Duplicate from ulamai/UnsolvedMath

Co-authored-by: Przemek Chojecki <przemekch@users.noreply.huggingface.co>

.gitattributes

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+*.pcm filter=lfs diff=lfs merge=lfs -text
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+# Audio files - compressed
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README.md

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+---
+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

categories.json

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+[
+  {
+    "id": 1,
+    "name": "number_theory",
+    "display_name": "Number Theory",
+    "description": "Properties of integers, prime numbers, Diophantine equations.",
+    "slug": "number-theory",
+    "order_index": 1,
+    "created_at": "2026-05-13T14:45:21.186Z"
+  },
+  {
+    "id": 2,
+    "name": "combinatorics",
+    "display_name": "Combinatorics",
+    "description": "Counting problems, graph theory, discrete structures.",
+    "slug": "combinatorics",
+    "order_index": 2,
+    "created_at": "2026-05-13T14:45:21.187Z"
+  },
+  {
+    "id": 3,
+    "name": "graph_theory",
+    "display_name": "Graph Theory",
+    "description": "Problems involving graphs, networks, and their properties.",
+    "slug": "graph-theory",
+    "order_index": 3,
+    "created_at": "2026-05-13T14:45:21.187Z"
+  },
+  {
+    "id": 4,
+    "name": "algebra",
+    "display_name": "Algebra",
+    "description": "Group theory, ring theory, field theory, and algebraic structures.",
+    "slug": "algebra",
+    "order_index": 4,
+    "created_at": "2026-05-13T14:45:21.187Z"
+  },
+  {
+    "id": 5,
+    "name": "algebraic_geometry",
+    "display_name": "Algebraic Geometry",
+    "description": "Geometric objects defined by polynomial equations.",
+    "slug": "algebraic-geometry",
+    "order_index": 5,
+    "created_at": "2026-05-13T14:45:21.187Z"
+  },
+  {
+    "id": 6,
+    "name": "geometry",
+    "display_name": "Geometry",
+    "description": "Euclidean and non-Euclidean geometry, geometric structures.",
+    "slug": "geometry",
+    "order_index": 6,
+    "created_at": "2026-05-13T14:45:21.187Z"
+  },
+  {
+    "id": 7,
+    "name": "topology",
+    "display_name": "Topology",
+    "description": "Properties preserved under continuous deformations.",
+    "slug": "topology",
+    "order_index": 7,
+    "created_at": "2026-05-13T14:45:21.187Z"
+  },
+  {
+    "id": 8,
+    "name": "analysis",
+    "display_name": "Analysis",
+    "description": "Limits, continuity, calculus, and function theory.",
+    "slug": "analysis",
+    "order_index": 8,
+    "created_at": "2026-05-13T14:45:21.187Z"
+  },
+  {
+    "id": 9,
+    "name": "pde",
+    "display_name": "Partial Differential Equations",
+    "description": "PDEs and their applications in physics and geometry.",
+    "slug": "pde",
+    "order_index": 9,
+    "created_at": "2026-05-13T14:45:21.187Z"
+  },
+  {
+    "id": 10,
+    "name": "set_theory",
+    "display_name": "Set Theory",
+    "description": "Foundations of mathematics, infinite sets, and cardinality.",
+    "slug": "set-theory",
+    "order_index": 10,
+    "created_at": "2026-05-13T14:45:21.187Z"
+  },
+  {
+    "id": 11,
+    "name": "dynamical_systems",
+    "display_name": "Dynamical Systems",
+    "description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
+    "slug": "dynamical-systems",
+    "order_index": 11,
+    "created_at": "2026-05-13T14:45:21.187Z"
+  },
+  {
+    "id": 15,
+    "name": "computer_science",
+    "display_name": "Computer Science",
+    "description": "Computational complexity, algorithms, and theoretical CS.",
+    "slug": "computer-science",
+    "order_index": 15,
+    "created_at": "2026-05-13T14:45:21.187Z"
+  },
+  {
+    "id": 16,
+    "name": "physics",
+    "display_name": "Mathematical Physics",
+    "description": "Problems at the intersection of mathematics and physics.",
+    "slug": "physics",
+    "order_index": 16,
+    "created_at": "2026-05-13T14:45:21.187Z"
+  },
+  {
+    "id": 17,
+    "name": "group_theory",
+    "display_name": "Group Theory",
+    "description": "Problems about groups, group actions, representations, and related algebraic structures.",
+    "slug": "group-theory",
+    "order_index": 17,
+    "created_at": "2026-05-13T14:45:21.187Z"
+  },
+  {
+    "id": 18,
+    "name": "logic",
+    "display_name": "Logic",
+    "description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
+    "slug": "logic",
+    "order_index": 18,
+    "created_at": "2026-05-13T14:45:21.187Z"
+  },
+  {
+    "id": 19,
+    "name": "probability",
+    "display_name": "Probability",
+    "description": "Problems involving probability theory, stochastic processes, and random structures.",
+    "slug": "probability",
+    "order_index": 19,
+    "created_at": "2026-05-13T14:45:21.187Z"
+  },
+  {
+    "id": 20,
+    "name": "miscellaneous",
+    "display_name": "Miscellaneous",
+    "description": "Problems whose source classification does not fit the main mathematical categories.",
+    "slug": "miscellaneous",
+    "order_index": 20,
+    "created_at": "2026-05-13T14:45:21.187Z"
+  }
+]

difficulty_levels.json

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+[
+  {
+    "id": 1,
+    "level": 1,
+    "name": "L1: Tractable",
+    "description": "Problems that may be within reach with current techniques. Reserved for future additions.",
+    "color_class": "text-green-600 bg-green-50 border-green-200"
+  },
+  {
+    "id": 2,
+    "level": 2,
+    "name": "L2: Intermediate",
+    "description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
+    "color_class": "text-blue-600 bg-blue-50 border-blue-200"
+  },
+  {
+    "id": 3,
+    "level": 3,
+    "name": "L3: Advanced",
+    "description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
+    "color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
+  },
+  {
+    "id": 4,
+    "level": 4,
+    "name": "L4: Expert",
+    "description": "Very challenging problems at the frontier of mathematical research.",
+    "color_class": "text-red-600 bg-red-50 border-red-200"
+  },
+  {
+    "id": 5,
+    "level": 5,
+    "name": "L5: Millennium Prize",
+    "description": "Millennium Prize Problems and problems of equivalent difficulty.",
+    "color_class": "text-purple-600 bg-purple-50 border-purple-200"
+  }
+]

sets.json

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+[
+  {
+    "id": 1,
+    "name": "millennium_prize",
+    "display_name": "Millennium Prize Problems",
+    "description": "Seven problems selected by the Clay Mathematics Institute in 2000, each with a $1,000,000 prize for solution.",
+    "slug": "millennium-prize",
+    "order_index": 1,
+    "created_at": "2026-05-13T14:45:21.187Z"
+  },
+  {
+    "id": 2,
+    "name": "hilbert_problems",
+    "display_name": "Hilbert's 23 Problems",
+    "description": "David Hilbert's list of 23 unsolved problems presented at the International Congress of Mathematicians in Paris in 1900.",
+    "slug": "hilbert-problems",
+    "order_index": 2,
+    "created_at": "2026-05-13T14:45:21.187Z"
+  },
+  {
+    "id": 3,
+    "name": "green_problems",
+    "display_name": "Ben Green's 100 Open Problems",
+    "description": "A collection of 100 open problems in additive combinatorics and related areas, compiled by Ben Green.",
+    "slug": "green-problems",
+    "order_index": 3,
+    "created_at": "2026-05-13T14:45:21.187Z"
+  },
+  {
+    "id": 4,
+    "name": "darpa_challenges",
+    "display_name": "DARPA's 23 Mathematical Challenges",
+    "description": "Mathematical challenges identified by DARPA to drive fundamental research in mathematics.",
+    "slug": "darpa-challenges",
+    "order_index": 4,
+    "created_at": "2026-05-13T14:45:21.187Z"
+  },
+  {
+    "id": 5,
+    "name": "smale_problems",
+    "display_name": "Smale's Problems",
+    "description": "Steve Smale's list of mathematical problems for the 21st century.",
+    "slug": "smale-problems",
+    "order_index": 5,
+    "created_at": "2026-05-13T14:45:21.187Z"
+  },
+  {
+    "id": 6,
+    "name": "landau_problems",
+    "display_name": "Landau's Problems",
+    "description": "Four basic problems about prime numbers posed by Edmund Landau at the 1912 International Congress of Mathematicians.",
+    "slug": "landau-problems",
+    "order_index": 6,
+    "created_at": "2026-05-13T14:45:21.187Z"
+  },
+  {
+    "id": 7,
+    "name": "hardy_littlewood_conjectures",
+    "display_name": "Hardy-Littlewood Conjectures",
+    "description": "A collection of fundamental conjectures on prime numbers, Goldbach-type problems, and Waring's problem from the \"Partitio Numerorum\" papers (1919-1923) by G.H. Hardy and J.E. Littlewood.",
+    "slug": "hardy-littlewood-conjectures",
+    "order_index": 7,
+    "created_at": "2026-05-13T14:45:21.187Z"
+  },
+  {
+    "id": 8,
+    "name": "erdos_problems",
+    "display_name": "Erdős Problems",
+    "description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
+    "slug": "erdos-problems",
+    "order_index": 8,
+    "created_at": "2026-05-13T14:45:21.187Z"
+  },
+  {
+    "id": 9,
+    "name": "guy_prime_numbers",
+    "display_name": "Richard Guy - A: Prime Numbers",
+    "description": "Problems from Chapter A (Prime Numbers) of Richard Guy's \"Unsolved Problems in Number Theory\", a comprehensive collection of open questions in prime number theory.",
+    "slug": "guy-prime-numbers",
+    "order_index": 9,
+    "created_at": "2026-05-13T14:45:21.187Z"
+  },
+  {
+    "id": 10,
+    "name": "kourovka_new_problems_21",
+    "display_name": "Kourovka Notebook - New Problems, Issue 21",
+    "description": "New group theory problems from the 21st issue of the Kourovka Notebook, published in 2026.",
+    "slug": "kourovka-new-problems-21",
+    "order_index": 10,
+    "created_at": "2026-05-13T14:45:21.187Z"
+  },
+  {
+    "id": 11,
+    "name": "kirby_low_dimensional_topology",
+    "display_name": "Kirby's Problems in Low-Dimensional Topology",
+    "description": "Problems from Kirby-style notes on low-dimensional topology, including knot theory, 3-manifolds, 4-manifolds, and related invariants.",
+    "slug": "kirby-low-dimensional-topology",
+    "order_index": 11,
+    "created_at": "2026-05-13T14:45:21.187Z"
+  },
+  {
+    "id": 12,
+    "name": "opengarden",
+    "display_name": "OpenGarden",
+    "description": "Problems imported from the Open Problem Garden collection, using source statements, discussion notes, and subject metadata.",
+    "slug": "opengarden",
+    "order_index": 12,
+    "created_at": "2026-05-13T14:45:21.187Z"
+  }
+]

statistics.json

@@ -0,0 +1,45 @@
+{
+  "total_problems": 2084,
+  "problems_by_difficulty": {
+    "L5: Millennium Prize": 136,
+    "L3: Advanced": 496,
+    "L4: Expert": 220,
+    "L2: Intermediate": 316,
+    "L1: Tractable": 916
+  },
+  "problems_by_category": {
+    "Computer Science": 24,
+    "Number Theory": 546,
+    "Mathematical Physics": 6,
+    "Partial Differential Equations": 8,
+    "Algebraic Geometry": 9,
+    "Combinatorics": 230,
+    "Graph Theory": 441,
+    "Topology": 424,
+    "Geometry": 117,
+    "Algebra": 89,
+    "Set Theory": 16,
+    "Dynamical Systems": 2,
+    "Group Theory": 155,
+    "Analysis": 5,
+    "Logic": 10,
+    "Probability": 1,
+    "Miscellaneous": 1
+  },
+  "problems_by_status": {
+    "open": 2075,
+    "solved": 9
+  },
+  "problems_by_set": {
+    "millennium_prize": 6,
+    "hilbert_problems": 11,
+    "landau_problems": 1,
+    "smale_problems": 8,
+    "darpa_challenges": 17,
+    "green_problems": 85,
+    "erdos_problems": 632,
+    "kourovka_new_problems_21": 150,
+    "kirby_low_dimensional_topology": 366,
+    "opengarden": 422
+  }
+}