---
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.