| --- |
| dataset_info: |
| features: |
| - name: problem |
| dtype: string |
| - name: solution |
| dtype: string |
| - name: candidates |
| sequence: string |
| - name: tags |
| sequence: string |
| - name: metadata |
| struct: |
| - name: answer_score |
| dtype: int64 |
| - name: boxed |
| dtype: bool |
| - name: end_of_proof |
| dtype: bool |
| - name: n_reply |
| dtype: int64 |
| - name: path |
| dtype: string |
| splits: |
| - name: train |
| num_bytes: 298608789 |
| num_examples: 80661 |
| download_size: 140630996 |
| dataset_size: 298608789 |
| configs: |
| - config_name: default |
| data_files: |
| - split: train |
| path: data/train-* |
| --- |
| |
| # AoPS: Art of Problem Solving Competition Mathematics |
|
|
| ## Dataset Description |
|
|
| This dataset is a collection of **80,661** competition mathematics problems and solutions obtained from the [Art of Problem Solving (AoPS)](https://artofproblemsolving.com/) community wiki and forums. It covers a wide range of mathematical contests and olympiads, including problems from events such as AIME, BAMO, IMO, and various national and memorial competitions. |
|
|
| The dataset was curated by [AI-MO (Project Numina)](https://huggingface.co/AI-MO), an initiative focused on building AI systems capable of mathematical reasoning at the olympiad level. |
|
|
| ## Dataset Structure |
|
|
| ### Fields |
|
|
| | Column | Type | Description | |
| |---|---|---| |
| | `problem` | `string` | The mathematical problem statement, typically formatted in LaTeX. | |
| | `solution` | `string` | A solution or proof for the problem. May be empty for some entries. | |
| | `candidates` | `list[string]` | Alternative or candidate solutions contributed by the community. | |
| | `tags` | `list[string]` | Metadata tags indicating the origin, contest name, and year (e.g., `"origin:aops"`, `"2022 AIME Problems"`). | |
| | `metadata` | `dict` | Additional metadata about the problem (see below). | |
|
|
| ### Metadata Fields |
|
|
| | Field | Type | Description | |
| |---|---|---| |
| | `answer_score` | `int64` | Community score or rating of the answer. | |
| | `boxed` | `bool` | Whether the answer contains a boxed final result (e.g., `\boxed{42}`). | |
| | `end_of_proof` | `bool` | Whether the solution includes a complete proof ending. | |
| | `n_reply` | `int64` | Number of community replies or comments on the problem thread. | |
| | `path` | `string` | Source path in the AoPS collection (e.g., `Contest Collections/2022 Contests/...`). | |
|
|
| ### Splits |
|
|
| | Split | Examples | |
| |---|---| |
| | `train` | 80,661 | |
|
|
| ## Example |
|
|
| ```python |
| { |
| "problem": "Let $ABC$ be an acute triangle with altitude $AD$ ($D \\in BC$). The line through $C$ parallel to $AB$ meets the perpendicular bisector of $AD$ at $G$. Show that $AC = BC$ if and only if $\\angle AGC = 90°$.", |
| "solution": "...", |
| "candidates": ["..."], |
| "tags": ["origin:aops", "2022 Contests", "2022 3rd Memorial \"Aleksandar Blazhevski-Cane\""], |
| "metadata": { |
| "answer_score": 130, |
| "boxed": false, |
| "end_of_proof": true, |
| "n_reply": 3, |
| "path": "Contest Collections/2022 Contests/2022 3rd Memorial .../2759376.json" |
| } |
| } |
| ``` |
|
|
| ## Topic Coverage |
|
|
| Problems span a broad range of competition mathematics topics, including: |
|
|
| - **Geometry** -- triangle properties, cyclic quadrilaterals, angle chasing |
| - **Number Theory** -- divisibility, modular arithmetic, Diophantine equations |
| - **Algebra** -- inequalities, polynomials, functional equations |
| - **Combinatorics** -- counting, graph theory, board coloring problems |
|
|
| ## Usage |
|
|
| ```python |
| from datasets import load_dataset |
| |
| dataset = load_dataset("AI-MO/aops") |
| |
| # Access a problem |
| print(dataset["train"][0]["problem"]) |
| print(dataset["train"][0]["solution"]) |
| ``` |
|
|
| ## Intended Use |
|
|
| - Training and evaluating mathematical reasoning models |
| - Benchmarking LLMs on competition-level mathematics |
| - Studying solution quality and problem difficulty distributions |
| - Building retrieval-augmented generation (RAG) systems for math tutoring |
|
|
| ## Source |
|
|
| All problems and solutions originate from the [Art of Problem Solving](https://artofproblemsolving.com/) community. |
|
|
|
|
