three checkpoints: the generally available model and the two specialists. It performs iterative search over candidate proofs, generating, verifying, and refining them in natural language, without a formal prover, external tools, or internet access. A separate high-compute stage selects the final submission for each problem. The system scores 30 of 42 points at IMO 2026, which reaches the competition’s gold-medal threshold. The authors release the two post-trained checkpoints, training data, training and inference code, submitted solutions, and Nemotron-IMO-Bench, a benchmark containing 200 new olympiad-level problems.