MATH-Hard

# Dataset Card for Mathematics Aptitude Test of Heuristics, hard subset (MATH-Hard) dataset
## Dataset Description

- **Homepage:** https://github.com/hendrycks/math
- **Repository:** https://github.com/hendrycks/math
- **Paper:** https://arxiv.org/pdf/2103.03874.pdf
- **Leaderboard:** N/A
- **Point of Contact:** Dan Hendrycks

### Dataset Summary

The Mathematics Aptitude Test of Heuristics (MATH) dataset consists of problems
from mathematics competitions, including the AMC 10, AMC 12, AIME, and more.
Each problem in MATH has a full step-by-step solution, which can be used to teach
models to generate answer derivations and explanations. For MATH-Hard, only the
hardest questions were kept (Level 5).

### Supported Tasks and Leaderboards

[More Information Needed]

### Languages

[More Information Needed]

## Dataset Structure

### Data Instances

A data instance consists of a competition math problem and its step-by-step solution written in LaTeX and natural language. The step-by-step solution contains the final answer enclosed in LaTeX's `\boxed` tag.

An example from the dataset is:
```
{'problem': 'A board game spinner is divided into three parts labeled $A$, $B$ and $C$. The probability of the spinner landing on $A$ is $\\frac{1}{3}$ and the probability of the spinner landing on $B$ is $\\frac{5}{12}$. What is the probability of the spinner landing on $C$? Express your answer as a common fraction.',
'level': 'Level 1',
'type': 'Counting & Probability',
'solution': 'The spinner is guaranteed to land on exactly one of the three regions, so we know that the sum of the probabilities of it landing in each region will be 1. If we let the probability of it landing in region $C$ be $x$, we then have the equation $1 = \\frac{5}{12}+\\frac{1}{3}+x$, from which we have $x=\\boxed{\\frac{1}{4}}$.'}
```

### Data Fields

* `problem`: The competition math problem.
* `solution`: The step-by-step solution.
* `level`: We only kept tasks tagged as 'Level 5', the hardest level for the dataset.
* `type`: The subject of the problem: Algebra, Counting & Probability, Geometry, Intermediate Algebra, Number Theory, Prealgebra and Precalculus.

### Licensing Information

https://github.com/hendrycks/math/blob/main/LICENSE

### Citation Information

```bibtex
@article{hendrycksmath2021,
title={Measuring Mathematical Problem Solving With the MATH Dataset},
author={Dan Hendrycks
and Collin Burns
and Saurav Kadavath
and Akul Arora
and Steven Basart
and Eric Tang
and Dawn Song
and Jacob Steinhardt},
journal={arXiv preprint arXiv:2103.03874},
year={2021}
}
```

# 启发式数学能力测试困难子集（MATH-Hard）数据集卡片
## 数据集描述
- **主页**：https://github.com/hendrycks/math
- **代码仓库**：https://github.com/hendrycks/math
- **相关论文**：https://arxiv.org/pdf/2103.03874.pdf
- **排行榜**：无
- **联系人**：丹·亨德里克斯（Dan Hendrycks）

### 数据集概述
启发式数学能力测试（Mathematics Aptitude Test of Heuristics, MATH）数据集由各类数学竞赛题目组成，涵盖AMC 10、AMC 12、美国数学邀请赛（AIME）等赛事。MATH数据集中的每道题目均附带完整的分步解答，可用于指导大语言模型（Large Language Model, LLM）生成答案推导过程与解释说明。而MATH-Hard子集仅保留了其中难度最高的Level 5题目。

### 支持任务与排行榜
[需补充更多信息]

### 语言
[需补充更多信息]

## 数据集结构
### 数据实例
一条数据实例包含一道竞赛数学题目，以及采用LaTeX与自然语言编写的分步解答。该分步解答中的最终答案被包裹在LaTeX的`oxed`标签内。

数据集示例如下：

{'problem': '某桌游转盘被划分为标注为$A$、$B$、$C$的三个区域。转盘停在$A$区域的概率为$frac{1}{3}$，停在$B$区域的概率为$frac{5}{12}$。求转盘停在$C$区域的概率，并将答案以最简分数形式表示。',
'level': 'Level 1',
'type': '计数与概率',
'solution': '转盘必然停在三个区域中的某一个，因此各区域概率之和为1。设转盘停在$C$区域的概率为$x$，可得方程$1 = frac{5}{12}+frac{1}{3}+x$，解得$x=oxed{frac{1}{4}}$。'}

### 数据字段
* `problem`：竞赛数学题目
* `solution`：分步解答
* `level`：本数据集仅保留了标注为"Level 5"的题目，即该数据集的最高难度等级
* `type`：题目所属学科，包括代数、计数与概率、几何、中级代数、数论、预备代数与微积分预备

### 许可证信息
https://github.com/hendrycks/math/blob/main/LICENSE

### 引用信息
bibtex
@article{hendrycksmath2021,
title={Measuring Mathematical Problem Solving With the MATH Dataset},
author={Dan Hendrycks
and Collin Burns
and Saurav Kadavath
and Akul Arora
and Steven Basart
and Eric Tang
and Dawn Song
and Jacob Steinhardt},
journal={arXiv preprint arXiv:2103.03874},
year={2021}
}