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UnsolvedMath

A comprehensive curated collection of 8,785 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.

Paper: "Open Mathematical Problems as an AI Reasoning Benchmark"

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

Dataset Summary

Total Problems: 8785
Erdős Problems: 632 problems with citations and references
Version: 1.5.0
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 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.

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:

problems.json - Main dataset containing all problems
categories.json - Mathematical domain classifications
difficulty_levels.json - 5-tier difficulty system
sets.json - Problem set metadata (Millennium Prize, Hilbert's 23, etc.)
dataset.json - Combined file with all data
statistics.json - Dataset statistics
research_results.json - Per-problem AMR and AIM research notes (status, literature, result, what remains)
aim_statement_audit.json - Per-problem AIM statement-recovery evidence and verification status

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

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: 6246
L4: Expert: 963
L5: Millennium Prize: 137

Problems by Status

Open: 4462
Solved: 696
Partially Solved: 3627

Usage

Loading the Dataset

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

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

# 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

Citation

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

@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
Dataset: huggingface.co/datasets/ulamai/UnsolvedMath

Generated: 2026-08-18T00:00:00Z Version: 1.5.0

Downloads last month: 3,080

Total file size:

164 MB

UnsolvedMath Dataset