An Open Recipe for IMO Gold: Training Nemotron for Olympiad Mathematics
Ivan Moshkov, Stephen Ge, George Armstrong, Wei Du, Sadegh Mahdavi, Igor Gitman
NVIDIA
Published September 9, 2026 · on the feed September 11, 2026 · ▲ 43 · arXiv 2609.10712
The abstract
We study how model post-training and test-time inference design affect natural-language proof generation for hard olympiad mathematics. Starting from Nemotron 3 Ultra, we train two specialist checkpoints using supervised fine-tuning and reinforcement learning, and evaluate checkpoint choice, verification, and refinement. Based on these findings, we present an open-model test-time-compute pipeline. The system operates entirely in natural language, with no formal prover, external tools, or internet access. Three Nemotron 3 Ultra checkpoints - the general-availability model and two post-trained specialists - power an iterative search that generates, verifies, and refines candidate proofs; a separate high-compute stage then selects each final submission. The system scored 30 out of 42 points at IMO 2026, reaching the gold-medal threshold. We release the two post-trained checkpoints as well as the training data, the training and inference code, the submitted solutions, and Nemotron-IMO-Bench, a new benchmark of 200 novel olympiad-level problems.
The Brief
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Transcript
An Open Recipe for IMO Gold. Training Nemotron for Olympiad Mathematics. By Ivan Moshkov and five others, from NVIDIA. Published on the ninth of September. No code repository is linked to it.
Writing natural-language proofs for hard olympiad mathematics is a demanding test for a language model. The authors ask how two sets of choices shape the result: how the model is post-trained, and how inference is designed at test time. Both matter. A strong model can be held back by a weak way of searching for proofs, and a clever search can only do so much with a model that was never trained for the task. The study treats the two together.
Their answer is an open recipe. Starting from Nemotron 3 Ultra, they train two specialist checkpoints and study checkpoint choice, verification and refinement. What they learn becomes an open-model pipeline that spends compute at test time, and that pipeline operates entirely in natural language: no formal prover, no external tools, no internet access.
The specialists are trained with supervised fine-tuning and reinforcement learning. Three Nemotron 3 Ultra checkpoints then power an iterative search: the general-availability model and the two post-trained specialists. The search generates candidate proofs, verifies them, and refines them. A separate, high-compute stage then selects the final submission for each problem.
At IMO 2026, the system scored thirty out of forty-two points, which reached the threshold for a gold medal. That result was produced by a system with no formal verification behind it. Every step, from drafting a proof to checking it to choosing which version to submit, was done by the models themselves, in ordinary mathematical prose.
The release is what gives the title its word open. It includes the two post-trained checkpoints, the training data, the code for training and for inference, and the submitted solutions. It also includes Nemotron-IMO-Bench, a new benchmark of two hundred novel olympiad-level problems. Gold-level olympiad proof writing, on this account, is reachable with open models, plain language, and a search that checks its own work.
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Chapter 1 🧩 · The problem
An olympiad, a proof to write, and no formal checker to lean on. Where would you start?
You want an open model to write full olympiad proofs in plain mathematical prose. No formal prover, no external tools, no internet: every check has to be done by the models themselves.
The road ahead
- 1 · The problem ~6 min An open model must write and check full olympiad proofs in plain prose, with no formal checker to lean on, and effort is limited.
- 2 · What came before ~3 min
- 3 · The key idea ~8 min Draft proofs from several differently trained checkpoints, let model verifiers score and critique them, refine over rounds, then pick each submission in a separate heavy judging stage.
- 4 · Choose your own research ~3 min
- 5 · Build the method ~8 min Train two specialists, draft proofs with three checkpoints, verify them with model panels, refine from critiques, then select each submission in a heavy final stage.
- 6 · The experiment ~6 min You’ll guess: Working only in natural language, with no formal prover, tools or internet, how did the open pipeline score at IMO 2026?
- 7 · The viva ~5 min Three questions from the examiners, answered in your own words. Win it for the paper’s trophy.
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