AIMO-2 Winning Solution: Building State-of-the-Art Mathematical Reasoning Models with OpenMathReasoning dataset
Paper • 2504.16891 • Published • 27
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expected_answer string | problem_type string | problem_source string | generation_model string | pass_rate_72b_tir string | problem string | generated_solution string | inference_mode string |
|---|---|---|---|---|---|---|---|
\(\frac{C_{n_1}^{a_1} \cdot C_{n_2}^{a_2} \cdot \ldots \cdot C_{n_C}^{a_C}}{C_N^A}\) | has_answer_extracted | aops_c6_high_school_olympiads | DeepSeek-R1 | 0.65625 | Given a group of \( N \) balls consisting of \( C \) colors, where the number of balls in each color is represented as \( n_1, n_2, \ldots, n_C \) (with \( n_1 + n_2 + \ldots + n_C = N \)), what is the probability that when \( A \) balls are randomly picked (where \( A \leq N \)), the picked balls consist of \( a_1, a_... | <think>
Okay, so I need to find the probability that when I pick A balls out of N, where there are C different colors, the number of each color I pick is exactly a1, a2, ..., aC. Hmm, let's think about how to approach this.
First, probability problems often involve combinations. The general formula for probability is ... | cot |
\frac{n(n-1)}{2} | no_answer_extracted | aops_c4_high_school_math | DeepSeek-R1 | n/a | How many lines can be drawn that are equidistant from \( n \) given points in the plane? | <think>
Okay, so the problem is asking how many lines can be drawn that are equidistant from n given points in the plane. Hmm, let me try to wrap my head around this.
First, I need to recall what it means for a line to be equidistant from points. I think when we say a line is equidistant from two points, it's the per... | cot |
\( f(x) = f(1)x \) | has_answer_extracted | aops_c6_high_school_olympiads | DeepSeek-R1 | 0.5625 | Find all functions \( f: \mathbb{R} \to \mathbb{R} \) such that
\[
(f(x^2) + f(xy) + f(y^2))(x - y) = f(x^3) - f(y^3)
\]
for all \( x, y \in \mathbb{R} \). | <think>
Okay, let's try to solve this functional equation problem. The equation given is:
\[
(f(x^2) + f(xy) + f(y^2))(x - y) = f(x^3) - f(y^3)
\]
We need to find all functions \( f: \mathbb{R} \to \mathbb{R} \) that satisfy this for all real numbers \( x \) and \( y \). Hmm, functional equations can be tricky, but m... | cot |
2 | has_answer_extracted | aops_c6_high_school_olympiads | DeepSeek-R1 | 0.625 | Find the sum of the roots of the equation \((x+6)^{1/3} + (x-2)^{1/2} = 2\). | <think>
Okay, let's see. I need to find the sum of the roots of the equation \((x+6)^{1/3} + (x-2)^{1/2} = 2\). Hmm, roots are the solutions for x that satisfy this equation. The sum of the roots would be all the solutions added together. But wait, how many roots does this equation have? Let me think.
First, let's ana... | cot |
32 | has_answer_extracted | aops_c6_high_school_olympiads | QwQ-32B | 0.0 | Determine how many 1000 digit numbers \( A \) have the property that when any digit of \( A \), aside from the first, is deleted to form a 999 digit number \( B \), then \( B \) divides \( A \). | <think>
Okay, so I need to figure out how many 109-digit numbers A have the property that if you delete any digit except the first one to form a 999-digit number B, then B divides A. Hmm, let's try to break this down step by step.
First, let's make sure I understand the problem correctly. We have a 1000-digit number A... | cot |
\(\frac{2}{\pi} + \frac{32}{9\pi^2}\) | has_answer_extracted | aops_c7_college_math | DeepSeek-R1 | 0.4375 | Calculate the integral
\[
\int^{\frac{3\pi}{2}}_{\frac{\pi}{2}} \left|\left(\frac{2}{x^3}+\frac{1}{x}\right)\sin x\right|dx
\] | <think>
Okay, let me try to solve this integral. So the problem is to compute the integral from π/2 to 3π/2 of the absolute value of (2/x³ + 1/x) times sin x dx. Hmm, that looks a bit intimidating at first glance, but let's break it down step by step.
First, I remember that when dealing with integrals involving absolu... | cot |
1 | converted_proof | aops_c6_high_school_olympiads | QwQ-32B | n/a | In $\triangle ABC$ with incenter $I$, points $P$ and $Q$ are on side $BC$ such that $AP$ and $AQ$ are isogonal conjugates with respect to $\angle BAC$. The tangent line at $B$ of $\odot (ABP)$ and the tangent line at $C$ of $\odot (ACQ)$ intersect at $D$. Let $E = AP \cap IB$ and $F = AQ \cap IC$. If $DI$ intersects $E... | <think>
Alright, let me try to tackle this geometry problem step by step. It's a bit complex, but I'll break it down as much as possible. First, let me restate the problem to make sure I understand it correctly.
We have triangle ABC with incenter I. Points P and Q are on side BC such that AP and AQ are isogonal conjug... | cot |
\(\frac{(3-\sqrt{3})(2-\sqrt{3})^{2016}+(3+\sqrt{3})(2+\sqrt{3})^{2016}}{6}\) | has_answer_extracted | aops_c6_high_school_olympiads | DeepSeek-R1 | 0.0 | Let \( x_0 = 1 \), and \( x_{n+1} = 2x_n + \sqrt{3x_n^2 - 2} \). Determine \( x_{2016} \). | "<think>\nOkay, let's see. The problem is about a recursive sequence where x₀ is 1, and each subse(...TRUNCATED) | cot |
$\sqrt[2012]{2013!} > \sqrt[2013]{2012!}$ | has_answer_extracted | aops_c6_high_school_olympiads | DeepSeek-R1 | 0.0625 | Which is greater, $\sqrt[2012]{2013!}$ or $\sqrt[2013]{2012!}$? | "<think>\nOkay, so I need to figure out whether the 2012th root of 2013 factorial is greater than th(...TRUNCATED) | cot |
20 | has_answer_extracted | aops_c6_high_school_olympiads | DeepSeek-R1 | 0.9375 | On average, how long will you have to flip a coin to get the sequence $HTHT$? | "<think>\nOkay, so I need to figure out the expected number of coin flips needed to get the sequence(...TRUNCATED) | cot |
End of preview.
OpenMathReasoning
OpenMathReasoning is a large-scale math reasoning dataset for training large language models (LLMs). This dataset contains
- 540K unique mathematical problems sourced from AoPS forums,
- 3.2M long chain-of-thought (CoT) solutions
- 1.7M long tool-integrated reasoning (TIR) solutions
- 566K samples that select the most promising solution out of many candidates (GenSelect)
We used Qwen2.5-32B-Instruct to preprocess problems, and DeepSeek-R1 and QwQ-32B to generate solutions.
This dataset was a foundation of our winning submission to the AIMO-2 Kaggle competition.
See our paper to learn more details!
NOTE: An early version of this data was released separately in Llama-Nemotron-Post-Training-Dataset.
Dataset fields
OpenMathReasoning dataset contains the following fields:
- problem: Problem statement extracted from AoPS forums and refined with Qwen2.5-32B-Instruct
- generated_solution: Synthetically generated solution using either DeepSeek-R1 or QwQ-32B
- generation_model: DeepSeek-R1 or QwQ-32B
- problem_type: Can be one of "has_answer_extracted", "no_answer_extracted" and "converted_proof" dependening on whether we were able to extract the answer or if this is a proof question converted to answer question.
- expected_answer: Extracted answer if "problem_type" is "has_answer_extracted". Otherwise this is the majority-voting answer across all generated solutions for this problem.
- problem_source: States the corresponding AoPS forum (e.g. "aops_c6_high_school_olympiads") or "MATH_training_set" as we also include a small set of generations from MATH.
- inference_mode: "cot", "tir" or "genselect"
- pass_rate_72b_tir: Pass rate out of 32 generations for Qwen2.5-Math-72B-Instruct run in TIR mode. This attribute is only available when "problem_type" is "has_answer_extracted" and is set to "n/a" for other cases.
OpenMath-Nemotron models
To demonstrate the quality of this dataset, we release a series of OpenMath-Nemotron models trained on this data.
- OpenMath-Nemotron-1.5B
- OpenMath-Nemotron-7B
- OpenMath-Nemotron-14B
- OpenMath-Nemotron-14B-Kaggle (this is the model used in AIMO-2 Kaggle competition)
- OpenMath-Nemotron-32B
The models achieve state-of-the-art results on popular mathematical benchmarks. We present metrics as pass@1 (maj@64) where pass@1 is an average accuracy across 64 generations and maj@64 is the result of majority voting. Please see our paper for more details on the evaluation setup.
| Model | AIME24 | AIME25 | HMMT-24-25 | HLE-Math |
|---|---|---|---|---|
| DeepSeek-R1-Distill-Qwen-1.5B | 26.8 (60.0) | 21.4 (36.7) | 14.2 (26.5) | 2.9 (5.0) |
| OpenMath-Nemotron-1.5B CoT | 61.6 (80.0) | 49.5 (66.7) | 39.9 (53.6) | 5.4 (5.4) |
| OpenMath-Nemotron-1.5B TIR | 52.0 (83.3) | 39.7 (70.0) | 37.2 (60.7) | 2.5 (6.2) |
| + Self GenSelect | 83.3 | 70.0 | 62.2 | 7.9 |
| + 32B GenSelect | 83.3 | 70.0 | 62.8 | 8.3 |
| DeepSeek-R1-Distill-Qwen-7B | 54.4 (80.0) | 38.6 (53.3) | 30.6 (42.9) | 3.3 (5.2) |
| OpenMath-Nemotron-7B CoT | 74.8 (80.0) | 61.2 (76.7) | 49.7 (57.7) | 6.6 (6.6) |
| OpenMath-Nemotron-7B TIR | 72.9 (83.3) | 57.5 (76.7) | 54.6 (66.3) | 7.8 (10.8) |
| + Self GenSelect | 86.7 | 76.7 | 68.4 | 11.5 |
| + 32B GenSelect | 86.7 | 76.7 | 69.9 | 11.9 |
| DeepSeek-R1-Distill-Qwen-14B | 65.8 (80.0) | 48.4 (60.0) | 40.1 (52.0) | 4.2 (4.8) |
| OpenMath-Nemotron-14B-MIX (kaggle) | 73.7 (86.7) | 57.9 (73.3) | 50.5 (64.8) | 5.7 (6.5) |
| OpenMath-Nemotron-14B CoT | 76.3 (83.3) | 63.0 (76.7) | 52.1 (60.7) | 7.5 (7.6) |
| OpenMath-Nemotron-14B TIR | 76.3 (86.7) | 61.3 (76.7) | 58.6 (70.9) | 9.5 (11.5) |
| + Self GenSelect | 86.7 | 76.7 | 72.4 | 14.1 |
| + 32B GenSelect | 90.0 | 76.7 | 71.9 | 13.7 |
| QwQ-32B | 78.1 (86.7) | 66.5 (76.7) | 55.9 (63.3) | 9.0 (9.5) |
| DeepSeek-R1-Distill-Qwen-32B | 66.9 (83.3) | 51.8 (73.3) | 39.9 (51.0) | 4.8 (6.0) |
| OpenMath-Nemotron-32B CoT | 76.5 (86.7) | 62.5 (73.3) | 53.0 (59.2) | 8.3 (8.3) |
| OpenMath-Nemotron-32B TIR | 78.4 (93.3) | 64.2 (76.7) | 59.7 (70.9) | 9.2 (12.5) |
| + Self GenSelect | 93.3 | 80.0 | 73.5 | 15.7 |
| DeepSeek-R1 | 79.1 (86.7) | 64.3 (73.3) | 53.0 (59.2) | 10.5 (11.4) |
Reproducing our results
The pipeline we used to produce the data and models is fully open-sourced!
We provide all instructions to fully reproduce our results, including data generation.
Citation
If you find our work useful, please consider citing us!
@article{moshkov2025aimo2,
title = {AIMO-2 Winning Solution: Building State-of-the-Art Mathematical Reasoning Models with OpenMathReasoning dataset},
author = {Ivan Moshkov and Darragh Hanley and Ivan Sorokin and Shubham Toshniwal and Christof Henkel and Benedikt Schifferer and Wei Du and Igor Gitman},
year = {2025},
journal = {arXiv preprint arXiv:2504.16891}
}
Dataset Owner(s):
NVIDIA Corporation
Release Date:
04/23/2025
Data Version
1.0 (04/23/2025)
License/Terms of Use:
cc-by-4.0
Intended Usage:
This dataset is intended to be used by the community to continue to improve models. The data may be freely used to train and evaluate.
Ethical Considerations:
NVIDIA believes Trustworthy AI is a shared responsibility and we have established policies and practices to enable development for a wide array of AI applications. When downloaded or used in accordance with our terms of service, developers should work with their internal model team to ensure this model meets requirements for the relevant industry and use case and addresses unforeseen product misuse.
Please report security vulnerabilities or NVIDIA AI Concerns here.
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