--- license: cc-by-4.0 task_categories: - question-answering - text-generation language: - en tags: - mathematics - unsolved-problems - math - research - latex size_categories: - 10K-` tags in `problem_number` and `research_results.json`. - **Difficulty**: conservative AMR-style assignment (L3 default, L4 for clearly live conjectural/frontier cases, L2 for context-only or invalid statements; no automatic L5 assignments). This release also replaces the coarse AIM `wording_corrected` heuristic with an individual statement-recovery audit for all 3,359 canonical AIM IDs. The exact canonical `original_statement` is stored separately from the reviewed `clean_statement`; unrecoverable or unsafe reconstructions remain null rather than being silently promoted into the public problem text. - `exact`: 2,886 - `corrected_verified`: 61 - `reconstructed_unverified`: 385 - `unrecoverable`: 27 For `exact` and `corrected_verified`, the public `statement` uses the clean formulation. For `reconstructed_unverified` and `unrecoverable`, it retains a visible rendering of the canonical source instead of silently adopting a conjectural repair. Full evidence is available in `aim_statement_audit.json`. *Caveat:* AIM reports and novelty labels are machine-generated research aids, not peer-reviewed claims. Full-solution and counterexample labels require independent expert verification before citation. ### New in v1.5.0 This release adds a dated **literature triage to all 2,084 problem records outside the AMR and AIM collections**. No problems were added or removed, and the existing AMR and AIM problem records and research reports are unchanged. Each review was checked on 2026-08-17 and is appended to the corresponding problem's `background` field, with a literature-status assessment, verified partial progress, resolution check, remaining work, and source links. - **Literature status**: 670 open, 1,215 partially solved, and 199 solved. - **Scope**: only non-AMR and non-AIM records; 3,342 AMR and 3,359 AIM records are preserved from v1.4. - **Data change**: `background` only; statements, identifiers, categories, difficulty assignments, and existing status fields are unchanged. The v1.5 literature labels are dated machine-generated research aids. They supplement the legacy `status` field and require independent verification before citation. A refutation or counterexample is classified as solved; uncertain literature status is classified as partially solved. ### New in v1.6.0 This release adds **6,673 open and partially solved problems from Oberwolfach Reports**, spanning Volumes 1–23 (2004–2026) and 1,106 source reports. The records capture explicit problems, conjectures, and research questions from conference reports together with the mathematical discussion needed to understand their current status. - **New OWR problems**: 6,673 (4,493 open; 2,180 partially solved). - **Provenance**: every record retains its OWR identifier, source-report DOI, report citation, and source links used by the literature assessment. - **Literature triage**: assessments were checked on 2026-08-21 or 2026-08-22. - **Difficulty**: all imported OWR records receive the conservative L3 default; this is a corpus-level default rather than an expert ranking of each problem. - **Categories**: OWR domains are assigned conservatively from workshop titles and statement terminology; ambiguous records remain Miscellaneous. - **Quality check**: a fixed-seed blind sample of ten records found eight clear, mathematically identifiable problems and two weaker programmatic or malformed extractions. The latter remain in the inclusion-first corpus and are flagged by their own literature assessments. Users should consult the source report where exact formulation matters. The OWR literature assessments are dated curation aids, not peer review. Status and source claims should be independently verified before citation. ### New in v1.7.0 This release reviews and cleans all **6,673 Oberwolfach Reports (OWR)** records introduced in v1.6.0. No problems were added or removed, and all 8,785 non-OWR records are preserved exactly. - **Titles**: every OWR record received a concise, descriptive title rather than an automatically truncated copy of its statement. - **Statements**: typography, extraction artifacts, and mathematical markup were reviewed conservatively. The original v1.6 statement is retained in `original_statement`, with the reviewed form in `clean_statement`. - **Safe publication**: `exact` and `corrected_verified` records publish the clean formulation. `reconstructed_unverified` and `unrecoverable` records continue to publish the original formulation instead of silently adopting an uncertain repair. - **Auditability**: `owr_statement_audit.json` records the original and reviewed title, original and clean statement, public promotion decision, evidence, source-check flag, and input hash for every OWR problem. - **Research metadata**: problem status, OWR provenance, literature assessments, literature sources, and review dates are unchanged from v1.6. The cleanup and literature assessments remain machine-assisted curation, not peer review. Verify formulations and time-sensitive claims against the linked source report before citation. ### 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 7. **research_results.json** - Per-problem AMR and AIM research notes (status, literature, result, what remains) 8. **aim_statement_audit.json** - Per-problem AIM statement-recovery evidence and verification status 9. **owr_statement_audit.json** - Per-problem OWR title and statement cleanup audit OWR records additionally expose `source_citation`, `literature_assessment`, `literature_sources`, `literature_checked_at`, `original_statement`, `clean_statement`, `statement_status`, and `statement_verification`. ### 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 - `research_classification` (string, optional): research verdict, e.g. `SOLVED-IN-LITERATURE`, `PARTIAL-PROGRESS`, `OPEN-TRIAGE` - `research_summary` (string, optional): 2–3 paragraph summary of the research findings - `research_difficulty_suggested` (string, optional): suggested difficulty level when it differs from the default #### 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 - L2: Intermediate: 523 - L3: Advanced: 12919 - L4: Expert: 963 - L5: Millennium Prize: 137 ### Problems by Category - Algebra: 927 - Algebraic Geometry: 830 - Analysis: 1143 - Combinatorics: 744 - Computer Science: 642 - Dynamical Systems: 667 - Geometry: 1967 - Graph Theory: 1222 - Group Theory: 848 - Logic: 286 - Mathematical Physics: 352 - Miscellaneous: 1530 - Number Theory: 1268 - Partial Differential Equations: 270 - Probability: 798 - Set Theory: 77 - Topology: 1887 ### Problems by Status - Open: 8955 - Partially Solved: 5807 - Solved: 696 ## Usage ### Loading the Dataset ```python from datasets import load_dataset # Load the full dataset dataset = load_dataset("ulamai/UnsolvedMath", data_files="problems.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 and AIM records retain `NEEDS_REVIEW` status or rights notes from the source audit; consult each record's provenance before reuse - Some OWR records are broad research directions or imperfect extractions; their literature assessments flag known formulation limitations ## 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 The UnsolvedMath curation and original metadata are released under the **Creative Commons Attribution 4.0 International (CC BY 4.0)** license. Linked source material remains subject to its own terms; recent open-access Oberwolfach Reports identify CC BY-SA 4.0 on their article pages, and those source terms are not superseded by this dataset card. 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**: 2026-09-16T12:06:53Z **Version**: 1.6.0