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Datasets:
ulamai
/
UnsolvedMath

Tasks:
Question Answering
Text Generation
Modalities:
Document
Languages:
English
Size:
1K<n<10K
Tags:
mathematics
unsolved-problems
math
research
latex
License:
Dataset card Data Studio Files
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The full dataset viewer is not available (click to read why). Only showing a preview of the rows.
The dataset generation failed
Error code:   DatasetGenerationError
Exception:    CastError
Message:      Couldn't cast
metadata: struct<name: string, version: string, description: string, exported_at: string, total_problems: int6 (... 78 chars omitted)
  child 0, name: string
  child 1, version: string
  child 2, description: string
  child 3, exported_at: string
  child 4, total_problems: int64
  child 5, total_categories: int64
  child 6, total_difficulty_levels: int64
  child 7, total_sets: int64
difficulty_levels: list<item: struct<id: int64, level: int64, name: string, description: string, color_class: string>>
  child 0, item: struct<id: int64, level: int64, name: string, description: string, color_class: string>
      child 0, id: int64
      child 1, level: int64
      child 2, name: string
      child 3, description: string
      child 4, color_class: string
categories: list<item: struct<id: int64, name: string, display_name: string, description: string, slug: string,  (... 40 chars omitted)
  child 0, item: struct<id: int64, name: string, display_name: string, description: string, slug: string, order_index (... 28 chars omitted)
      child 0, id: int64
      child 1, name: string
      child 2, display_name: string
      child 3, description: string
      child 4, slug: string
      child 5, order_index: int64
      child 6, created_at: string
sets: list<item: struct<id: int64, name: string, display_name: string, description: string, slug: string,  (... 40 chars omitted)
  child 0, item: struct<id: int64, name: string, display_name: string, description: string, slug: string, order_
...
  child 4, background: string
      child 5, difficulty_level_id: int64
      child 6, status: string
      child 7, proposed_by: string
      child 8, proposed_year: int64
      child 9, category_id: int64
      child 10, set_id: int64
      child 11, view_count: int64
      child 12, favorite_count: int64
      child 13, created_at: timestamp[s]
      child 14, updated_at: timestamp[s]
      child 15, published: bool
      child 16, category: struct<id: int64, name: string, display_name: string, description: string, slug: string, order_index (... 28 chars omitted)
          child 0, id: int64
          child 1, name: string
          child 2, display_name: string
          child 3, description: string
          child 4, slug: string
          child 5, order_index: int64
          child 6, created_at: string
      child 17, difficulty: struct<id: int64, level: int64, name: string, description: string, color_class: string>
          child 0, id: int64
          child 1, level: int64
          child 2, name: string
          child 3, description: string
          child 4, color_class: string
      child 18, set: struct<id: int64, name: string, display_name: string, description: string, slug: string, order_index (... 28 chars omitted)
          child 0, id: int64
          child 1, name: string
          child 2, display_name: string
          child 3, description: string
          child 4, slug: string
          child 5, order_index: int64
          child 6, created_at: string
to
{'id': Value('int64'), 'name': Value('string'), 'display_name': Value('string'), 'description': Value('string'), 'slug': Value('string'), 'order_index': Value('int64'), 'created_at': Value('string')}
because column names don't match
Traceback:    Traceback (most recent call last):
                File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 1800, in _prepare_split_single
                  writer.write_table(table)
                File "/usr/local/lib/python3.12/site-packages/datasets/arrow_writer.py", line 764, in write_table
                  self.write_rows_on_file()  # in case there are buffered rows to write first
                  ^^^^^^^^^^^^^^^^^^^^^^^^^
                File "/usr/local/lib/python3.12/site-packages/datasets/arrow_writer.py", line 663, in write_rows_on_file
                  self._write_table(table)
                File "/usr/local/lib/python3.12/site-packages/datasets/arrow_writer.py", line 773, in _write_table
                  pa_table = table_cast(pa_table, self._schema)
                             ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
                File "/usr/local/lib/python3.12/site-packages/datasets/table.py", line 2321, in table_cast
                  return cast_table_to_schema(table, schema)
                         ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
                File "/usr/local/lib/python3.12/site-packages/datasets/table.py", line 2249, in cast_table_to_schema
                  raise CastError(
              datasets.table.CastError: Couldn't cast
              metadata: struct<name: string, version: string, description: string, exported_at: string, total_problems: int6 (... 78 chars omitted)
                child 0, name: string
                child 1, version: string
                child 2, description: string
                child 3, exported_at: string
                child 4, total_problems: int64
                child 5, total_categories: int64
                child 6, total_difficulty_levels: int64
                child 7, total_sets: int64
              difficulty_levels: list<item: struct<id: int64, level: int64, name: string, description: string, color_class: string>>
                child 0, item: struct<id: int64, level: int64, name: string, description: string, color_class: string>
                    child 0, id: int64
                    child 1, level: int64
                    child 2, name: string
                    child 3, description: string
                    child 4, color_class: string
              categories: list<item: struct<id: int64, name: string, display_name: string, description: string, slug: string,  (... 40 chars omitted)
                child 0, item: struct<id: int64, name: string, display_name: string, description: string, slug: string, order_index (... 28 chars omitted)
                    child 0, id: int64
                    child 1, name: string
                    child 2, display_name: string
                    child 3, description: string
                    child 4, slug: string
                    child 5, order_index: int64
                    child 6, created_at: string
              sets: list<item: struct<id: int64, name: string, display_name: string, description: string, slug: string,  (... 40 chars omitted)
                child 0, item: struct<id: int64, name: string, display_name: string, description: string, slug: string, order_
              ...
                child 4, background: string
                    child 5, difficulty_level_id: int64
                    child 6, status: string
                    child 7, proposed_by: string
                    child 8, proposed_year: int64
                    child 9, category_id: int64
                    child 10, set_id: int64
                    child 11, view_count: int64
                    child 12, favorite_count: int64
                    child 13, created_at: timestamp[s]
                    child 14, updated_at: timestamp[s]
                    child 15, published: bool
                    child 16, category: struct<id: int64, name: string, display_name: string, description: string, slug: string, order_index (... 28 chars omitted)
                        child 0, id: int64
                        child 1, name: string
                        child 2, display_name: string
                        child 3, description: string
                        child 4, slug: string
                        child 5, order_index: int64
                        child 6, created_at: string
                    child 17, difficulty: struct<id: int64, level: int64, name: string, description: string, color_class: string>
                        child 0, id: int64
                        child 1, level: int64
                        child 2, name: string
                        child 3, description: string
                        child 4, color_class: string
                    child 18, set: struct<id: int64, name: string, display_name: string, description: string, slug: string, order_index (... 28 chars omitted)
                        child 0, id: int64
                        child 1, name: string
                        child 2, display_name: string
                        child 3, description: string
                        child 4, slug: string
                        child 5, order_index: int64
                        child 6, created_at: string
              to
              {'id': Value('int64'), 'name': Value('string'), 'display_name': Value('string'), 'description': Value('string'), 'slug': Value('string'), 'order_index': Value('int64'), 'created_at': Value('string')}
              because column names don't match
              
              During handling of the above exception, another exception occurred:
              
              Traceback (most recent call last):
                File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 1802, in _prepare_split_single
                  raise DatasetGenerationCastError.from_cast_error(
              datasets.exceptions.DatasetGenerationCastError: An error occurred while generating the dataset
              
              All the data files must have the same columns, but at some point there are 5 new columns ({'difficulty_levels', 'problems', 'sets', 'categories', 'metadata'}) and 7 missing columns ({'created_at', 'id', 'display_name', 'description', 'slug', 'order_index', 'name'}).
              
              This happened while the json dataset builder was generating data using
              
              hf://datasets/ulamai/UnsolvedMath/difficulty_levels.json (at revision b95f746139ec70f9a01b9bfa3f1908131645cb37), [/tmp/hf-datasets-cache/medium/datasets/26766065908751-config-parquet-and-info-ulamai-UnsolvedMath-48447135/hub/datasets--ulamai--UnsolvedMath/snapshots/b95f746139ec70f9a01b9bfa3f1908131645cb37/categories.json (origin=hf://datasets/ulamai/UnsolvedMath@b95f746139ec70f9a01b9bfa3f1908131645cb37/categories.json), /tmp/hf-datasets-cache/medium/datasets/26766065908751-config-parquet-and-info-ulamai-UnsolvedMath-48447135/hub/datasets--ulamai--UnsolvedMath/snapshots/b95f746139ec70f9a01b9bfa3f1908131645cb37/dataset.json (origin=hf://datasets/ulamai/UnsolvedMath@b95f746139ec70f9a01b9bfa3f1908131645cb37/dataset.json), /tmp/hf-datasets-cache/medium/datasets/26766065908751-config-parquet-and-info-ulamai-UnsolvedMath-48447135/hub/datasets--ulamai--UnsolvedMath/snapshots/b95f746139ec70f9a01b9bfa3f1908131645cb37/difficulty_levels.json (origin=hf://datasets/ulamai/UnsolvedMath@b95f746139ec70f9a01b9bfa3f1908131645cb37/difficulty_levels.json), /tmp/hf-datasets-cache/medium/datasets/26766065908751-config-parquet-and-info-ulamai-UnsolvedMath-48447135/hub/datasets--ulamai--UnsolvedMath/snapshots/b95f746139ec70f9a01b9bfa3f1908131645cb37/problems.json (origin=hf://datasets/ulamai/UnsolvedMath@b95f746139ec70f9a01b9bfa3f1908131645cb37/problems.json), /tmp/hf-datasets-cache/medium/datasets/26766065908751-config-parquet-and-info-ulamai-UnsolvedMath-48447135/hub/datasets--ulamai--UnsolvedMath/snapshots/b95f746139ec70f9a01b9bfa3f1908131645cb37/sets.json (origin=hf://datasets/ulamai/UnsolvedMath@b95f746139ec70f9a01b9bfa3f1908131645cb37/sets.json), /tmp/hf-datasets-cache/medium/datasets/26766065908751-config-parquet-and-info-ulamai-UnsolvedMath-48447135/hub/datasets--ulamai--UnsolvedMath/snapshots/b95f746139ec70f9a01b9bfa3f1908131645cb37/statistics.json (origin=hf://datasets/ulamai/UnsolvedMath@b95f746139ec70f9a01b9bfa3f1908131645cb37/statistics.json)], ['hf://datasets/ulamai/UnsolvedMath@b95f746139ec70f9a01b9bfa3f1908131645cb37/categories.json', 'hf://datasets/ulamai/UnsolvedMath@b95f746139ec70f9a01b9bfa3f1908131645cb37/dataset.json', 'hf://datasets/ulamai/UnsolvedMath@b95f746139ec70f9a01b9bfa3f1908131645cb37/difficulty_levels.json', 'hf://datasets/ulamai/UnsolvedMath@b95f746139ec70f9a01b9bfa3f1908131645cb37/problems.json', 'hf://datasets/ulamai/UnsolvedMath@b95f746139ec70f9a01b9bfa3f1908131645cb37/sets.json', 'hf://datasets/ulamai/UnsolvedMath@b95f746139ec70f9a01b9bfa3f1908131645cb37/statistics.json']
              
              Please either edit the data files to have matching columns, or separate them into different configurations (see docs at https://hf.co/docs/hub/datasets-manual-configuration#multiple-configurations)
              
              During handling of the above exception, another exception occurred:
              
              Traceback (most recent call last):
                File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 1821, in _prepare_split_single
                  num_examples, num_bytes = writer.finalize()
                                            ^^^^^^^^^^^^^^^^^
                File "/usr/local/lib/python3.12/site-packages/datasets/arrow_writer.py", line 781, in finalize
                  self.write_rows_on_file()
                File "/usr/local/lib/python3.12/site-packages/datasets/arrow_writer.py", line 663, in write_rows_on_file
                  self._write_table(table)
                File "/usr/local/lib/python3.12/site-packages/datasets/arrow_writer.py", line 773, in _write_table
                  pa_table = table_cast(pa_table, self._schema)
                             ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
                File "/usr/local/lib/python3.12/site-packages/datasets/table.py", line 2321, in table_cast
                  return cast_table_to_schema(table, schema)
                         ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
                File "/usr/local/lib/python3.12/site-packages/datasets/table.py", line 2249, in cast_table_to_schema
                  raise CastError(
              datasets.table.CastError: Couldn't cast
              metadata: struct<name: string, version: string, description: string, exported_at: string, total_problems: int6 (... 78 chars omitted)
                child 0, name: string
                child 1, version: string
                child 2, description: string
                child 3, exported_at: string
                child 4, total_problems: int64
                child 5, total_categories: int64
                child 6, total_difficulty_levels: int64
                child 7, total_sets: int64
              difficulty_levels: list<item: struct<id: int64, level: int64, name: string, description: string, color_class: string>>
                child 0, item: struct<id: int64, level: int64, name: string, description: string, color_class: string>
                    child 0, id: int64
                    child 1, level: int64
                    child 2, name: string
                    child 3, description: string
                    child 4, color_class: string
              categories: list<item: struct<id: int64, name: string, display_name: string, description: string, slug: string,  (... 40 chars omitted)
                child 0, item: struct<id: int64, name: string, display_name: string, description: string, slug: string, order_index (... 28 chars omitted)
                    child 0, id: int64
                    child 1, name: string
                    child 2, display_name: string
                    child 3, description: string
                    child 4, slug: string
                    child 5, order_index: int64
                    child 6, created_at: string
              sets: list<item: struct<id: int64, name: string, display_name: string, description: string, slug: string,  (... 40 chars omitted)
                child 0, item: struct<id: int64, name: string, display_name: string, description: string, slug: string, order_
              ...
                child 4, background: string
                    child 5, difficulty_level_id: int64
                    child 6, status: string
                    child 7, proposed_by: string
                    child 8, proposed_year: int64
                    child 9, category_id: int64
                    child 10, set_id: int64
                    child 11, view_count: int64
                    child 12, favorite_count: int64
                    child 13, created_at: timestamp[s]
                    child 14, updated_at: timestamp[s]
                    child 15, published: bool
                    child 16, category: struct<id: int64, name: string, display_name: string, description: string, slug: string, order_index (... 28 chars omitted)
                        child 0, id: int64
                        child 1, name: string
                        child 2, display_name: string
                        child 3, description: string
                        child 4, slug: string
                        child 5, order_index: int64
                        child 6, created_at: string
                    child 17, difficulty: struct<id: int64, level: int64, name: string, description: string, color_class: string>
                        child 0, id: int64
                        child 1, level: int64
                        child 2, name: string
                        child 3, description: string
                        child 4, color_class: string
                    child 18, set: struct<id: int64, name: string, display_name: string, description: string, slug: string, order_index (... 28 chars omitted)
                        child 0, id: int64
                        child 1, name: string
                        child 2, display_name: string
                        child 3, description: string
                        child 4, slug: string
                        child 5, order_index: int64
                        child 6, created_at: string
              to
              {'id': Value('int64'), 'name': Value('string'), 'display_name': Value('string'), 'description': Value('string'), 'slug': Value('string'), 'order_index': Value('int64'), 'created_at': Value('string')}
              because column names don't match
              
              The above exception was the direct cause of the following exception:
              
              Traceback (most recent call last):
                File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 1347, in compute_config_parquet_and_info_response
                  parquet_operations = convert_to_parquet(builder)
                                       ^^^^^^^^^^^^^^^^^^^^^^^^^^^
                File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 980, in convert_to_parquet
                  builder.download_and_prepare(
                File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 882, in download_and_prepare
                  self._download_and_prepare(
                File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 943, in _download_and_prepare
                  self._prepare_split(split_generator, **prepare_split_kwargs)
                File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 1646, in _prepare_split
                  for job_id, done, content in self._prepare_split_single(
                                               ^^^^^^^^^^^^^^^^^^^^^^^^^^^
                File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 1832, in _prepare_split_single
                  raise DatasetGenerationError("An error occurred while generating the dataset") from e
              datasets.exceptions.DatasetGenerationError: An error occurred while generating the dataset

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id
int64
name
string
display_name
string
description
string
slug
string
order_index
int64
created_at
string
1
number_theory
Number Theory
Properties of integers, prime numbers, Diophantine equations.
number-theory
1
2026-05-13T14:45:21.186Z
2
combinatorics
Combinatorics
Counting problems, graph theory, discrete structures.
combinatorics
2
2026-05-13T14:45:21.187Z
3
graph_theory
Graph Theory
Problems involving graphs, networks, and their properties.
graph-theory
3
2026-05-13T14:45:21.187Z
4
algebra
Algebra
Group theory, ring theory, field theory, and algebraic structures.
algebra
4
2026-05-13T14:45:21.187Z
5
algebraic_geometry
Algebraic Geometry
Geometric objects defined by polynomial equations.
algebraic-geometry
5
2026-05-13T14:45:21.187Z
6
geometry
Geometry
Euclidean and non-Euclidean geometry, geometric structures.
geometry
6
2026-05-13T14:45:21.187Z
7
topology
Topology
Properties preserved under continuous deformations.
topology
7
2026-05-13T14:45:21.187Z
8
analysis
Analysis
Limits, continuity, calculus, and function theory.
analysis
8
2026-05-13T14:45:21.187Z
9
pde
Partial Differential Equations
PDEs and their applications in physics and geometry.
pde
9
2026-05-13T14:45:21.187Z
10
set_theory
Set Theory
Foundations of mathematics, infinite sets, and cardinality.
set-theory
10
2026-05-13T14:45:21.187Z
11
dynamical_systems
Dynamical Systems
Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.
dynamical-systems
11
2026-05-13T14:45:21.187Z
15
computer_science
Computer Science
Computational complexity, algorithms, and theoretical CS.
computer-science
15
2026-05-13T14:45:21.187Z
16
physics
Mathematical Physics
Problems at the intersection of mathematics and physics.
physics
16
2026-05-13T14:45:21.187Z
17
group_theory
Group Theory
Problems about groups, group actions, representations, and related algebraic structures.
group-theory
17
2026-05-13T14:45:21.187Z
18
logic
Logic
Problems in mathematical logic, model theory, proof theory, and finite model theory.
logic
18
2026-05-13T14:45:21.187Z
19
probability
Probability
Problems involving probability theory, stochastic processes, and random structures.
probability
19
2026-05-13T14:45:21.187Z
20
miscellaneous
Miscellaneous
Problems whose source classification does not fit the main mathematical categories.
miscellaneous
20
2026-05-13T14:45:21.187Z
null
null
null
null
null
null
null
1
L1: Tractable
null
Problems that may be within reach with current techniques. Reserved for future additions.
null
null
null
2
L2: Intermediate
null
Challenging problems requiring solid mathematical background. Reserved for future additions.
null
null
null
3
L3: Advanced
null
Difficult problems requiring specialized knowledge and sophisticated techniques.
null
null
null
4
L4: Expert
null
Very challenging problems at the frontier of mathematical research.
null
null
null
5
L5: Millennium Prize
null
Millennium Prize Problems and problems of equivalent difficulty.
null
null
null
1
null
null
null
null
null
2024-01-01T00:00:00
2
null
null
null
null
null
2024-01-01T00:00:00
3
null
null
null
null
null
2024-01-01T00:00:00
4
null
null
null
null
null
2024-01-01T00:00:00
5
null
null
null
null
null
2024-01-01T00:00:00
6
null
null
null
null
null
2024-01-01T00:00:00
8
null
null
null
null
null
2024-01-01T00:00:00
9
null
null
null
null
null
2024-01-01T00:00:00
11
null
null
null
null
null
2024-01-01T00:00:00
12
null
null
null
null
null
2024-01-01T00:00:00
13
null
null
null
null
null
2024-01-01T00:00:00
10
null
null
null
null
null
2024-01-01T00:00:00
14
null
null
null
null
null
2024-01-01T00:00:00
15
null
null
null
null
null
2024-01-01T00:00:00
18
null
null
null
null
null
2024-01-01T00:00:00
19
null
null
null
null
null
2024-01-01T00:00:00
20
null
null
null
null
null
2024-01-01T00:00:00
21
null
null
null
null
null
2024-01-01T00:00:00
22
null
null
null
null
null
2024-01-01T00:00:00
25
null
null
null
null
null
2024-01-01T00:00:00
26
null
null
null
null
null
2024-01-01T00:00:00
27
null
null
null
null
null
2024-01-01T00:00:00
28
null
null
null
null
null
2024-01-01T00:00:00
29
null
null
null
null
null
2024-01-01T00:00:00
30
null
null
null
null
null
2024-01-01T00:00:00
31
null
null
null
null
null
2024-01-01T00:00:00
32
null
null
null
null
null
2024-01-01T00:00:00
33
null
null
null
null
null
2024-01-01T00:00:00
34
null
null
null
null
null
2024-01-01T00:00:00
36
null
null
null
null
null
2024-01-01T00:00:00
37
null
null
null
null
null
2024-01-01T00:00:00
38
null
null
null
null
null
2024-01-01T00:00:00
40
null
null
null
null
null
2024-01-01T00:00:00
41
null
null
null
null
null
2024-01-01T00:00:00
42
null
null
null
null
null
2024-01-01T00:00:00
43
null
null
null
null
null
2024-01-01T00:00:00
44
null
null
null
null
null
2024-01-01T00:00:00
45
null
null
null
null
null
2024-01-01T00:00:00
46
null
null
null
null
null
2024-01-01T00:00:00
47
null
null
null
null
null
2024-01-01T00:00:00
48
null
null
null
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🌐 Browse UnsolvedMath online

✅ Paper: Open Mathematical Problems as an AI Reasoning Benchmark

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.

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

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 

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

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:

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