| --- |
| 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 **5,444 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 |
| - AMR Open Problem Lists |
| - Terminal-Bench Verifiable Open Problems |
|
|
| ### Dataset Summary |
|
|
| - **Total Problems**: 5444 |
| - **Erdős Problems**: 632 problems with citations and references |
| - **Version**: 1.2.0 |
| - **Categories**: 17 mathematical domains |
| - **Difficulty Levels**: 5 (L1: Tractable → L5: Millennium Prize) |
| - **Problem Sets**: 14 curated collections |
| - **Format**: JSON |
| - **License**: CC BY 4.0 |
|
|
| ### New in v1.2.0 |
|
|
| This release adds problems collected from public source lists in the AMR index. AIM workshop lists are intentionally excluded because they are maintained as a separate collection. |
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| - **AMR Open Problem Lists**: 3342 problems |
|
|
| Every AMR record retains its source URL, extraction method, and status/rights review notes in the `background` field. |
|
|
| ### 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 |
| |
| - L5: Millennium Prize: 136 |
| - L3: Advanced: 3842 |
| - L4: Expert: 234 |
| - L2: Intermediate: 316 |
| - L1: Tractable: 916 |
| |
| ### Problems by Category |
| |
| - Computer Science: 69 |
| - Number Theory: 677 |
| - Mathematical Physics: 51 |
| - Partial Differential Equations: 35 |
| - Algebraic Geometry: 26 |
| - Combinatorics: 401 |
| - Graph Theory: 728 |
| - Topology: 1217 |
| - Geometry: 605 |
| - Algebra: 147 |
| - Set Theory: 16 |
| - Dynamical Systems: 421 |
| - Group Theory: 299 |
| - Analysis: 559 |
| - Logic: 50 |
| - Probability: 142 |
| - Miscellaneous: 1 |
| |
| ### Problems by Status |
| |
| - Open: 5174 |
| - Solved: 9 |
| - Partially Solved: 261 |
| |
| ## 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 |
| - Some AMR records retain `NEEDS_REVIEW` status or rights notes from the source audit; consult each record's provenance before reuse |
| |
| ## 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**: 2026-07-31T15:26:26.167Z |
| **Version**: 1.2.0 |
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|
