README.md

---
license: cc-by-4.0
task_categories:
  - question-answering
  - text-generation
language:
  - en
tags:
  - mathematics
  - unsolved-problems
  - math
  - research
  - latex
size_categories:
  - 1K<n<10K
pretty_name: UnsolvedMath
---

[🌐 Browse UnsolvedMath online](https://unsolvedmath.com)

[✅ Paper: Open Mathematical Problems as an AI Reasoning Benchmark](https://huggingface.co/datasets/ulamai/UnsolvedMath/blob/main/open-math.pdf)

# UnsolvedMath Dataset

A comprehensive curated collection of **2,084 open mathematics problems** across all domains and difficulty levels, including the largest collection of Erdős problems available in machine-readable format. Available for browsing at [unsolvedmath.com](https://unsolvedmath.com).

Paper: "[Open Mathematical Problems as an AI Reasoning Benchmark](https://huggingface.co/datasets/ulamai/UnsolvedMath/blob/main/open-math.pdf)"

## Dataset Description

**UnsolvedMath** is a comprehensive dataset of unsolved and historically significant mathematical problems, organized by domain, difficulty level, and problem set. This dataset aggregates problems from prestigious collections including:

- Millennium Prize Problems
- Hilbert's 23 Problems
- Smale's 18 Problems for the 21st Century
- DARPA's 23 Mathematical Challenges
- Ben Green's 100 Open Problems
- Erdős Problems
- Kourovka Notebook New Problems
- Kirby's Problems in Low-Dimensional Topology
- OpenGarden / Open Problem Garden

### Dataset Summary

- **Total Problems**: 2084
- **Erdős Problems**: 632 problems with citations and references
- **Version**: 1.1.0
- **Categories**: 17 mathematical domains
- **Difficulty Levels**: 5 (L1: Tractable → L5: Millennium Prize)
- **Problem Sets**: 12 curated collections
- **Format**: JSON
- **License**: CC BY 4.0

### New in v1.1.0

This release adds three large source collections:

- **OpenGarden / Open Problem Garden**: 422 problems
- **Kirby's Problems in Low-Dimensional Topology**: 366 problems
- **Kourovka Notebook New Problems**: 150 problems

### Supported Tasks

- Mathematical research and exploration
- Mathematical question answering
- LaTeX/mathematical notation processing
- Problem classification and organization
- Educational content generation

## Dataset Structure

### Data Files

The dataset consists of multiple JSON files:

1. **problems.json** - Main dataset containing all problems
2. **categories.json** - Mathematical domain classifications
3. **difficulty_levels.json** - 5-tier difficulty system
4. **sets.json** - Problem set metadata (Millennium Prize, Hilbert's 23, etc.)
5. **dataset.json** - Combined file with all data
6. **statistics.json** - Dataset statistics

### Data Fields

#### Problems

Each problem contains:

- `id` (int): Unique identifier
- `title` (string): Problem title
- `statement` (string): Complete problem statement with LaTeX notation
- `background` (string, optional): Historical context and background
- `category` (object): Mathematical domain
  - `id`, `name`, `display_name`, `description`, `slug`
- `difficulty` (object): Difficulty classification
  - `id`, `level`, `name`, `description`, `color_class`
- `status` (string): "open", "solved", or "partially_solved"
- `source_url` (string, optional): Reference URL
- `sets` (array, optional): Associated problem sets
- `tags` (array, optional): Additional tags
- `year_proposed` (int, optional): Year the problem was first posed
- `solved_year` (int, optional): Year solved (if applicable)
- `solved_by` (string, optional): Solver's name
- `prize_amount` (int, optional): Prize money (USD)
- `created_at` (string): Timestamp

#### Categories

17 mathematical domains:
- **Number Theory**: Properties of integers, prime numbers, Diophantine equations.
- **Combinatorics**: Counting problems, graph theory, discrete structures.
- **Graph Theory**: Problems involving graphs, networks, and their properties.
- **Algebra**: Group theory, ring theory, field theory, and algebraic structures.
- **Algebraic Geometry**: Geometric objects defined by polynomial equations.
- **Geometry**: Euclidean and non-Euclidean geometry, geometric structures.
- **Topology**: Properties preserved under continuous deformations.
- **Analysis**: Limits, continuity, calculus, and function theory.
- **Partial Differential Equations**: PDEs and their applications in physics and geometry.
- **Set Theory**: Foundations of mathematics, infinite sets, and cardinality.
- **Dynamical Systems**: Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.
- **Computer Science**: Computational complexity, algorithms, and theoretical CS.
- **Mathematical Physics**: Problems at the intersection of mathematics and physics.
- **Group Theory**: Problems about groups, group actions, representations, and related algebraic structures.
- **Logic**: Problems in mathematical logic, model theory, proof theory, and finite model theory.
- **Probability**: Problems involving probability theory, stochastic processes, and random structures.
- **Miscellaneous**: Problems whose source classification does not fit the main mathematical categories.

#### Difficulty Levels

- **L1: Tractable**: Problems that may be within reach with current techniques. Reserved for future additions.
- **L2: Intermediate**: Challenging problems requiring solid mathematical background. Reserved for future additions.
- **L3: Advanced**: Difficult problems requiring specialized knowledge and sophisticated techniques.
- **L4: Expert**: Very challenging problems at the frontier of mathematical research.
- **L5: Millennium Prize**: Millennium Prize Problems and problems of equivalent difficulty.

## Dataset Statistics

### Problems by Difficulty

- L1: Tractable: 916
- L3: Advanced: 496
- L2: Intermediate: 316
- L4: Expert: 220
- L5: Millennium Prize: 136

### Problems by Category

- Number Theory: 546
- Graph Theory: 441
- Topology: 424
- Combinatorics: 230
- Group Theory: 155
- Geometry: 117
- Algebra: 89
- Computer Science: 24
- Set Theory: 16
- Logic: 10
- Algebraic Geometry: 9
- Partial Differential Equations: 8
- Mathematical Physics: 6
- Analysis: 5
- Dynamical Systems: 2
- Probability: 1
- Miscellaneous: 1

### Problems by Status

- Open: 2075
- Solved: 9
- Partially Solved: 0

## Usage

### Loading the Dataset

```python
from datasets import load_dataset

# Load the full dataset
dataset = load_dataset("ulamai/UnsolvedMath", data_files="dataset.json")

# Or load individual files
problems = load_dataset("ulamai/UnsolvedMath", data_files="problems.json")
categories = load_dataset("ulamai/UnsolvedMath", data_files="categories.json")
```

### Example: Filtering by Difficulty

```python
import json

with open('problems.json', 'r') as f:
    problems = json.load(f)

# Get all Millennium Prize problems (L5)
millennium_problems = [
    p for p in problems
    if p.get('difficulty', {}).get('level') == 5
]

print(f"Found {len(millennium_problems)} Millennium Prize problems")
```

### Example: LaTeX Rendering

```python
# Problems contain LaTeX notation in the statement field
problem = problems[0]
print(problem['statement'])

# Use a LaTeX renderer like matplotlib or sympy to display
from sympy import latex, sympify
# ... render LaTeX content
```

## Data Collection and Curation

This dataset was curated from:
- Official Millennium Prize Problems documentation
- Historical mathematical problem collections
- Published research papers and mathematical surveys
- Reputable mathematical organizations (Clay Mathematics Institute, AMS, etc.)

All problems include:
- Accurate mathematical statements with LaTeX notation
- Historical context and background
- Proper attribution and source references
- Classification by domain and difficulty

## Ethical Considerations

- **Academic Integrity**: This dataset is for research and educational purposes
- **Attribution**: All problems are properly attributed to their original sources
- **Open Problems**: Status accuracy maintained to the best of our knowledge as of the dataset creation date
- **Updates**: Some problems may be solved after dataset publication

## Limitations

- The dataset represents a curated selection, not an exhaustive list of all unsolved problems
- Problem difficulty is subjective and based on expert consensus
- LaTeX notation may require preprocessing for some applications
- Status (open/solved) should be verified for time-sensitive applications

## Citation

If you use this dataset in your research, please cite:

```bibtex
@misc{unsolvedmath2026,
  title={UnsolvedMath: A Curated Collection of Open Mathematics Problems},
  author={UnsolvedMath Contributors},
  year={2026},
  howpublished={\url{https://huggingface.co/datasets/ulamai/UnsolvedMath}},
}
```

## Additional Information

### Dataset Curators

UnsolvedMath project contributors

### Licensing Information

This dataset is released under the **Creative Commons Attribution 4.0 International (CC BY 4.0)** license.

You are free to:
- Share — copy and redistribute the material in any medium or format
- Adapt — remix, transform, and build upon the material for any purpose, even commercially

Under the following terms:
- Attribution — You must give appropriate credit and indicate if changes were made

### Contact

For questions, issues, or contributions:
- Website: [unsolvedmath.com](https://unsolvedmath.com)
- Dataset: [huggingface.co/datasets/ulamai/UnsolvedMath](https://huggingface.co/datasets/ulamai/UnsolvedMath)

---

**Generated**: 2026-05-13T14:59:38.597Z
**Version**: 1.1.0