README.md

---
license: cc-by-4.0
task_categories:
  - question-answering
  - text-generation
language:
  - en
tags:
  - mathematics
  - unsolved-problems
  - math
  - research
  - latex
size_categories:
  - 10K<n<100K
configs:
  - config_name: default
    data_files:
      - split: train
        path: problems.json
pretty_name: UnsolvedMath
---

# UnsolvedMath Dataset

[🌐 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)

A comprehensive curated collection of **15,458 open and partially solved 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).

[🟢 Support future development](https://www.unsolvedmath.com/donate)

## 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
- AIM Workshop Problem Lists
- Oberwolfach Reports workshop problems and discussions

### Dataset Summary

- **Total Problems**: 15458
- **Erdős Problems**: 632 problems with citations and references
- **Version**: 1.6.0
- **Categories**: 17 mathematical domains
- **Difficulty Levels**: 5 (L1: Tractable → L5: Millennium Prize)
- **Problem Sets**: 15 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 added in v1.4.0 below.

- **AMR Open Problem Lists**: 3342 problems

Every AMR record retains its source URL, extraction method, and status/rights review notes in the `background` field.

### New in v1.3.0

This release adds a **research status audit** for every AMR open-problem record. Each of the 3,342 AMR problems was investigated by an AI research fleet (literature triage with web-verified citations, solution attempts, and partial progress), and every report was then re-checked in a supervised verification pass (statement alignment, citation-fabrication screening, classification normalization, difficulty assignment). Each AMR problem now carries: a `research_classification` (`SOLVED-BY-YOU`, `SOLVED-IN-LITERATURE`, `PARTIAL-PROGRESS`, `OPEN-TRIAGE`), an updated `status` derived from the classification, an optional `research_difficulty_suggested`, and a `research_summary`. AMR difficulty levels are now differentiated across L2–L5 (previously all L3). The structured per-problem research notes (problem, literature status, work done, result, what remains) are provided in `research_results.json`. The v1.3 tag also preserves the individual Markdown reports in `research/`.

- **Research audit**: 3,342 AMR problems classified; 183 solved (181 in the literature, 2 by the AI fleet), 963 partial progress, 2,196 open after triage.
- **New file**: `research_results.json` — structured per-problem research notes.
- **v1.3 archive directory**: `research/` — full per-problem research reports in Markdown, preserved under the v1.3 tag.
- **New fields** per AMR problem: `research_classification`, `research_summary`, `research_difficulty_suggested`.

*Caveat:* classifications and summaries are machine-generated research aids, not peer-reviewed results; `SOLVED-*` entries were citation-checked, but independent verification is recommended before citing.

### New in v1.4.0

This release adds the complete canonical **AIM Workshop Problem Lists** corpus:
**3,359 problems** from 26 AIM domain files. Every problem uses its exact
`AIM-...` canonical identifier, preserves source/workshop provenance, and is
paired with the effective validated research attempt produced by the AIM
multi-agent research run. All problems added in v1.4 come from AIM workshops,
and each received one solution attempt using **GPT-5.6 Sol** at **xhigh**
reasoning effort. The structured reports include **351 new AI results**: 174
full solutions and 177 counterexamples. They are machine-generated claims and
have not been peer reviewed.

- **AIM research audit**: 3,359 validated reports: 174 full solutions, 177 counterexamples, 2,589 partial results, 45 conditional results, 182 reductions, 150 context-only reports, 41 invalid-statement reports, and 1 heuristic result.
- **Research classifications**: 461 `SOLVED-IN-LITERATURE`, 43 `SOLVED-BY-YOU`, 2,664 `PARTIAL-PROGRESS`, and 191 `OPEN-TRIAGE`. These classifications describe the status of the underlying problem and are not a novelty filter for the AI result.
- **Identifiers**: exact `AIM-<DOMAIN>-<NUMBER>` 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.

### 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

OWR records additionally expose `source_citation`, `literature_assessment`, `literature_sources`, and `literature_checked_at`.

### 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**: 2026-08-25T00:00:00Z
**Version**: 1.6.0