README.md

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

# UnsolvedMath Dataset

A comprehensive curated collection of **1,146 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 https://unsolvedmath.com 

## Dataset Description

**UnsolvedMath** is a meticulously curated dataset of unsolved and historically significant mathematical problems, organized by domain, difficulty level, and problem set. This dataset aggregates problems from the most prestigious collections in mathematics, with a particular focus on Paul Erdős's extensive problem collection.

### Featured Collections

- **Erdős Problems** (632 problems) - Extensive collection from Paul Erdős, one of the most prolific mathematicians of the 20th century
- **Millennium Prize Problems** - Clay Mathematics Institute's seven $1M problems
- **Hilbert's 23 Problems** - David Hilbert's foundational problems from 1900
- **Smale's Problems** - Steve Smale's 18 problems for the 21st century
- **DARPA's 23 Mathematical Challenges** - Fundamental research challenges
- **Ben Green's 100 Open Problems** - Problems in additive combinatorics
- **Hardy-Littlewood Conjectures** - Foundational problems on primes and partitions
- **Landau's Problems** - Four classic problems on prime numbers
- **Richard Guy - Prime Numbers** - Problems from "Unsolved Problems in Number Theory"

### Dataset Summary

- **Total Problems**: 1,146
- **Erdős Problems**: 632 (with full citations and references)
- **Categories**: 12 mathematical domains
- **Difficulty Levels**: 5 (L1: Tractable → L5: Millennium Prize)
- **Problem Sets**: 9 curated collections
- **Format**: JSON with LaTeX mathematical notation
- **License**: CC BY 4.0

### What's New

This dataset includes the most comprehensive collection of Erdős problems available in structured format:
- **632 Erdős problems** (EP-1 through EP-1135) from the Erdos Problems website
- Complete problem statements with LaTeX mathematical notation
- Detailed backgrounds with historical context
- Full bibliographic references for each problem
- Difficulty classifications (L1-L3)
- Category assignments (Number Theory, Combinatorics, Graph Theory, etc.)

### Supported Tasks

- Mathematical research and exploration
- Mathematical question answering systems
- LaTeX/mathematical notation processing
- Problem classification and organization
- Educational content generation
- Research bibliography extraction
- Historical mathematics analysis

## Dataset Structure

### Data Files

The dataset consists of multiple JSON files:

1. **problems.json** (1.4 MB) - Main dataset containing all 1,146 problems
2. **categories.json** (3.0 KB) - 12 mathematical domain classifications
3. **difficulty_levels.json** (1.1 KB) - 5-tier difficulty system
4. **sets.json** (3.1 KB) - Problem set metadata
5. **dataset.json** (1.5 MB) - Combined file with all data and metadata

### Data Fields

#### Problems

Each problem contains:

- `id` (int): Unique identifier
- `problem_number` (string): Problem code (e.g., "EP-1", "MPP-001")
- `title` (string): Problem title
- `statement` (string): Complete problem statement with LaTeX notation
- `background` (string): Historical context, references, and related work
- `difficulty_level_id` (int): Difficulty level (1-5)
- `status` (string): "open" or "solved"
- `category_id` (int): Mathematical domain identifier
- `set_id` (int, optional): Problem set identifier
- `proposed_by` (string, optional): Person who proposed the problem
- `proposed_year` (int, optional): Year the problem was first posed
- `view_count` (int): Number of views
- `favorite_count` (int): Number of favorites
- `created_at` (string): Timestamp
- `updated_at` (string): Timestamp
- `published` (boolean): Publication status

#### Categories

12 mathematical domains:
- **Number Theory** - Properties of integers, primes, Diophantine equations
- **Combinatorics** - Counting, arrangements, combinatorial structures
- **Graph Theory** - Networks, graphs, and their properties
- **Algebra** - Algebraic structures and equations
- **Algebraic Geometry** - Geometric objects defined by polynomials
- **Geometry** - Euclidean and non-Euclidean geometry
- **Topology** - Properties preserved under continuous deformations
- **Analysis** - Limits, continuity, calculus, function theory
- **Partial Differential Equations** - PDEs and applications
- **Set Theory** - Foundations, infinite sets, cardinality
- **Computer Science** - Computational complexity, algorithms
- **Mathematical Physics** - Mathematics-physics intersection

#### Difficulty Levels

- **L1: Tractable** - Problems potentially within reach with current techniques
- **L2: Intermediate** - Challenging problems requiring solid mathematical background
- **L3: Advanced** - Difficult problems requiring specialized knowledge
- **L4: Expert** - Very challenging problems at the frontier of research
- **L5: Millennium Prize** - Millennium Prize Problems and equivalent difficulty

#### Problem Sets

- Millennium Prize Problems (7 problems)
- Hilbert's 23 Problems
- Smale's Problems (18 problems)
- DARPA's 23 Mathematical Challenges
- Ben Green's 100 Open Problems
- **Erdős Problems (632 problems)**
- Hardy-Littlewood Conjectures
- Landau's Problems (4 problems)
- Richard Guy - A: Prime Numbers

## Usage

### Loading the Dataset

```python
import json

# Load all problems
with open('problems.json', 'r', encoding='utf-8') as f:
    problems = json.load(f)

print(f"Total problems: {len(problems)}")

# Load the complete dataset
with open('dataset.json', 'r', encoding='utf-8') as f:
    data = json.load(f)

print(f"Problems: {data['metadata']['total_problems']}")
print(f"Categories: {len(data['categories'])}")
print(f"Sets: {len(data['sets'])}")
```

### Example: Filtering Erdős Problems

```python
import json

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

# Get all Erdős problems
erdos_problems = [
    p for p in problems
    if p['problem_number'].startswith('EP-')
]

print(f"Found {len(erdos_problems)} Erdős problems")

# Get Erdős problems in Number Theory
erdos_nt = [
    p for p in erdos_problems
    if p['category_id'] == 1  # Number Theory
]

print(f"Erdős problems in Number Theory: {len(erdos_nt)}")
```

### 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 = [
    p for p in problems
    if p['difficulty_level_id'] == 5
]

# Get tractable problems (L1)
tractable = [
    p for p in problems
    if p['difficulty_level_id'] == 1
]

print(f"Millennium Prize problems: {len(millennium)}")
print(f"Tractable problems: {len(tractable)}")
```

### Example: Working with LaTeX

```python
# Problems contain LaTeX notation in statement and background fields
problem = problems[0]
print(f"Title: {problem['title']}")
print(f"Statement: {problem['statement']}")

# Example statement with LaTeX:
# "If $A\\subseteq \\{1,\\ldots,N\\}$ with $\\lvert A\\rvert=n$
#  is such that the subset sums $\\sum_{a\\in S}a$ are distinct
#  for all $S\\subseteq A$ then $N \\gg 2^{n}$."

# Use KaTeX, MathJax, or sympy to render LaTeX
from IPython.display import display, Markdown
display(Markdown(problem['statement']))
```

### Example: Extracting Citations from Erdős Problems

```python
import json
import re

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

# Get all Erdős problems
erdos = [p for p in problems if p['problem_number'].startswith('EP-')]

# Extract citations from background
citations = set()
for problem in erdos:
    bg = problem.get('background', '')
    # Find citations like \\cite{Er98}
    refs = re.findall(r'\\cite\{([^}]+)\}', bg)
    citations.update(refs)

print(f"Unique citations in Erdős problems: {len(citations)}")
print(f"Examples: {list(citations)[:10]}")
```

## Data Collection and Curation

### Sources

This dataset was curated from:
- Erdős problems website by Thomas Bloom (erdosproblems.com)
- Clay Mathematics Institute - Official Millennium Prize documentation
- Historical mathematical problem collections (Hilbert, Smale, Landau)
- Published research papers and mathematical surveys
- Reputable mathematical organizations (AMS, IMU, etc.)
- Richard Guy's "Unsolved Problems in Number Theory"
- Ben Green's additive combinatorics problem collection

### Erdős Problems Special Notes

The 632 Erdős problems include:
- Complete problem statements
- Detailed backgrounds with historical context from original sources
- Full bibliographic references (e.g., Erdős papers from 1931-1999)
- Cross-references between related problems
- Citations to recent progress and partial results
- OEIS sequence references where applicable
- Connections to other famous problems and conjectures

### Quality Assurance

All problems include:
- Accurate mathematical statements with proper LaTeX notation (mostly, there might be some smaller corrections needed)
- Historical context and background information
- Proper attribution and source references
- Classification by mathematical domain and difficulty

## Statistics

### By Difficulty Level
- **L1 (Tractable)**: 662 problems (57.8%)
- **L2 (Intermediate)**: 56 problems (4.9%)
- **L3 (Advanced)**: 72 problems (6.3%)
- **L4 (Expert)**: 220 problems (19.2%)
- **L5 (Millennium)**: 136 problems (11.9%)

### By Category
- **Number Theory**: 497 problems (43.4%) - heavily represented in Erdős problems
- **Graph Theory**: 214 problems (18.7%)
- **Combinatorics**: 195 problems (17.0%)
- **Other categories**: 240 problems (20.9%)

### By Set
- **Erdős Problems**: 632 problems (55.1% of total)
- **Other historical collections**: 514 problems (44.9% of total)

## Ethical Considerations

- **Academic Integrity**: This dataset is for research and educational purposes
- **Attribution**: All problems properly attributed to original sources
- **Open Problems**: Status accuracy maintained as of January 2026
- **Updates**: Some problems may be solved after dataset publication
- **Citations**: Erdős problems include full bibliographic references for verification

## Limitations

- The dataset represents a curated selection, not an exhaustive list of all unsolved problems
- Problem difficulty is subjective
- LaTeX notation may require preprocessing for some applications
- Status (open/solved) should be verified for time-sensitive applications
- Some Erdős problem backgrounds contain extensive LaTeX citations that may need special handling

## Citation

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

```bibtex
@misc{unsolvedmath2026,
  title={UnsolvedMath: A Curated Collection of Open Mathematics Problems},
  author={P. Chojecki},
  year={2026},
  howpublished={\url{https://huggingface.co/datasets/ulamai/UnsolvedMath}},
  note={Includes over 1000 open mathematical problems}
}
```

For the Erdős problems specifically:

```bibtex
@misc{erdos-problems,
  title={Erdős Problems},
  author={T. F. Bloom},
  year={2026},
  howpublished={\url{https://www.erdosproblems.com}},
  note={Forum}
}
```

## Additional Information

### Dataset Curators

Przemek Chojecki

### 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

### Updates and Maintenance

- **Version**: 1.0.0
- **Last Updated**: 2026-01-24
- **Total Problems**: 1,146
- **Erdős Problems Added**: 2026-01-24

### Contact

For questions, issues, or contributions, visit the project repository.

---

**Generated**: 2026-01-24
**Version**: 1.0.0
**Total Problems**: 1,146
**Erdős Problems**: 632