UnsolvedMath Dataset

A comprehensive curated collection of 1,146 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 https://unsolvedmath.com

Dataset Description

UnsolvedMath is a meticulously curated dataset of unsolved and historically significant mathematical problems, organized by domain, difficulty level, and problem set. This dataset aggregates problems from the most prestigious collections in mathematics, with a particular focus on Paul Erdős's extensive problem collection.

Featured Collections

• Erdős Problems (632 problems) - Extensive collection from Paul Erdős, one of the most prolific mathematicians of the 20th century
• Millennium Prize Problems - Clay Mathematics Institute's seven $1M problems
• Hilbert's 23 Problems - David Hilbert's foundational problems from 1900
• Smale's Problems - Steve Smale's 18 problems for the 21st century
• DARPA's 23 Mathematical Challenges - Fundamental research challenges
• Ben Green's 100 Open Problems - Problems in additive combinatorics
• Hardy-Littlewood Conjectures - Foundational problems on primes and partitions
• Landau's Problems - Four classic problems on prime numbers
• Richard Guy - Prime Numbers - Problems from "Unsolved Problems in Number Theory"

Dataset Summary

• Total Problems: 1,146
• Erdős Problems: 632 (with full citations and references)
• Categories: 12 mathematical domains
• Difficulty Levels: 5 (L1: Tractable → L5: Millennium Prize)
• Problem Sets: 9 curated collections
• Format: JSON with LaTeX mathematical notation
• License: CC BY 4.0

What's New

This dataset includes the most comprehensive collection of Erdős problems available in structured format:

• 632 Erdős problems (EP-1 through EP-1135) from the Erdos Problems website
• Complete problem statements with LaTeX mathematical notation
• Detailed backgrounds with historical context
• Full bibliographic references for each problem
• Difficulty classifications (L1-L3)
• Category assignments (Number Theory, Combinatorics, Graph Theory, etc.)

Supported Tasks

• Mathematical research and exploration
• Mathematical question answering systems
• LaTeX/mathematical notation processing
• Problem classification and organization
• Educational content generation
• Research bibliography extraction
• Historical mathematics analysis

Dataset Structure

Data Files

The dataset consists of multiple JSON files:

1. problems.json (1.4 MB) - Main dataset containing all 1,146 problems
2. categories.json (3.0 KB) - 12 mathematical domain classifications
3. difficulty_levels.json (1.1 KB) - 5-tier difficulty system
4. sets.json (3.1 KB) - Problem set metadata
5. dataset.json (1.5 MB) - Combined file with all data and metadata

Data Fields

Problems

Each problem contains:

• id (int): Unique identifier
• problem_number (string): Problem code (e.g., "EP-1", "MPP-001")
• title (string): Problem title
• statement (string): Complete problem statement with LaTeX notation
• background (string): Historical context, references, and related work
• difficulty_level_id (int): Difficulty level (1-5)
• status (string): "open" or "solved"
• category_id (int): Mathematical domain identifier
• set_id (int, optional): Problem set identifier
• proposed_by (string, optional): Person who proposed the problem
• proposed_year (int, optional): Year the problem was first posed
• view_count (int): Number of views
• favorite_count (int): Number of favorites
• created_at (string): Timestamp
• updated_at (string): Timestamp
• published (boolean): Publication status

Categories

12 mathematical domains:

• Number Theory - Properties of integers, primes, Diophantine equations
• Combinatorics - Counting, arrangements, combinatorial structures
• Graph Theory - Networks, graphs, and their properties
• Algebra - Algebraic structures and equations
• Algebraic Geometry - Geometric objects defined by polynomials
• Geometry - Euclidean and non-Euclidean geometry
• Topology - Properties preserved under continuous deformations
• Analysis - Limits, continuity, calculus, function theory
• Partial Differential Equations - PDEs and applications
• Set Theory - Foundations, infinite sets, cardinality
• Computer Science - Computational complexity, algorithms
• Mathematical Physics - Mathematics-physics intersection

Difficulty Levels

• L1: Tractable - Problems potentially within reach with current techniques
• L2: Intermediate - Challenging problems requiring solid mathematical background
• L3: Advanced - Difficult problems requiring specialized knowledge
• L4: Expert - Very challenging problems at the frontier of research
• L5: Millennium Prize - Millennium Prize Problems and equivalent difficulty

Problem Sets

• Millennium Prize Problems (7 problems)
• Hilbert's 23 Problems
• Smale's Problems (18 problems)
• DARPA's 23 Mathematical Challenges
• Ben Green's 100 Open Problems
• Erdős Problems (632 problems)
• Hardy-Littlewood Conjectures
• Landau's Problems (4 problems)
• Richard Guy - A: Prime Numbers

Usage

Loading the Dataset

import json

# Load all problems
with open('problems.json', 'r', encoding='utf-8') as f:
    problems = json.load(f)

print(f"Total problems: {len(problems)}")

# Load the complete dataset
with open('dataset.json', 'r', encoding='utf-8') as f:
    data = json.load(f)

print(f"Problems: {data['metadata']['total_problems']}")
print(f"Categories: {len(data['categories'])}")
print(f"Sets: {len(data['sets'])}")

Example: Filtering Erdős Problems

import json

with open('problems.json', 'r') as f:
    problems = json.load(f)

# Get all Erdős problems
erdos_problems = [
    p for p in problems
    if p['problem_number'].startswith('EP-')
]

print(f"Found {len(erdos_problems)} Erdős problems")

# Get Erdős problems in Number Theory
erdos_nt = [
    p for p in erdos_problems
    if p['category_id'] == 1  # Number Theory
]

print(f"Erdős problems in Number Theory: {len(erdos_nt)}")

Example: Filtering by Difficulty

import json

with open('problems.json', 'r') as f:
    problems = json.load(f)

# Get all Millennium Prize problems (L5)
millennium = [
    p for p in problems
    if p['difficulty_level_id'] == 5
]

# Get tractable problems (L1)
tractable = [
    p for p in problems
    if p['difficulty_level_id'] == 1
]

print(f"Millennium Prize problems: {len(millennium)}")
print(f"Tractable problems: {len(tractable)}")

Example: Working with LaTeX

# Problems contain LaTeX notation in statement and background fields
problem = problems[0]
print(f"Title: {problem['title']}")
print(f"Statement: {problem['statement']}")

# Example statement with LaTeX:
# "If $A\\subseteq \\{1,\\ldots,N\\}$ with $\\lvert A\\rvert=n$
#  is such that the subset sums $\\sum_{a\\in S}a$ are distinct
#  for all $S\\subseteq A$ then $N \\gg 2^{n}$."

# Use KaTeX, MathJax, or sympy to render LaTeX
from IPython.display import display, Markdown
display(Markdown(problem['statement']))

Example: Extracting Citations from Erdős Problems

import json
import re

with open('problems.json', 'r') as f:
    problems = json.load(f)

# Get all Erdős problems
erdos = [p for p in problems if p['problem_number'].startswith('EP-')]

# Extract citations from background
citations = set()
for problem in erdos:
    bg = problem.get('background', '')
    # Find citations like \\cite{Er98}
    refs = re.findall(r'\\cite\{([^}]+)\}', bg)
    citations.update(refs)

print(f"Unique citations in Erdős problems: {len(citations)}")
print(f"Examples: {list(citations)[:10]}")

Data Collection and Curation

Sources

This dataset was curated from:

• Erdős problems website by Thomas Bloom (erdosproblems.com)
• Clay Mathematics Institute - Official Millennium Prize documentation
• Historical mathematical problem collections (Hilbert, Smale, Landau)
• Published research papers and mathematical surveys
• Reputable mathematical organizations (AMS, IMU, etc.)
• Richard Guy's "Unsolved Problems in Number Theory"
• Ben Green's additive combinatorics problem collection

Erdős Problems Special Notes

The 632 Erdős problems include:

• Complete problem statements
• Detailed backgrounds with historical context from original sources
• Full bibliographic references (e.g., Erdős papers from 1931-1999)
• Cross-references between related problems
• Citations to recent progress and partial results
• OEIS sequence references where applicable
• Connections to other famous problems and conjectures

Quality Assurance

All problems include:

• Accurate mathematical statements with proper LaTeX notation (mostly, there might be some smaller corrections needed)
• Historical context and background information
• Proper attribution and source references
• Classification by mathematical domain and difficulty

Statistics

By Difficulty Level

• L1 (Tractable): 662 problems (57.8%)
• L2 (Intermediate): 56 problems (4.9%)
• L3 (Advanced): 72 problems (6.3%)
• L4 (Expert): 220 problems (19.2%)
• L5 (Millennium): 136 problems (11.9%)

By Category

• Number Theory: 497 problems (43.4%) - heavily represented in Erdős problems
• Graph Theory: 214 problems (18.7%)
• Combinatorics: 195 problems (17.0%)
• Other categories: 240 problems (20.9%)

By Set

• Erdős Problems: 632 problems (55.1% of total)
• Other historical collections: 514 problems (44.9% of total)

Ethical Considerations

• Academic Integrity: This dataset is for research and educational purposes
• Attribution: All problems properly attributed to original sources
• Open Problems: Status accuracy maintained as of January 2026
• Updates: Some problems may be solved after dataset publication
• Citations: Erdős problems include full bibliographic references for verification

Limitations

• The dataset represents a curated selection, not an exhaustive list of all unsolved problems
• Problem difficulty is subjective
• LaTeX notation may require preprocessing for some applications
• Status (open/solved) should be verified for time-sensitive applications
• Some Erdős problem backgrounds contain extensive LaTeX citations that may need special handling

Citation

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

@misc{unsolvedmath2026,
  title={UnsolvedMath: A Curated Collection of Open Mathematics Problems},
  author={P. Chojecki},
  year={2026},
  howpublished={\url{https://huggingface.co/datasets/ulamai/UnsolvedMath}},
  note={Includes over 1000 open mathematical problems}
}

For the Erdős problems specifically:

@misc{erdos-problems,
  title={Erdős Problems},
  author={T. F. Bloom},
  year={2026},
  howpublished={\url{https://www.erdosproblems.com}},
  note={Forum}
}

Additional Information

Dataset Curators

Przemek Chojecki

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

Updates and Maintenance

• Version: 1.0.0
• Last Updated: 2026-01-24
• Total Problems: 1,146
• Erdős Problems Added: 2026-01-24

Contact

For questions, issues, or contributions, visit the project repository.

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Generated: 2026-01-24 Version: 1.0.0 Total Problems: 1,146 Erdős Problems: 632