NVIDIA's Nemotron Scored 30 of 42 at IMO 2026 and Released the Entire Recipe

NVIDIA researchers reported in the technical report "An Open Recipe for IMO Gold," posted to arXiv on September 9, 2026, that a system built from three Nemotron 3 Ultra checkpoints scored 30 out of 42 points at the International Mathematical Olympiad 2026, clearing the gold-medal cutoff of 29. The system operates entirely in natural language, with no formal prover, external tools, or internet access, and every submitted proof was graded by official IMO graders. ASAP works only from the figures and design decisions stated in the report to identify what is actually new in this result.

The system is three checkpoints that take turns writing and grading

The backbone of the pipeline is an iterative generate-verify-refine search that the report credits to DeepSeekMath-V2. Generation draws on the general-availability model Nemotron-3-Ultra-GA, the supervised fine-tuning specialist Nemotron-3-Ultra-SFT, and the reinforcement learning specialist Nemotron-3-Ultra-RL. Round 1 produces 384 proof attempts, with each checkpoint sampling 16 attempts from each of eight complementary generation prompts. Those templates instruct the model to follow different solution strategies such as lemma-first decomposition, route comparison, and counterexample search, with the stated purpose of decorrelating round-1 generations.

Verification is handled by the SFT and RL checkpoints. Each produces eight independent judgments per proof, giving 16 equally weighted judgments. The scale has three values: 1 for a complete and correct proof, 0.5 for a generally correct proof with minor errors or omissions, and 0 for a proof with fatal errors or severe omissions. A proof is accepted only when all 16 judgments are valid and every one assigns a score of 1. The report states explicitly that accepted means satisfying this internal criterion and does not by itself imply correctness under independent or official grading.

When nothing is accepted, refinement rounds begin. The system selects up to 16 highest-ranked proofs from the pool, builds one refinement prompt for each with up to eight verifier critiques attached, sends every prompt to all three generation checkpoints and samples four outputs from each, producing 192 refinement attempts per round. Search runs for at most eight rounds.

A separate stage with a different objective sits before submission. The search-time verifier exists to produce critiques that guide refinement, while final selection exists to rank proofs for submission. Each finalist receives 16 independent IMO-style judgments from each of the three checkpoints, for 48 judgments in total, and finalists are ranked by the mean of those 48 scores with ties broken in favor of the shorter proof.

The competition log shows most of the work finished within 76 minutes

The official result is 30 out of 42 points against a gold-medal cutoff of 29 points. Problems 1, 2, 4, and 5 received full credit of 7 points each, while Problems 3 and 6 received one point each. The contest ran as two 4.5-hour sessions, with three problem searches running concurrently each day and sharing the full competition GPU allocation.

The time distribution is the most striking part of the log. The four full-credit proofs cleared the final-selection panel within the first 76 minutes of their session, and the remaining two within 100 minutes. Search plateaued thereafter, well before the 4.5-hour deadline.

Resource accounting is published alongside. All six submitted proofs were found within approximately 707 million generated tokens and 1,464 GB200 GPU-hours, and completing the rounds already in flight brought the full competition run to roughly 2.31 billion tokens and about 4,800 GPU-hours. The spread across problems is wide. Problem 1 reached its submitted proof on 5.57 million tokens and 11.7 GPU-hours, while Problem 6 consumed 312 million tokens and 612.9 GPU-hours and still scored one point.

The post-cutoff run is reported too. In round 8, after 8 hours and 25 minutes of total search time, Problem 6 produced a new solution that the internal verifier did not accept but that scored higher than the contest submission, at a cost of an additional 610 million tokens and 890 GPU-hours. A panel of independent human mathematicians awarded it 4 out of 7 points, which would raise the total to 33. The report notes this grading was performed without access to the official marking schemes and is not an official IMO result.

The release covers checkpoints, data, code, and a benchmark

The full release is gathered in the Hugging Face collection nvidia/nemotron-labs-imo-2026, covering checkpoints, training data, code, submitted proofs, and a new benchmark. The two post-trained checkpoints are released as nvidia/Nemotron-3-Labs-Ultra-Math-SFT and nvidia/Nemotron-3-Labs-Ultra-Math-RL under the OpenMDW-1.1 license of the base model, and the SFT corpus and RL problem set are released under CC BY 4.0.

Training composition is given down to the counts. The SFT corpus contains 414,890 quality-filtered examples over 15,818 unique problems, split into 58,543 proof-generation traces, 67,971 refinement traces, 236,360 verification traces, and 52,016 meta-verification traces. Verification traces making up more than half the corpus shows that the training objective was judging proofs as much as writing them. The SFT run used 512 GB200 GPUs, and the checkpoint at step 1300 was selected on evaluation performance across 133 proof-based problems drawn from IMO-ProofBench and recent competitions.

RL drew problems from Nemotron-Math-Proofs-v1, keeping only those Nemotron 3 Ultra solved in one to three of four attempts as judged by DeepSeek-V3.2-Speciale, which yielded 9,597 problems. Training used 128 trainer nodes, 128 inference nodes, and 16 judge nodes, each node holding four GB200 GPUs.

The benchmark is a separate artifact. Nemotron-IMO-Bench, created with olympiad problem author Professor Titu Andreescu, contains 200 novel olympiad-level problems never published before, released under CC BY 4.0. Experiments in the report run on a 30-problem development set combining 20 problems from that benchmark with 10 from recent competitions, containing 3 easy, 7 medium, 10 hard, and 10 unsolved problems, and spanning 6 algebra, 8 combinatorics, 8 geometry, and 8 number-theory problems.

What is new here is the accounting, not the gold medal

What follows is ASAP's reading. Reaching gold-medal level in natural language is not itself news in 2026. The report states plainly that Gemini Deep Think and an experimental OpenAI model both reached gold with end-to-end natural-language systems at IMO 2025, and that AlphaProof combined with AlphaGeometry 2 landed one point below the gold cutoff at IMO 2024. On score alone, this result extends a line rather than breaking one.

Where this report diverges from those predecessors is after-the-fact verifiability. The two 2025 gold results shipped no models, no data, and no pipeline; outsiders could inspect only the announced scores and solutions. This time the two post-trained checkpoints, the training data, the training and inference code, the submitted proofs, and the resource accounting all arrived together. Putting the same score into a state where another team can reproduce or refute it is the report's real contribution.

Publishing the resource accounting belongs to the same logic. Papers rarely state how many tokens and GPU-hours a medal cost. Once 707 million tokens and 1,464 GPU-hours are public, the achievement stops being a question of whether a capability exists and becomes a question of price, which turns follow-up work into competition over reaching the same score more cheaply. Against the convention of reporting benchmark scores alone, that shift is not small.

The gap between the verifier's 32 and the graders' 30 marks the system's ceiling

The most candid passage in the report is where the authors show their own verification failing. At the contest cutoff, both the internal search verifier and the post-hoc independent model jury assigned roughly 32 points, while the official result was 30. The discrepancy came entirely from Problems 3 and 6, where both model-based evaluations credited proofs that official graders scored at one point.

The diagnosis attached to that gap matters. The report attributes it to a shared blind spot in model-based verification rather than noise specific to the search-time verifier. If separate models grouped into a jury fail together at the same place, enlarging the jury cannot erase the error.

The verifier audit points the same way. The researchers audited verification rules on 300 proofs, and of the 25 proofs the deployed panel accepted, 23 received a jury score of 7. One received 6 for a minor quantifier formality. One received 0: its argument rests on an invalid column-permutation symmetry step, refuted by an explicit counterexample. Every checkpoint gave both of those proofs eight full-score judgments, so no unanimity rule over those 24 judgments would have caught them.

Treating false accepts and false rejects as different costs drove the design

The stated basis for the verifier design is asymmetry rather than accuracy. A false accept ends the search for a problem on an invalid proof, and no later stage generates new candidates. A false reject only delays: the proof keeps its high mean score, typically stays among the top-ranked refinement candidates, and remains eligible as the fallback submission if nothing is accepted. That is why the search-time verifier uses only the two selective checkpoints and demands unanimity.

The numbers support the choice. Lowering the acceptance rule from 16 of 16 to 14 of 16 raises the false-accept rate from about 1% to 17%, meaning each correct proof the relaxed rule recovers is matched by an incorrect one it admits. Adding the permissive GA checkpoint's eight judgments to the panel does not help either; the only two proofs it removes are correct ones.

The source of the panel's precision is decomposed as well. SFT alone accepts eight incorrect proofs, and RL's eight judgments reject six of them, cutting the false-accept rate from 4.5% to 1.1%, while GA in the same slot rejects only two and leaves it at 3.4%. Under unanimity every judgment is another veto, and RL's vetoes land where SFT's do not.

Sampling from a different model beat sampling more from the same one

The experiment behind the ensemble design compares where to spend the round-1 budget. Running the RL checkpoint for 128 attempts accepts 13 of the 30 development-set problems and earns 87 independent-jury points on accepted proofs and 135 across all 30. Doubling that same checkpoint to 256 attempts moves the result to 14 accepted problems with 92 and 139 points. Spending the same tokens on 64 SFT attempts instead reaches 15 accepted problems with 98 and 159 points.

The cause is non-overlapping coverage. Of the 18 problems accepted by the combined RL 128 plus SFT 128 pool, six are accepted from both checkpoints, seven only from RL, and five only from SFT, and doubling RL to 256 attempts recovers just one of those five.

One caution applies when generalizing this. All three checkpoints descend from the same base model and differ only in post-training. That they still solve disjoint problems suggests returns from more samples saturate quickly on hard reasoning tasks and that mixing models with different training histories pays better. GA added no problem in round 1 that RL or SFT did not already accept, yet stayed in every round as a source of refinement diversity.

The transferable part of this report is the verification design

The part of NVIDIA's pipeline that transfers to any scale is the verification design, not the 272 GB200 nodes behind it. First is the habit of refusing to collapse two error types into one metric. Any system with automated approval or automated scoring has different costs for wrongly passing and wrongly blocking, and this report sets its threshold by asking which error is irreversible before asking which rule is most accurate.

Second is mixing judge models while keeping permissive ones out of a unanimity panel. The moment a panel requires unanimity rather than majority, an added model should be evaluated by the distribution of its vetoes rather than by its accuracy. A permissive model rarely vetoes, so it cannot raise precision and only strips out correct results.

Third is acknowledging the ceiling of self-grading. This system predicted 32 points for itself and received 30, and the report states directly that the gap came from a blind spot the models share. Any team introducing AI review of AI output should design a recurring measurement of the gap between internal review and external grading from the start.

Three questions the report leaves open

NVIDIA's September 2026 report leaves three notable gaps, and the first is a basis for comparing cost against performance. The authors state directly that the ensemble run is not compute-matched to the single-checkpoint runs, and only the round-1 budget experiment equalizes tokens. Neither Gemini Deep Think nor the experimental OpenAI model ever disclosed what their 2025 gold results cost, so whether this system is cheaper or more expensive remains unknown.

The second is why Problems 3 and 6 stalled. Both scored one point, and Problem 3 did not improve even in the extended post-cutoff search. The report accounts for them in tokens and GPU-hours without analyzing what kind of reasoning blocked them. Including 10 unsolved problems in the development set shows the researchers know where that boundary sits, but characterizing it is left to future work.

The third is the independence of evaluation. RL training used GPT-5.5 as its evaluator, the ablation jury consists of GPT-5.5, Gemini 3.1 Pro, and Claude Opus 4.8, and RL data filtering was judged by DeepSeek-V3.2-Speciale. Handing evaluation of one's own model to competitors' models reduces self-grading bias, yet the 32 versus 30 split against official graders shows the common blind spot of model-based grading survives that precaution.

The center of this result is not the number 30 out of 42 but the decision to leave the machinery behind that number open for other teams to take apart. Gold-medal level natural-language proving was reached in 2025; what 2026 adds is a reproducible reference point with checkpoints, data, and token accounting attached.

Source: Ivan Moshkov et al., "An Open Recipe for IMO Gold: Training Nemotron for Olympiad Mathematics" (arXiv:2609.10712, September 9, 2026); artifacts in the Hugging Face collection nvidia/nemotron-labs-imo-2026