id int64 1 30M | problem_number stringlengths 4 34 | title stringlengths 8 149 | statement stringlengths 11 35.2k | background stringlengths 395 52.6k | difficulty_level_id int64 1 5 | status stringclasses 3
values | proposed_by stringclasses 310
values | proposed_year int64 1.74k 2.03k ⌀ | category_id int64 1 20 | set_id int64 1 15 ⌀ | view_count int64 0 2.34k | favorite_count int64 0 156 | created_at timestamp[s]date 2024-01-01 00:00:00 2026-08-25 00:00:00 | updated_at timestamp[s]date 2024-01-01 00:00:00 2026-09-28 00:00:00 | published bool 2
classes | category dict | difficulty dict | set dict | literature_assessment stringlengths 80 804 ⌀ | literature_sources listlengths 1 6 ⌀ | literature_checked_at timestamp[s]date 2026-08-21 00:00:00 2026-09-28 00:00:00 ⌀ | solution_reference stringclasses 257
values | status_review dict | tags listlengths 1 5 ⌀ | clean_statement stringlengths 11 35.2k ⌀ | original_statement stringlengths 11 35.7k ⌀ | statement_status stringclasses 4
values | statement_verification stringlengths 5 900 ⌀ | archive_reason stringclasses 26
values | research_classification stringclasses 4
values | research_summary stringlengths 40 1.95k ⌀ | research_difficulty_suggested stringclasses 14
values | historical_research_summary stringclasses 22
values | research_summary_reviewed_at timestamp[s]date 2026-09-28 00:00:00 2026-09-28 00:00:00 ⌀ | source_url stringlengths 25 84 ⌀ | source_citation stringlengths 75 207 ⌀ | duplicate_of listlengths 0 2 ⌀ |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1,418 | GRAPH-031 | Erdős-Hajnal Conjecture | Does every graph family defined by a forbidden induced subgraph have polynomial-sized cliques or independent sets? | The Erdős-Hajnal conjecture states that for any graph H, there exists ε > 0 such that every H-free graph on n vertices contains a clique or independent set of size at least n^ε. This would be a dramatic strengthening of Ramsey theory, which only guarantees log-size structures. Proven for many specific H, but the genera... | 5 | partially_solved | null | null | 3 | null | 234 | 19 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 5,
"level": 5,
"name": "L5: Millennium Prize",
"description": "Millennium Prize Problems and problems of equivalent difficulty.",
"color_class": "text-purple-600 bg-purple-50 border-purple-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,419 | GRAPH-032 | Linear Arboricity Conjecture | Can every graph with maximum degree Δ be decomposed into at most ⌈(Δ+1)/2⌉ linear forests? | A linear forest is a disjoint union of paths. The linear arboricity conjecture states that graphs decompose into roughly Δ/2 linear forests. This would provide tight bounds on a natural graph decomposition parameter. Proven for many graph classes (planar graphs, graphs with large girth), but the general case remains op... | 4 | partially_solved | null | null | 3 | null | 156 | 12 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 4,
"level": 4,
"name": "L4: Expert",
"description": "Very challenging problems at the frontier of mathematical research.",
"color_class": "text-red-600 bg-red-50 border-red-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,420 | GRAPH-033 | Lovász Conjecture | Does every finite connected vertex-transitive graph contain a Hamiltonian path? | Lovász conjectured that vertex-transitive graphs (graphs looking the same from every vertex) always have Hamiltonian paths. Even stronger: do they have Hamiltonian cycles (except for K₂ and some Cayley graphs)? Known for many classes, but a general proof eludes us. This connects group theory, algebraic graph theory, an... | 4 | open | null | null | 3 | null | 189 | 15 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 4,
"level": 4,
"name": "L4: Expert",
"description": "Very challenging problems at the frontier of mathematical research.",
"color_class": "text-red-600 bg-red-50 border-red-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,421 | GRAPH-034 | Oberwolfach Problem | For which 2-regular graphs H can the complete graph be decomposed into edge-disjoint copies of H? | The Oberwolfach problem asks: given a 2-regular graph H (disjoint union of cycles), can K_n be decomposed into copies of H? This generalizes cycle decompositions and connects to the famous Oberwolfach conferences. Solutions are known for many cases (like single cycles), but a complete characterization remains open. Thi... | 4 | partially_solved | null | null | 3 | null | 167 | 13 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 4,
"level": 4,
"name": "L4: Expert",
"description": "Very challenging problems at the frontier of mathematical research.",
"color_class": "text-red-600 bg-red-50 border-red-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,422 | GRAPH-035 | Cubic Graph Pathwidth | What is the maximum pathwidth of an n-vertex cubic graph? | Pathwidth measures how closely a graph resembles a path. For cubic (3-regular) graphs, the maximum pathwidth is conjectured to be around n/6, but exact bounds are unknown. This problem connects graph width parameters with regular graphs. Understanding pathwidth has implications for algorithms—many NP-hard problems beco... | 3 | partially_solved | null | null | 3 | null | 134 | 10 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,423 | GRAPH-036 | Snake-in-the-Box Problem | What is the longest induced path in an n-dimensional hypercube graph? | A snake-in-the-box is a longest induced path in the n-dimensional hypercube Q_n. Known exact values for small n, but no formula for general n. This problem combines combinatorics, coding theory (Gray codes), and graph theory. Snakes have applications in error-correcting codes and analog-to-digital conversion. Finding o... | 3 | partially_solved | null | null | 3 | null | 178 | 14 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,424 | GRAPH-037 | Sumner's Conjecture | Does every (2n-2)-vertex tournament contain every n-vertex oriented tree? | Sumner conjectured that tournaments (complete directed graphs) on 2n-2 vertices contain all oriented trees on n vertices as subgraphs. This would be a directed analogue of various tree embedding results. The best known bound is (4+o(1))n instead of 2n-2. This problem connects tournament theory with tree embeddings and ... | 4 | partially_solved | null | null | 3 | null | 156 | 12 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 4,
"level": 4,
"name": "L4: Expert",
"description": "Very challenging problems at the frontier of mathematical research.",
"color_class": "text-red-600 bg-red-50 border-red-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,425 | GRAPH-038 | Tuza's Conjecture | Can the edges of any graph be covered by at most 2ν triangles, where ν is the maximum size of a triangle packing? | Tuza conjectured that the minimum number of edges needed to hit all triangles is at most twice the maximum number of edge-disjoint triangles. This is a covering-packing duality question. Best known bound is 3ν. The conjecture would provide a tight relationship between triangle packings and triangle covers, with applica... | 4 | open | null | null | 3 | null | 189 | 15 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 4,
"level": 4,
"name": "L4: Expert",
"description": "Very challenging problems at the frontier of mathematical research.",
"color_class": "text-red-600 bg-red-50 border-red-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,426 | GRAPH-039 | Unfriendly Partition Conjecture | Does every countable graph admit a partition where every vertex has at least as many neighbors outside its part as inside? | The unfriendly partition conjecture asks if vertices can be partitioned into two sets such that each vertex has at least as many "unfriendly" neighbors (in the other set) as "friendly" ones (in its own set). Proven for finite graphs, but open for countably infinite graphs. This problem combines graph theory with infini... | 4 | open | null | null | 3 | null | 145 | 11 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 4,
"level": 4,
"name": "L4: Expert",
"description": "Very challenging problems at the frontier of mathematical research.",
"color_class": "text-red-600 bg-red-50 border-red-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,427 | GRAPH-040 | Zarankiewicz Problem | What is the maximum number of edges in a bipartite graph on (m,n) vertices with no complete bipartite subgraph $K_{s,t}$? | The Zarankiewicz problem asks for ex(m,n;K_{s,t})—the maximum edges in an (m,n)-bipartite graph avoiding K_{s,t} as a subgraph. This is a fundamental problem in extremal graph theory, generalizing the Kővári–Sós–Turán theorem. Exact values are known for some parameters, but most cases remain open. Applications include ... | 4 | partially_solved | null | null | 3 | null | 198 | 16 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 4,
"level": 4,
"name": "L4: Expert",
"description": "Very challenging problems at the frontier of mathematical research.",
"color_class": "text-red-600 bg-red-50 border-red-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,428 | GRAPH-041 | Vizing's Conjecture | For the Cartesian product of graphs $G \square H$, is the domination number at least $\gamma(G) \cdot \gamma(H)$? | Vizing conjectured that the domination number of the Cartesian product of two graphs is at least the product of their domination numbers. This would give a lower bound on how efficiently one can dominate product graphs. The conjecture has been verified for many special cases but remains open in general. It has connecti... | 4 | open | null | null | 3 | null | 172 | 13 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 4,
"level": 4,
"name": "L4: Expert",
"description": "Very challenging problems at the frontier of mathematical research.",
"color_class": "text-red-600 bg-red-50 border-red-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,429 | GRAPH-042 | Hamiltonian Decomposition of Hypergraphs | Do complete k-uniform hypergraphs admit Hamiltonian decompositions into tight cycles? | Walescki's theorem states that complete graphs have Hamiltonian decompositions. The hypergraph version asks whether complete k-uniform hypergraphs can be decomposed into tight Hamiltonian cycles. This is a natural generalization from graphs to hypergraphs, with connections to design theory and combinatorial structures.... | 4 | partially_solved | null | null | 3 | null | 134 | 10 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 4,
"level": 4,
"name": "L4: Expert",
"description": "Very challenging problems at the frontier of mathematical research.",
"color_class": "text-red-600 bg-red-50 border-red-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,430 | GRAPH-043 | Word-Representable Graphs: Letter Copies Bound | Are there graphs on n vertices requiring more than floor(n/2) copies of each letter for word-representation? | Word-representable graphs can be encoded by words where two vertices are adjacent if their letters alternate in the word. The question asks whether any graph needs more than half the number of vertices as copies of each letter. This connects graph theory to formal languages and combinatorics on words.
<!-- LITERATURE-... | 3 | open | null | null | 3 | null | 98 | 7 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,431 | GRAPH-044 | Characterization of Word-Representable Planar Graphs | Characterize which planar graphs are word-representable. | Word-representable graphs are those that can be encoded by words over their vertex set where adjacency corresponds to letter alternation. While some characterizations exist for special graph classes, characterizing word-representable planar graphs remains open. This combines planar graph structure with formal language ... | 4 | open | null | null | 3 | null | 87 | 6 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 4,
"level": 4,
"name": "L4: Expert",
"description": "Very challenging problems at the frontier of mathematical research.",
"color_class": "text-red-600 bg-red-50 border-red-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,432 | GRAPH-045 | Word-Representable Graphs: Forbidden Subgraph Characterization | Characterize word-representable graphs in terms of forbidden induced subgraphs. | Many graph classes have elegant characterizations via forbidden subgraphs (e.g., planar graphs avoid K₅ and K₃,₃). The question asks for a similar characterization of word-representable graphs. Such a characterization would provide deep insight into the structure of these graphs and their connection to formal languages... | 4 | partially_solved | null | null | 3 | null | 92 | 7 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 4,
"level": 4,
"name": "L4: Expert",
"description": "Very challenging problems at the frontier of mathematical research.",
"color_class": "text-red-600 bg-red-50 border-red-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,433 | GRAPH-046 | Word-Representable Near-Triangulations | Characterize word-representable near-triangulations containing K₄. | Near-triangulations are planar graphs close to being triangulations. A characterization is known for K₄-free cases. The question asks to extend this to near-triangulations containing the complete graph K₄. This combines planar graph structure with word-representability constraints.
<!-- LITERATURE-TRIAGE:BEGIN -->
## ... | 4 | solved | null | null | 3 | null | 76 | 5 | 2024-01-01T00:00:00 | 2026-09-27T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 4,
"level": 4,
"name": "L4: Expert",
"description": "Very challenging problems at the frontier of mathematical research.",
"color_class": "text-red-600 bg-red-50 border-red-200"
} | null | Reconciled with the existing literature review of 2026-08-17: A May 2026 preprint gives a complete forbidden-induced-subgraph characterization of all word-representable near-triangulations, directly including the requested K4-containing case. This is a consistency correction based on that cited review; the discussion d... | [
{
"url": "https://arxiv.org/abs/2605.25733",
"label": "Suchanda Roy and Ramesh Hariharasubramanian, Characterization of Word-Representable Near-Triangulations, arXiv:2605.25733 (2026)."
},
{
"url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"label": "UnsolvedMath discus... | 2026-09-27T00:00:00 | Suchanda Roy and Ramesh Hariharasubramanian, Characterization of Word-Representable Near-Triangulations, arXiv:2605.25733 (2026).: https://arxiv.org/abs/2605.25733 | {
"source_url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"checked_at": "2026-09-27T00:00:00",
"kind": "triage_reconciliation",
"evidence": "existing_literature_review"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,434 | GRAPH-047 | Representation Number 3 Classification | Classify graphs with representation number exactly 3. | The representation number is the minimum number of letter copies needed to word-represent a graph. Graphs with representation number 1 and 2 are relatively well understood. The question asks for a complete classification of graphs requiring exactly 3 copies—not representable with 2, but possible with 3.
<!-- LITERATUR... | 3 | open | null | null | 3 | null | 81 | 6 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,435 | GRAPH-048 | Crown Graphs and Longest Word-Representants | Among bipartite graphs, do crown graphs require the longest word-representants? | Crown graphs are a specific family of bipartite graphs with a symmetric structure. The conjecture suggests they are extremal for word-representation length among bipartite graphs. This would identify which bipartite graphs are hardest to encode as words, with implications for the complexity of word-representation.
<!-... | 3 | open | null | null | 3 | null | 73 | 5 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,436 | GRAPH-049 | Line Graphs of Non-Word-Representable Graphs | Is the line graph of a non-word-representable graph always non-word-representable? | The line graph operation transforms a graph into one where edges become vertices. The question asks whether word-non-representability is preserved under this operation. A positive answer would show that line graphs amplify the complexity of word-representation, while a counterexample would reveal subtle structural prop... | 4 | solved | null | null | 3 | null | 84 | 6 | 2024-01-01T00:00:00 | 2026-09-27T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 4,
"level": 4,
"name": "L4: Expert",
"description": "Very challenging problems at the frontier of mathematical research.",
"color_class": "text-red-600 bg-red-50 border-red-200"
} | null | Reconciled with the existing literature review of 2026-08-17: A 2025 primary manuscript gives infinitely many non-word-representable Mycielski graphs whose line graphs are word-representable, answering the question negatively. This is a consistency correction based on that cited review; the discussion does not independ... | [
{
"url": "https://arxiv.org/abs/2509.03339",
"label": "Khyodeno Mozhui, Tithi Dwary, and K. V. Krishna, Line Graphs of Non-Word-Representable Graphs are Not Always Non-Word-Representable, arXiv:2509.03339 (2025)."
},
{
"url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"... | 2026-09-27T00:00:00 | Khyodeno Mozhui, Tithi Dwary, and K. V. Krishna, Line Graphs of Non-Word-Representable Graphs are Not Always Non-Word-Representable, arXiv:2509.03339 (2025).: https://arxiv.org/abs/2509.03339 | {
"source_url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"checked_at": "2026-09-27T00:00:00",
"kind": "triage_reconciliation",
"evidence": "existing_literature_review"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,437 | GRAPH-050 | Translating Graph Problems to Word Problems | Which hard graph problems can be efficiently solved by translating graphs to their word representations? | Word-representation provides an alternative encoding of graphs as strings over an alphabet. The question asks which computationally hard graph problems become tractable when working with word representations instead of adjacency lists or matrices. This could reveal new algorithmic techniques leveraging string algorithm... | 4 | partially_solved | null | null | 3 | null | 105 | 8 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 4,
"level": 4,
"name": "L4: Expert",
"description": "Very challenging problems at the frontier of mathematical research.",
"color_class": "text-red-600 bg-red-50 border-red-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,438 | GRAPH-051 | Imbalance Conjecture | If every edge has imbalance ≥1, is the multiset of edge imbalances always graphic? | The imbalance of an edge is the absolute difference between the degrees of its endpoints. The conjecture asks whether the multiset of these imbalances can always realize a degree sequence of some graph when all imbalances are positive. This connects degree sequences with edge properties in a novel way.
<!-- LITERATURE... | 3 | partially_solved | null | null | 3 | null | 94 | 7 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,439 | GRAPH-052 | Implicit Graph Conjecture | Do slowly-growing hereditary graph families admit implicit representations? | The implicit graph conjecture concerns the existence of succinct encodings for hereditary families of graphs (closed under induced subgraphs) whose growth rate is subexponential. An implicit representation would allow efficient storage and adjacency queries. This has implications for data structures and graph databases... | 4 | solved | null | null | 3 | null | 112 | 9 | 2024-01-01T00:00:00 | 2026-09-27T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 4,
"level": 4,
"name": "L4: Expert",
"description": "Very challenging problems at the frontier of mathematical research.",
"color_class": "text-red-600 bg-red-50 border-red-200"
} | null | Hatami and Hatami refuted the implicit graph conjecture by constructing hereditary graph families of factorial speed without logarithmic-length adjacency labels.
**What remains.** No unresolved part of the stated question is identified in the cited result. | [
{
"url": "https://arxiv.org/abs/2111.13198",
"label": "Hamed Hatami and Pooya Hatami, The Implicit Graph Conjecture is False (FOCS 2022)"
},
{
"url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"label": "UnsolvedMath discussion #4 — Alper Ferudun, status updates and foll... | 2026-09-27T00:00:00 | Hamed Hatami and Pooya Hatami, The Implicit Graph Conjecture is False (FOCS 2022): https://arxiv.org/abs/2111.13198 | {
"source_url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"checked_at": "2026-09-27T00:00:00",
"kind": "resolution",
"evidence": "published"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,440 | GRAPH-053 | Ryser's Conjecture | For r-partite r-uniform hypergraphs, is the vertex cover number at most (r-1) times the matching number? | Ryser's conjecture relates the minimum transversal (vertex cover) size to maximum matching size in hypergraphs. For graphs (r=2) this is König's theorem. The conjecture proposes a tight bound for hypergraphs: τ ≤ (r-1)ν. This is a central open problem in hypergraph theory with connections to combinatorial optimization.... | 4 | partially_solved | null | null | 3 | null | 156 | 12 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 4,
"level": 4,
"name": "L4: Expert",
"description": "Very challenging problems at the frontier of mathematical research.",
"color_class": "text-red-600 bg-red-50 border-red-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,441 | GRAPH-054 | Second Neighborhood Problem | Does every oriented graph have a vertex with at least as many vertices at distance 2 as at distance 1? | The second neighborhood problem asks whether oriented graphs always contain a vertex whose second neighborhood (vertices at distance exactly 2) is at least as large as its first neighborhood (out-neighbors). This has been conjectured by several researchers and has connections to tournament theory and Seymour's second n... | 4 | open | null | null | 3 | null | 128 | 10 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 4,
"level": 4,
"name": "L4: Expert",
"description": "Very challenging problems at the frontier of mathematical research.",
"color_class": "text-red-600 bg-red-50 border-red-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,442 | GRAPH-055 | Teschner's Bondage Number Conjecture | Is the bondage number of a graph always ≤ 3Δ/2, where Δ is the maximum degree? | The bondage number is the minimum number of edges whose removal increases the domination number. Teschner conjectured an upper bound of 3Δ/2 in terms of maximum degree Δ. This would establish a fundamental relationship between edge removal sensitivity and local graph structure in domination problems.
<!-- LITERATURE-T... | 3 | partially_solved | null | null | 3 | null | 89 | 7 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,443 | GRAPH-056 | Tutte's 5-Flow Conjecture | Does every bridgeless graph have a nowhere-zero 5-flow? | Tutte's 5-flow conjecture is one of the most famous problems in graph theory. A nowhere-zero k-flow is an orientation and edge-labeling with values in {±1,...,±(k-1)} satisfying flow conservation. The conjecture states that 5 colors suffice for all bridgeless graphs. Related to the four-color theorem and still wide ope... | 5 | open | null | null | 3 | null | 267 | 21 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 5,
"level": 5,
"name": "L5: Millennium Prize",
"description": "Millennium Prize Problems and problems of equivalent difficulty.",
"color_class": "text-purple-600 bg-purple-50 border-purple-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,444 | GRAPH-057 | Tutte's 4-Flow Conjecture for Petersen-Minor-Free Graphs | Does every Petersen-minor-free bridgeless graph have a nowhere-zero 4-flow? | This is a refinement of Tutte's 5-flow conjecture for graphs without Petersen graph minors. The Petersen graph is known to require 5 colors for nowhere-zero flows, so excluding it might allow 4-flows. This conjecture connects graph minors, nowhere-zero flows, and the special role of the Petersen graph in combinatorics.... | 5 | partially_solved | null | null | 3 | null | 198 | 16 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 5,
"level": 5,
"name": "L5: Millennium Prize",
"description": "Millennium Prize Problems and problems of equivalent difficulty.",
"color_class": "text-purple-600 bg-purple-50 border-purple-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,445 | GRAPH-058 | Woodall's Conjecture | Is the minimum dicut size equal to the maximum number of disjoint dijoins in a directed graph? | Woodall's conjecture is a directed graph analogue of Menger's theorem. A dicut is a set of arcs whose removal disconnects the graph directionally, and a dijoin connects specified vertex pairs. The conjecture proposes a min-max relation, which would be a fundamental packing-covering duality for directed graphs.
<!-- LI... | 4 | partially_solved | null | null | 3 | null | 134 | 11 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 4,
"level": 4,
"name": "L4: Expert",
"description": "Very challenging problems at the frontier of mathematical research.",
"color_class": "text-red-600 bg-red-50 border-red-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,446 | ALG-001 | Birch-Tate Conjecture | Relate the order of the center of the Steinberg group of the ring of integers to the Dedekind zeta function. | The Birch-Tate conjecture connects algebraic K-theory to special values of zeta functions. It predicts a precise relationship between the center of the Steinberg group St(O_K) of a number field K and the value of its Dedekind zeta function at s=-1. This is a fundamental connection between algebra and analytic number th... | 5 | partially_solved | null | null | 4 | null | 187 | 14 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 5,
"level": 5,
"name": "L5: Millennium Prize",
"description": "Millennium Prize Problems and problems of equivalent difficulty.",
"color_class": "text-purple-600 bg-purple-50 border-purple-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,447 | ALG-002 | Casas-Alvero Conjecture | If a polynomial of degree d over a field of characteristic 0 shares a factor with each of its first d-1 derivatives, must it be $(x-a)^d$? | The Casas-Alvero conjecture states that a polynomial sharing roots with all its derivatives (up to degree d-1) must be a power of a linear polynomial. Despite its elementary statement, it remains open. The conjecture has been verified for many special cases but lacks a general proof.
<!-- LITERATURE-TRIAGE:BEGIN -->
#... | 4 | partially_solved | null | null | 4 | null | 203 | 16 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 4,
"level": 4,
"name": "L4: Expert",
"description": "Very challenging problems at the frontier of mathematical research.",
"color_class": "text-red-600 bg-red-50 border-red-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,448 | ALG-003 | Connes Embedding Problem | Can every finite von Neumann algebra be embedded into an ultrapower of the hyperfinite II₁ factor? | The Connes embedding problem is a central question in operator algebra theory. It asks whether all separable II₁ factors embed into the ultrapower of the hyperfinite II₁ factor. This problem connects functional analysis, quantum information theory, and logic. Recent claimed solutions using quantum computing have genera... | 5 | solved | null | null | 4 | null | 289 | 22 | 2024-01-01T00:00:00 | 2026-09-27T00:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 5,
"level": 5,
"name": "L5: Millennium Prize",
"description": "Millennium Prize Problems and problems of equivalent difficulty.",
"color_class": "text-purple-600 bg-purple-50 border-purple-200"
} | null | Ji, Natarajan, Vidick, Wright and Yuen refute Connes embedding through MIP*=RE (2020).
**What remains.** No unresolved part of the stated question is identified in the cited result. | [
{
"url": "https://arxiv.org/abs/2001.04383",
"label": "Ji et al., MIP*=RE"
},
{
"url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"label": "UnsolvedMath discussion #4 — Alper Ferudun, status updates and follow-ups"
}
] | 2026-09-27T00:00:00 | Ji et al., MIP*=RE: https://arxiv.org/abs/2001.04383 | {
"source_url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"checked_at": "2026-09-27T00:00:00",
"kind": "resolution",
"evidence": "published"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,449 | ALG-004 | Crouzeix's Conjecture | Is $\|f(A)\| \leq 2 \sup_{z \in W(A)} |f(z)|$ for any matrix A and analytic function f on the numerical range W(A)? | Crouzeix's conjecture bounds the matrix norm of f(A) by twice the supremum of |f| over the numerical range of A. The constant 2 would be optimal. This conjecture connects matrix theory, complex analysis, and numerical analysis. The best known bound is approximately 11.08, far from the conjectured 2.
<!-- LITERATURE-TR... | 4 | solved | null | null | 4 | null | 156 | 12 | 2024-01-01T00:00:00 | 2026-09-27T00:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 4,
"level": 4,
"name": "L4: Expert",
"description": "Very challenging problems at the frontier of mathematical research.",
"color_class": "text-red-600 bg-red-50 border-red-200"
} | null | Lorist and Schwenninger (August 2026) claim the constant-2 Crouzeix bound; Shanmu Jin independently announced a proof in July 2026. These are unrefereed preprints. The analytic formulation uses functions holomorphic on a neighborhood of the numerical range.
**What remains.** Independent expert verification and peer re... | [
{
"url": "https://arxiv.org/abs/2608.03841",
"label": "Emiel Lorist and Felix Schwenninger, A solution to Crouzeix’s conjecture (2026)"
},
{
"url": "https://www.preprints.org/manuscript/202607.1919",
"label": "Shanmu Jin, The Numerical Range Is a 2-Spectral Set (2026)"
},
{
"url": "https... | 2026-09-27T00:00:00 | Emiel Lorist and Felix Schwenninger, A solution to Crouzeix’s conjecture (2026): https://arxiv.org/abs/2608.03841
Shanmu Jin, The Numerical Range Is a 2-Spectral Set (2026): https://www.preprints.org/manuscript/202607.1919 | {
"source_url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"checked_at": "2026-09-27T00:00:00",
"kind": "resolution",
"evidence": "unrefereed_preprint"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,450 | ALG-005 | Determinantal Conjecture | Characterize the determinant of the sum of two normal matrices. | The determinantal conjecture seeks inequalities or characterizations for det(A+B) when A and B are normal matrices. While det(AB) = det(A)det(B) is well known, the sum of normal matrices presents challenges. This problem connects linear algebra with operator theory and has applications in quantum mechanics.
<!-- LITER... | 4 | partially_solved | null | null | 4 | null | 134 | 10 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 4,
"level": 4,
"name": "L4: Expert",
"description": "Very challenging problems at the frontier of mathematical research.",
"color_class": "text-red-600 bg-red-50 border-red-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,451 | ALG-006 | Eilenberg-Ganea Conjecture | Does every group with cohomological dimension 2 have a 2-dimensional Eilenberg-MacLane space K(G,1)? | The Eilenberg-Ganea conjecture asks whether cohomological dimension equals geometric dimension for groups. Specifically, if cd(G)=2, does there exist a 2-dimensional CW complex with fundamental group G? The conjecture is known to hold for cd ≠ 2. This connects algebraic topology with group theory.
<!-- LITERATURE-TRIA... | 4 | partially_solved | null | null | 4 | null | 178 | 14 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 4,
"level": 4,
"name": "L4: Expert",
"description": "Very challenging problems at the frontier of mathematical research.",
"color_class": "text-red-600 bg-red-50 border-red-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,452 | ALG-007 | Farrell-Jones Conjecture | Are the assembly maps in algebraic K-theory and L-theory isomorphisms? | The Farrell-Jones conjecture predicts that certain assembly maps are isomorphisms for all groups. This would have major consequences for the computation of algebraic K-theory and L-theory groups. The conjecture has been verified for many important classes of groups including hyperbolic groups and arithmetic groups.
<!... | 5 | partially_solved | null | null | 4 | null | 165 | 13 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 5,
"level": 5,
"name": "L5: Millennium Prize",
"description": "Millennium Prize Problems and problems of equivalent difficulty.",
"color_class": "text-purple-600 bg-purple-50 border-purple-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,453 | ALG-008 | Finite Lattice Representation Problem | Is every finite lattice isomorphic to the congruence lattice of some finite algebra? | The finite lattice representation problem asks whether every finite lattice can be realized as the congruence lattice of a finite algebra. While every finite lattice is the congruence lattice of some algebra, requiring finiteness of the algebra is much more restrictive. This is a central problem in universal algebra.
... | 4 | partially_solved | null | null | 4 | null | 142 | 11 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 4,
"level": 4,
"name": "L4: Expert",
"description": "Very challenging problems at the frontier of mathematical research.",
"color_class": "text-red-600 bg-red-50 border-red-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,454 | ALG-009 | Hadamard Matrix Conjecture | Does a Hadamard matrix of order 4k exist for every positive integer k? | The Hadamard conjecture states that Hadamard matrices (square matrices with entries ±1 and mutually orthogonal rows) exist for all orders divisible by 4. These matrices have applications in coding theory, cryptography, and experimental design. The smallest open case is k=167 (order 668).
<!-- LITERATURE-TRIAGE:BEGIN -... | 4 | open | null | null | 4 | null | 245 | 19 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 4,
"level": 4,
"name": "L4: Expert",
"description": "Very challenging problems at the frontier of mathematical research.",
"color_class": "text-red-600 bg-red-50 border-red-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,455 | ALG-010 | Köthe Conjecture | If a ring has no nil two-sided ideal besides {0}, does it also have no nil one-sided ideal besides {0}? | The Köthe conjecture asks whether the absence of nontrivial nil ideals implies the absence of nontrivial nil one-sided ideals. A nil ideal is one where every element is nilpotent. This has been a central problem in ring theory for decades, with connections to the structure theory of noncommutative rings.
<!-- LITERATU... | 4 | solved | null | null | 4 | null | 167 | 13 | 2024-01-01T00:00:00 | 2026-09-27T00:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 4,
"level": 4,
"name": "L4: Expert",
"description": "Very challenging problems at the frontier of mathematical research.",
"color_class": "text-red-600 bg-red-50 border-red-200"
} | null | Adamczewski, Böhmler and Marczinzik announce a counterexample to Köthe’s conjecture (September 2026). Recorded as a claimed negative resolution in an unrefereed preprint.
**What remains.** Independent expert verification and peer review of the recent counterexample remain. | [
{
"url": "https://arxiv.org/abs/2609.07996",
"label": "Tom Adamczewski, Bernhard Böhmler and Rene Marczinzik, A counterexample to Köthe’s conjecture and a question of Rowen"
},
{
"url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"label": "UnsolvedMath discussion #4 — Al... | 2026-09-27T00:00:00 | Tom Adamczewski, Bernhard Böhmler and Rene Marczinzik, A counterexample to Köthe’s conjecture and a question of Rowen: https://arxiv.org/abs/2609.07996 | {
"source_url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"checked_at": "2026-09-27T00:00:00",
"kind": "resolution",
"evidence": "unrefereed_preprint"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,456 | ALG-011 | Perfect Cuboid | Does there exist a perfect cuboid—a rectangular parallelepiped with integer edges, face diagonals, and space diagonal? | A perfect cuboid would be a box where all edges, face diagonals, and the space diagonal are integers. Despite extensive computational searches, no perfect cuboid has been found, nor has non-existence been proven. This is a Diophantine problem with connections to number theory and geometry.
<!-- LITERATURE-TRIAGE:BEGIN... | 3 | open | null | null | 4 | null | 312 | 24 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,457 | ALG-012 | Rota's Basis Conjecture | Given n bases of an n-dimensional matroid, can we find n disjoint rainbow bases? | Rota's basis conjecture asks whether n disjoint bases B₁,...,Bₙ of a matroid of rank n can be rearranged into an n×n matrix where each row is a basis and each column is a transversal (rainbow basis). This elegant conjecture connects matroid theory with combinatorics and has resisted many attempts at proof.
<!-- LITERA... | 4 | partially_solved | null | null | 4 | null | 189 | 15 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 4,
"level": 4,
"name": "L4: Expert",
"description": "Very challenging problems at the frontier of mathematical research.",
"color_class": "text-red-600 bg-red-50 border-red-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,458 | MOD-001 | Cherlin-Zilber Conjecture | Is every simple group with a stable first-order theory an algebraic group over an algebraically closed field? | The Cherlin-Zilber conjecture (also called the algebraicity conjecture) proposes that infinite simple groups with stable theories are essentially algebraic groups. This would classify a vast class of model-theoretically tame groups. The conjecture connects model theory, group theory, and algebraic geometry in a profoun... | 5 | partially_solved | null | null | 4 | null | 176 | 14 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 5,
"level": 5,
"name": "L5: Millennium Prize",
"description": "Millennium Prize Problems and problems of equivalent difficulty.",
"color_class": "text-purple-600 bg-purple-50 border-purple-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,459 | MOD-002 | Generalized Star Height Problem | Can all regular languages be expressed with generalized regular expressions having bounded star height? | The generalized star height problem asks whether there's a universal bound on the nesting depth of Kleene stars needed to express regular languages. This is a fundamental question in formal language theory and automata theory, with connections to computational complexity and logic.
<!-- LITERATURE-TRIAGE:BEGIN -->
## ... | 4 | open | null | null | 4 | null | 143 | 11 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 4,
"level": 4,
"name": "L4: Expert",
"description": "Very challenging problems at the frontier of mathematical research.",
"color_class": "text-red-600 bg-red-50 border-red-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,460 | MOD-003 | Hilbert's Tenth Problem for Number Fields | For which number fields is there an algorithm to determine if a Diophantine equation has solutions? | Hilbert's tenth problem asked for an algorithm to solve Diophantine equations over the integers—proven impossible by Matiyasevich. The question for other number fields remains open. It's known to be undecidable for some fields and decidable for others. Determining exactly which fields admit such algorithms is a major o... | 5 | partially_solved | null | null | 4 | null | 234 | 18 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 5,
"level": 5,
"name": "L5: Millennium Prize",
"description": "Millennium Prize Problems and problems of equivalent difficulty.",
"color_class": "text-purple-600 bg-purple-50 border-purple-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,461 | MOD-004 | Vaught Conjecture | Does every complete first-order theory in a countable language have countably many, $\aleph_0$, or $2^{\aleph_0}$ countable models? | Vaught's conjecture states that the number of countable models of a complete theory is either finite, countably infinite, or continuum. This would rule out intermediate cardinalities. The conjecture connects model theory with descriptive set theory and has deep connections to the structure of mathematical logic.
<!-- ... | 5 | partially_solved | null | null | 4 | null | 198 | 16 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 5,
"level": 5,
"name": "L5: Millennium Prize",
"description": "Millennium Prize Problems and problems of equivalent difficulty.",
"color_class": "text-purple-600 bg-purple-50 border-purple-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,462 | MOD-005 | Tarski's Exponential Function Problem | Is the theory of the real numbers with addition, multiplication, and exponentiation decidable? | Tarski proved that the theory of real closed fields is decidable. Adding exponentiation makes the question much harder. Decidability would mean an algorithm exists to determine truth of statements involving exp. This has implications for automated theorem proving and connections to transcendental number theory.
<!-- L... | 5 | open | null | null | 4 | null | 256 | 20 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 5,
"level": 5,
"name": "L5: Millennium Prize",
"description": "Millennium Prize Problems and problems of equivalent difficulty.",
"color_class": "text-purple-600 bg-purple-50 border-purple-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,463 | MOD-006 | Stable Field Conjecture | Is every infinite field with a stable first-order theory separably closed? | The stable field conjecture predicts that infinite fields with stable theories are separably closed. Stable theories are model-theoretically well-behaved. This conjecture would classify all stable fields, providing a complete understanding of these algebraically important structures through a model-theoretic lens.
<!-... | 5 | partially_solved | null | null | 4 | null | 167 | 13 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 5,
"level": 5,
"name": "L5: Millennium Prize",
"description": "Millennium Prize Problems and problems of equivalent difficulty.",
"color_class": "text-purple-600 bg-purple-50 border-purple-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,464 | MOD-007 | Henson Graphs Finite Model Property | Do Henson graphs have the finite model property? | Henson graphs are universal homogeneous graphs omitting certain finite subgraphs. The finite model property asks whether every satisfiable sentence has a finite model. This question connects infinite graph theory, model theory, and combinatorics, with implications for the decidability of their first-order theories.
<!... | 4 | partially_solved | null | null | 4 | null | 123 | 9 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 4,
"level": 4,
"name": "L4: Expert",
"description": "Very challenging problems at the frontier of mathematical research.",
"color_class": "text-red-600 bg-red-50 border-red-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,465 | MOD-008 | O-Minimal Theory with Trans-Exponential Growth | Does there exist an o-minimal first-order theory with a trans-exponential (rapid growth) function? | O-minimal structures are ordered structures where definable sets have simple topology. Known o-minimal structures include real closed fields and structures with restricted analytic functions. The question asks whether o-minimality is compatible with very fast-growing functions, testing the limits of tame model theory.
... | 5 | open | null | null | 4 | null | 145 | 11 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 5,
"level": 5,
"name": "L5: Millennium Prize",
"description": "Millennium Prize Problems and problems of equivalent difficulty.",
"color_class": "text-purple-600 bg-purple-50 border-purple-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,466 | MOD-009 | Infinite Minimal Field Algebraic Closure | Is every infinite minimal field of characteristic zero algebraically closed? | A minimal structure is one where every definable subset is finite or cofinite. The question asks whether infinite fields with this property must be algebraically closed (when char=0). This would characterize the simplest infinite fields from a model-theoretic perspective, connecting field theory with minimality.
<!-- ... | 4 | partially_solved | null | null | 4 | null | 134 | 10 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 4,
"level": 4,
"name": "L4: Expert",
"description": "Very challenging problems at the frontier of mathematical research.",
"color_class": "text-red-600 bg-red-50 border-red-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,467 | MOD-010 | Keisler's Order | Determine the structure of Keisler's order on first-order theories. | Keisler's order compares first-order theories based on the complexity of their ultrapowers. Understanding this order would classify theories by their model-theoretic complexity. Recent breakthroughs have shed light on the order's structure, but a complete classification remains elusive. This connects with classificatio... | 5 | partially_solved | null | null | 4 | null | 156 | 12 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 5,
"level": 5,
"name": "L5: Millennium Prize",
"description": "Millennium Prize Problems and problems of equivalent difficulty.",
"color_class": "text-purple-600 bg-purple-50 border-purple-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,468 | ALG-013 | Serre's Conjecture II | For simply connected semisimple algebraic groups over fields of cohomological dimension ≤2, is $H^1(F,G) = 0$? | Serre's Conjecture II predicts that the first Galois cohomology of simply connected semisimple groups vanishes over fields of small cohomological dimension. This would have major implications for the classification of algebraic groups and forms. The conjecture is known for various classes of fields but remains open in ... | 5 | partially_solved | null | null | 4 | null | 178 | 14 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 5,
"level": 5,
"name": "L5: Millennium Prize",
"description": "Millennium Prize Problems and problems of equivalent difficulty.",
"color_class": "text-purple-600 bg-purple-50 border-purple-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,469 | ALG-014 | Serre's Positivity Conjecture | If R is a regular local ring and P,Q are prime ideals with $\dim(R/P) + \dim(R/Q) = \dim(R)$, is $\chi(R/P, R/Q) > 0$? | Serre's positivity conjecture predicts that the Euler characteristic (intersection multiplicity) is positive when dimensions add correctly. This is part of a broader set of homological conjectures in commutative algebra. The conjecture would provide fundamental information about the structure of modules over regular ri... | 5 | partially_solved | null | null | 4 | null | 145 | 11 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 5,
"level": 5,
"name": "L5: Millennium Prize",
"description": "Millennium Prize Problems and problems of equivalent difficulty.",
"color_class": "text-purple-600 bg-purple-50 border-purple-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,470 | ALG-015 | Uniform Boundedness Conjecture for Rational Points | Is there a bound N(g,d) such that all curves of genus g≥2 over degree d number fields have at most N(g,d) rational points? | The uniform boundedness conjecture asks whether the number of rational points on curves of genus ≥2 is uniformly bounded in terms of genus and field degree. This would be a remarkable strengthening of Faltings' theorem (finite number of points). The conjecture connects arithmetic geometry with Diophantine equations.
<... | 5 | open | null | null | 4 | null | 213 | 17 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 5,
"level": 5,
"name": "L5: Millennium Prize",
"description": "Millennium Prize Problems and problems of equivalent difficulty.",
"color_class": "text-purple-600 bg-purple-50 border-purple-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,479 | TOP-001 | Baum-Connes Conjecture | Is the assembly map in K-theory an isomorphism for all locally compact groups? | The Baum-Connes conjecture predicts that a certain assembly map from equivariant K-homology to the K-theory of group C*-algebras is an isomorphism. This would have major consequences for the Novikov conjecture, index theory, and the structure of operator algebras. Known for many groups, general case open.
<!-- LITERAT... | 5 | partially_solved | null | null | 7 | null | 198 | 15 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 5,
"level": 5,
"name": "L5: Millennium Prize",
"description": "Millennium Prize Problems and problems of equivalent difficulty.",
"color_class": "text-purple-600 bg-purple-50 border-purple-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,480 | TOP-002 | Berge Conjecture | Are Berge knots the only knots in S³ admitting lens space surgeries? | The Berge conjecture states that Berge knots (constructed via a specific procedure) are the only knots in the 3-sphere that admit Dehn surgeries yielding lens spaces. This would classify all such knots, providing deep insight into the relationship between knot theory and 3-manifold topology.
<!-- LITERATURE-TRIAGE:BEG... | 4 | partially_solved | null | null | 7 | null | 167 | 13 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 4,
"level": 4,
"name": "L4: Expert",
"description": "Very challenging problems at the frontier of mathematical research.",
"color_class": "text-red-600 bg-red-50 border-red-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,481 | TOP-003 | Borel Conjecture | Are aspherical closed manifolds determined up to homeomorphism by their fundamental groups? | The Borel conjecture predicts that aspherical closed manifolds (those with contractible universal cover) are rigid—completely determined by their fundamental group up to homeomorphism. This would be a remarkable topological rigidity result, currently known only for special classes of manifolds.
<!-- LITERATURE-TRIAGE:... | 5 | partially_solved | null | null | 7 | null | 189 | 15 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 5,
"level": 5,
"name": "L5: Millennium Prize",
"description": "Millennium Prize Problems and problems of equivalent difficulty.",
"color_class": "text-purple-600 bg-purple-50 border-purple-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,482 | TOP-004 | Hilbert-Smith Conjecture | If a locally compact group acts faithfully and continuously on a manifold, must it be a Lie group? | The Hilbert-Smith conjecture asks whether every locally compact group with a continuous faithful action on a manifold is necessarily a Lie group. This would rule out p-adic groups acting on manifolds, resolving a fundamental question about the symmetries of topological spaces.
<!-- LITERATURE-TRIAGE:BEGIN -->
## Liter... | 5 | partially_solved | null | null | 7 | null | 212 | 17 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 5,
"level": 5,
"name": "L5: Millennium Prize",
"description": "Millennium Prize Problems and problems of equivalent difficulty.",
"color_class": "text-purple-600 bg-purple-50 border-purple-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,483 | TOP-005 | Novikov Conjecture | Are certain polynomials in Pontryagin classes homotopy invariants? | The Novikov conjecture states that higher signatures (certain rational combinations of Pontryagin numbers) are oriented homotopy invariants. This has profound consequences for manifold topology, surgery theory, and K-theory. Proven for many classes of groups, but the general case remains open.
<!-- LITERATURE-TRIAGE:B... | 5 | partially_solved | null | null | 7 | null | 234 | 18 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 5,
"level": 5,
"name": "L5: Millennium Prize",
"description": "Millennium Prize Problems and problems of equivalent difficulty.",
"color_class": "text-purple-600 bg-purple-50 border-purple-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,484 | TOP-006 | Unknotting Problem | Can unknots be recognized in polynomial time? | The unknotting problem asks whether there exists a polynomial-time algorithm to determine if a knot diagram represents the unknot. While algorithms exist (exponential time), polynomial-time decidability remains open. This is a central problem in computational topology with connections to complexity theory.
<!-- LITERA... | 4 | partially_solved | null | null | 7 | null | 256 | 20 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 4,
"level": 4,
"name": "L4: Expert",
"description": "Very challenging problems at the frontier of mathematical research.",
"color_class": "text-red-600 bg-red-50 border-red-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,485 | TOP-007 | Volume Conjecture | Do quantum invariants of knots determine their hyperbolic volume? | The volume conjecture predicts an exponential relationship between the colored Jones polynomial (a quantum invariant) and the hyperbolic volume of a knot complement. This would connect quantum topology with hyperbolic geometry in a striking way, revealing deep structures in 3-dimensional topology.
<!-- LITERATURE-TRIA... | 5 | partially_solved | null | null | 7 | null | 201 | 16 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 5,
"level": 5,
"name": "L5: Millennium Prize",
"description": "Millennium Prize Problems and problems of equivalent difficulty.",
"color_class": "text-purple-600 bg-purple-50 border-purple-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,486 | TOP-008 | Whitehead Conjecture | Is every connected subcomplex of a 2-dimensional aspherical CW complex also aspherical? | The Whitehead conjecture asks whether asphericity (having contractible universal cover) is preserved under taking subcomplexes in dimension 2. This would clarify the local structure of aspherical spaces and has connections to group theory and low-dimensional topology.
<!-- LITERATURE-TRIAGE:BEGIN -->
## Literature rev... | 4 | open | null | null | 7 | null | 143 | 11 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 4,
"level": 4,
"name": "L4: Expert",
"description": "Very challenging problems at the frontier of mathematical research.",
"color_class": "text-red-600 bg-red-50 border-red-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,487 | TOP-009 | Zeeman Conjecture | Is $K \times [0,1]$ collapsible for every finite contractible 2-dimensional CW complex K? | The Zeeman conjecture predicts that the product of any finite contractible 2-complex with an interval is collapsible (can be reduced to a point by elementary collapses). This relates to the Poincaré conjecture and questions about higher-dimensional manifolds. A counterexample would have major implications.
<!-- LITERA... | 4 | open | null | null | 7 | null | 134 | 10 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 4,
"level": 4,
"name": "L4: Expert",
"description": "Very challenging problems at the frontier of mathematical research.",
"color_class": "text-red-600 bg-red-50 border-red-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,488 | COMB-001 | 1/3-2/3 Conjecture | Does every non-total finite poset have two elements x,y with P(x before y in random linear extension) ∈ [1/3, 2/3]? | The 1/3-2/3 conjecture asks whether finite partially ordered sets (not totally ordered) always contain a pair with intermediate probability of appearing in a certain order. This connects order theory with probability and has implications for sorting algorithms and social choice theory.
<!-- LITERATURE-TRIAGE:BEGIN -->... | 3 | partially_solved | null | null | 2 | null | 124 | 9 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,489 | COMB-002 | Lonely Runner Conjecture | If k runners with distinct speeds run on a unit circle, will each runner be "lonely" (≥1/k away from others) at some time? | The lonely runner conjecture predicts that in a system of runners with different speeds on a circular track, each runner will at some point be far from all others. Verified for k≤7, this problem connects view obstruction, Diophantine approximation, and number theory.
<!-- LITERATURE-TRIAGE:BEGIN -->
## Literature revi... | 4 | partially_solved | null | null | 2 | null | 156 | 12 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 4,
"level": 4,
"name": "L4: Expert",
"description": "Very challenging problems at the frontier of mathematical research.",
"color_class": "text-red-600 bg-red-50 border-red-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,490 | COMB-003 | Sunflower Conjecture | Can the minimum size for sunflowers be bounded by an exponential (not super-exponential) function of k? | The sunflower conjecture asks whether families of k-element sets containing a sunflower (r sets with common "core") require only exponentially many sets in k. Recent progress by Alweiss et al. improved bounds but the original conjecture remains open. Fundamental for extremal combinatorics.
<!-- LITERATURE-TRIAGE:BEGIN... | 4 | partially_solved | null | null | 2 | null | 178 | 14 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 4,
"level": 4,
"name": "L4: Expert",
"description": "Very challenging problems at the frontier of mathematical research.",
"color_class": "text-red-600 bg-red-50 border-red-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,491 | COMB-004 | Union-Closed Sets Conjecture | For any finite union-closed family of sets, does some element appear in at least half the sets? | Frankl's union-closed sets conjecture (also called the union-closed set conjecture) states that in any family of sets closed under unions, at least one element appears in ≥50% of the sets. Despite its elementary statement, this problem has resisted all attempts at proof.
<!-- LITERATURE-TRIAGE:BEGIN -->
## Literature ... | 4 | partially_solved | null | null | 2 | null | 189 | 15 | 2024-01-01T00:00:00 | 2026-09-27T00:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 4,
"level": 4,
"name": "L4: Expert",
"description": "Very challenging problems at the frontier of mathematical research.",
"color_class": "text-red-600 bg-red-50 border-red-200"
} | null | The family containing only the empty set refutes a degenerate literal formulation. Frankl’s union-closed sets conjecture excludes this case and remains open.
**What remains.** The earlier solved label is not accepted for the intended or insufficiently specified problem. The cited partial result or literal observation ... | [
{
"url": "https://arxiv.org/abs/2211.09055",
"label": "J. Gilmer, A constant lower bound for the union-closed sets conjecture, arXiv:2211.09055 (2022)."
},
{
"url": "https://doi.org/10.3390/e25050767",
"label": "L. Yu, Dimension-Free Bounds for the Union-Closed Sets Conjecture, Entropy 25 (2023)... | 2026-09-27T00:00:00 | null | {
"source_url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"checked_at": "2026-09-27T00:00:00",
"kind": "scope_correction",
"evidence": "scope_review"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,492 | COMB-005 | Ramsey Number R(5,5) | What is the exact value of the Ramsey number R(5,5)? | Ramsey theory asks: in any 2-coloring of edges of the complete graph Kₙ, what's the minimum n guaranteeing a monochromatic K₅? Known: 43 ≤ R(5,5) ≤ 48. Finding the exact value would be a major breakthrough. Paul Erdős famously said R(6,6) would require alien technology.
<!-- LITERATURE-TRIAGE:BEGIN -->
## Literature r... | 4 | partially_solved | null | null | 2 | null | 267 | 21 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 4,
"level": 4,
"name": "L4: Expert",
"description": "Very challenging problems at the frontier of mathematical research.",
"color_class": "text-red-600 bg-red-50 border-red-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,495 | NUM-001 | Singmaster's Conjecture | Is there a finite upper bound on multiplicities of entries >1 in Pascal's triangle? | Singmaster's conjecture asks whether any number (other than 1) appears in Pascal's triangle only finitely many times. Known: no entry appears more than 8 times. A proof would reveal deep structure in binomial coefficients and their divisibility properties.
<!-- LITERATURE-TRIAGE:BEGIN -->
## Literature review (checked... | 4 | partially_solved | null | null | 1 | null | 178 | 14 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 4,
"level": 4,
"name": "L4: Expert",
"description": "Very challenging problems at the frontier of mathematical research.",
"color_class": "text-red-600 bg-red-50 border-red-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,496 | NUM-002 | Odd Perfect Numbers | Do any odd perfect numbers exist? | A perfect number equals the sum of its proper divisors. All known perfect numbers are even (form 2^(p-1)(2^p-1) for Mersenne primes). Whether odd perfect numbers exist is one of the oldest open problems in mathematics, dating to ancient Greece. If they exist, they must be very large (>10^1500).
<!-- LITERATURE-TRIAGE:... | 5 | partially_solved | null | null | 1 | null | 412 | 32 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 5,
"level": 5,
"name": "L5: Millennium Prize",
"description": "Millennium Prize Problems and problems of equivalent difficulty.",
"color_class": "text-purple-600 bg-purple-50 border-purple-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,497 | NUM-003 | Infinitude of Perfect Numbers | Are there infinitely many perfect numbers? | All known perfect numbers are even and correspond to Mersenne primes via Euclid-Euler theorem. The question reduces to: are there infinitely many Mersenne primes? This remains open despite extensive computational searches. Connected to the distribution of primes and special number forms.
<!-- LITERATURE-TRIAGE:BEGIN -... | 5 | open | null | null | 1 | null | 345 | 27 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 5,
"level": 5,
"name": "L5: Millennium Prize",
"description": "Millennium Prize Problems and problems of equivalent difficulty.",
"color_class": "text-purple-600 bg-purple-50 border-purple-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,498 | NUM-004 | Quasiperfect Numbers | Do quasiperfect numbers exist? | A quasiperfect number n has σ(n) = 2n+1 (sum of divisors is one more than twice the number). No quasiperfect numbers are known. If they exist, they must be odd perfect squares >10^35. This problem connects divisor functions with perfect number theory.
<!-- LITERATURE-TRIAGE:BEGIN -->
## Literature review (checked 2026... | 4 | partially_solved | null | null | 1 | null | 167 | 13 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 4,
"level": 4,
"name": "L4: Expert",
"description": "Very challenging problems at the frontier of mathematical research.",
"color_class": "text-red-600 bg-red-50 border-red-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,499 | NUM-005 | Lychrel Numbers | Do Lychrel numbers exist in base 10? | A Lychrel number never forms a palindrome through iterative reverse-and-add process. 196 is the first candidate—after billions of iterations, no palindrome found. Proving existence or non-existence would resolve this computational mystery connecting palindromes with iteration dynamics.
<!-- LITERATURE-TRIAGE:BEGIN -->... | 3 | open | null | null | 1 | null | 234 | 18 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,500 | NUM-006 | Odd Weird Numbers | Do odd weird numbers exist? | Weird numbers are abundant but not semiperfect (no subset of divisors sums to the number). All known weird numbers are even. Finding an odd weird number or proving none exist would reveal deep structure in additive properties of divisors.
<!-- LITERATURE-TRIAGE:BEGIN -->
## Literature review (checked 2026-08-17)
**St... | 4 | partially_solved | null | null | 1 | null | 189 | 15 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 4,
"level": 4,
"name": "L4: Expert",
"description": "Very challenging problems at the frontier of mathematical research.",
"color_class": "text-red-600 bg-red-50 border-red-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,501 | NUM-007 | Infinitude of Amicable Pairs | Are there infinitely many pairs of amicable numbers? | Amicable pairs (m,n) satisfy σ(m)-m=n and σ(n)-n=m. Over 12 million pairs known, but infinity unproven. Related to perfect numbers and sociable chains. Erdős-Rieger heuristics suggest infinity, but proof remains elusive.
<!-- LITERATURE-TRIAGE:BEGIN -->
## Literature review (checked 2026-08-17)
**Status:** open
**C... | 4 | open | null | null | 1 | null | 212 | 17 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 4,
"level": 4,
"name": "L4: Expert",
"description": "Very challenging problems at the frontier of mathematical research.",
"color_class": "text-red-600 bg-red-50 border-red-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,502 | NUM-008 | Pi Normality | Is π a normal number (all digits equally frequent in all bases)? | A normal number has each digit appearing with equal asymptotic frequency in every base. While π appears statistically normal (verified to trillions of digits), no proof exists. This connects transcendental numbers, digit distribution, and randomness in mathematical constants.
<!-- LITERATURE-TRIAGE:BEGIN -->
## Litera... | 5 | open | null | null | 1 | null | 389 | 30 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 5,
"level": 5,
"name": "L5: Millennium Prize",
"description": "Millennium Prize Problems and problems of equivalent difficulty.",
"color_class": "text-purple-600 bg-purple-50 border-purple-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,503 | NUM-009 | Algebraic Number Normality | Are all irrational algebraic numbers normal? | The question asks whether every irrational root of a polynomial with integer coefficients has all digits equally distributed in every base. A positive answer would be a remarkable connection between algebraic structure and digit statistics. Currently, we cannot prove normality for any specific algebraic irrational.
<!... | 5 | open | null | null | 1 | null | 201 | 16 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 5,
"level": 5,
"name": "L5: Millennium Prize",
"description": "Millennium Prize Problems and problems of equivalent difficulty.",
"color_class": "text-purple-600 bg-purple-50 border-purple-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,504 | NUM-010 | Gilbreath's Conjecture | Does iterating unsigned differences on prime sequence always yield 1 as first element? | Start with primes 2,3,5,7,11,... Take absolute differences: 1,2,2,4,... Repeat. Conjecture: first element is always 1. Verified to huge primes, but unproven. This reveals hidden regularity in prime gaps with implications for prime distribution.
<!-- LITERATURE-TRIAGE:BEGIN -->
## Literature review (checked 2026-08-17)... | 4 | open | null | null | 1 | null | 156 | 12 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 4,
"level": 4,
"name": "L4: Expert",
"description": "Very challenging problems at the frontier of mathematical research.",
"color_class": "text-red-600 bg-red-50 border-red-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,505 | NUM-011 | Lander-Parkin-Selfridge Conjecture | If Σᵢ aᵢᵏ = Σⱼ bⱼᵏ with m terms on left, n on right, is m+n ≥ k? | The LPS conjecture generalizes Fermat's Last Theorem to sums of k-th powers. It predicts you need at least k terms total for nontrivial solutions. Counterexamples exist for specific cases, but the general conjecture remains open with implications for Diophantine equations.
<!-- LITERATURE-TRIAGE:BEGIN -->
## Literatur... | 4 | open | null | null | 1 | null | 178 | 14 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 4,
"level": 4,
"name": "L4: Expert",
"description": "Very challenging problems at the frontier of mathematical research.",
"color_class": "text-red-600 bg-red-50 border-red-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,506 | NUM-012 | Class Number Problem | Are there infinitely many real quadratic fields with class number 1 (unique factorization)? | The class number problem asks whether infinitely many real quadratic number fields Q(√d) have unique factorization. For imaginary quadratic fields, Heegner-Baker-Stark proved only finitely many exist. The real case remains open—a fundamental question in algebraic number theory.
<!-- LITERATURE-TRIAGE:BEGIN -->
## Lite... | 5 | open | null | null | 1 | null | 198 | 16 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 5,
"level": 5,
"name": "L5: Millennium Prize",
"description": "Millennium Prize Problems and problems of equivalent difficulty.",
"color_class": "text-purple-600 bg-purple-50 border-purple-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,507 | NUM-013 | Hilbert's 12th Problem | Extend Kronecker-Weber theorem to abelian extensions of arbitrary number fields. | Hilbert's 12th problem asks for explicit construction of abelian extensions of number fields via special values of transcendental functions (generalizing cyclotomic fields for Q). Partial progress via complex multiplication, but general case remains one of Hilbert's unsolved problems.
<!-- LITERATURE-TRIAGE:BEGIN -->
... | 5 | partially_solved | null | null | 1 | null | 187 | 15 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 5,
"level": 5,
"name": "L5: Millennium Prize",
"description": "Millennium Prize Problems and problems of equivalent difficulty.",
"color_class": "text-purple-600 bg-purple-50 border-purple-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,508 | NUM-014 | Leopoldt's Conjecture | Does the p-adic regulator of an algebraic number field never vanish? | Leopoldt's conjecture predicts that the p-adic regulator (a p-adic analogue of the classical regulator from Dirichlet's unit theorem) is always nonzero. This has major implications for Iwasawa theory and the structure of p-adic L-functions.
<!-- LITERATURE-TRIAGE:BEGIN -->
## Literature review (checked 2026-08-17)
**... | 5 | partially_solved | null | null | 1 | null | 156 | 12 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 5,
"level": 5,
"name": "L5: Millennium Prize",
"description": "Millennium Prize Problems and problems of equivalent difficulty.",
"color_class": "text-purple-600 bg-purple-50 border-purple-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,509 | NUM-015 | Siegel Zeros | Do Siegel zeros (real zeros of Dirichlet L-functions near s=1) exist? | Siegel zeros are hypothetical exceptional real zeros of L-functions very close to s=1. If they exist, they violate the Generalized Riemann Hypothesis. Their existence would have major consequences for prime distribution in arithmetic progressions. Most believe they don't exist.
<!-- LITERATURE-TRIAGE:BEGIN -->
## Lite... | 5 | partially_solved | null | null | 1 | null | 234 | 18 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 5,
"level": 5,
"name": "L5: Millennium Prize",
"description": "Millennium Prize Problems and problems of equivalent difficulty.",
"color_class": "text-purple-600 bg-purple-50 border-purple-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,510 | NUM-016 | Schanuel's Conjecture | For e and π: are they algebraically independent? Is e+π, eπ, π^e, etc. transcendental? | Schanuel's conjecture is a fundamental statement about transcendence degrees. It implies e and π are algebraically independent and that expressions like e+π, eπ, π^π are transcendental. Proving it would resolve many open questions in transcendental number theory at once.
<!-- LITERATURE-TRIAGE:BEGIN -->
## Literature ... | 5 | open | null | null | 1 | null | 287 | 22 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 5,
"level": 5,
"name": "L5: Millennium Prize",
"description": "Millennium Prize Problems and problems of equivalent difficulty.",
"color_class": "text-purple-600 bg-purple-50 border-purple-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,511 | NUM-017 | Euler-Mascheroni Constant Irrationality | Is the Euler-Mascheroni constant γ irrational? Transcendental? | The Euler-Mascheroni constant γ ≈ 0.5772 appears throughout analysis and number theory. We don't even know if it's irrational! Proving irrationality or transcendence would be a major achievement. Related constants like Catalan's G and ζ(3) face similar questions.
<!-- LITERATURE-TRIAGE:BEGIN -->
## Literature review (... | 5 | open | null | null | 1 | null | 323 | 25 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 5,
"level": 5,
"name": "L5: Millennium Prize",
"description": "Millennium Prize Problems and problems of equivalent difficulty.",
"color_class": "text-purple-600 bg-purple-50 border-purple-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,512 | NUM-018 | Littlewood Conjecture | For any α,β ∈ ℝ, is lim inf_{n→∞} n·||nα||·||nβ|| = 0? | Littlewood's conjecture connects Diophantine approximation of pairs of real numbers. It predicts that for any two reals, you can simultaneously approximate both well infinitely often. Related to continued fractions and dynamics on homogeneous spaces. Proved for many special cases.
<!-- LITERATURE-TRIAGE:BEGIN -->
## L... | 5 | partially_solved | null | null | 1 | null | 189 | 15 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 5,
"level": 5,
"name": "L5: Millennium Prize",
"description": "Millennium Prize Problems and problems of equivalent difficulty.",
"color_class": "text-purple-600 bg-purple-50 border-purple-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,513 | NUM-019 | Four Exponentials Conjecture | If x₁,x₂ and y₁,y₂ are linearly independent over ℚ, is at least one of e^(xᵢyⱼ) transcendental? | The four exponentials conjecture states that you can't have all four values e^(x₁y₁), e^(x₁y₂), e^(x₂y₁), e^(x₂y₂) algebraic when the xᵢ and yⱼ satisfy independence conditions. Weaker than Schanuel's conjecture but still wide open. Six exponentials theorem is the proven weaker version.
<!-- LITERATURE-TRIAGE:BEGIN -->... | 5 | partially_solved | null | null | 1 | null | 167 | 13 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 5,
"level": 5,
"name": "L5: Millennium Prize",
"description": "Millennium Prize Problems and problems of equivalent difficulty.",
"color_class": "text-purple-600 bg-purple-50 border-purple-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,514 | NUM-020 | Integer Factorization Polynomial Time | Can integer factorization be done in polynomial time? | The integer factorization problem asks whether factoring large integers into primes can be done efficiently (polynomial time). RSA cryptography relies on it being hard. Shor's algorithm solves it on quantum computers, but classical complexity remains unknown. Related to P vs NP.
<!-- LITERATURE-TRIAGE:BEGIN -->
## Lit... | 5 | partially_solved | null | null | 1 | null | 456 | 35 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 5,
"level": 5,
"name": "L5: Millennium Prize",
"description": "Millennium Prize Problems and problems of equivalent difficulty.",
"color_class": "text-purple-600 bg-purple-50 border-purple-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,515 | PDE-001 | Navier-Stokes Existence and Smoothness | Do smooth solutions to Navier-Stokes equations exist globally in 3D? Or do finite-time singularities occur? | The Navier-Stokes existence and smoothness problem is one of the seven Millennium Prize Problems. It asks whether smooth solutions to the 3D Navier-Stokes equations exist for all time, or whether finite-time blow-up can occur. Fundamental for fluid dynamics and mathematical physics.
<!-- LITERATURE-TRIAGE:BEGIN -->
##... | 5 | open | null | null | 9 | 2 | 512 | 39 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 5,
"level": 5,
"name": "L5: Millennium Prize",
"description": "Millennium Prize Problems and problems of equivalent difficulty.",
"color_class": "text-purple-600 bg-purple-50 border-purple-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,516 | GEOM-001 | Sphere Packing Problem Higher Dimensions | What is the optimal sphere packing density in dimensions >3? | The sphere packing problem asks for the densest way to pack spheres in n-dimensional space. Solved in dimensions 1,2,3 (Kepler's conjecture, proved by Hales), 8, and 24 (Viazovska). Dimensions 4-7 and ≥9 remain open. Connections to lattices, coding theory, and optimization.
<!-- LITERATURE-TRIAGE:BEGIN -->
## Literatu... | 5 | partially_solved | null | null | 6 | null | 298 | 23 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 5,
"level": 5,
"name": "L5: Millennium Prize",
"description": "Millennium Prize Problems and problems of equivalent difficulty.",
"color_class": "text-purple-600 bg-purple-50 border-purple-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,517 | HL-A | Hardy-Littlewood Conjecture A (Prime k-tuples) | Let $a_1, \ldots, a_k$ be given integers. Then there exist infinitely many positive integers $n$ such that $n + a_1, \ldots, n + a_k$ are all prime, provided that for every prime $p$, there exists an integer $m$ such that $(m + a_i, p) = 1$ for all $i$. | The first Hardy-Littlewood conjecture, also known as the prime k-tuples conjecture, generalizes the twin prime conjecture. It states that the asymptotic frequency of any admissible prime constellation can be computed explicitly. The case $k=2$ with $(a_1, a_2) = (0, 2)$ is the twin prime conjecture. Yitang Zhang proved... | 5 | open | null | null | 1 | 7 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 5,
"level": 5,
"name": "L5: Millennium Prize",
"description": "Millennium Prize Problems and problems of equivalent difficulty.",
"color_class": "text-purple-600 bg-purple-50 border-purple-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,518 | HL-B | Hardy-Littlewood Conjecture B (Second Conjecture) | For all integers $x, y \geq 2$, we have $\pi(x+y) \leq \pi(x) + \pi(y)$, where $\pi(n)$ denotes the prime counting function (the number of primes less than or equal to $n$). | The second Hardy-Littlewood conjecture states the subadditivity of the prime counting function. In 1974, Hensley and Richards proved that Conjecture A and Conjecture B are incompatible with each other - they cannot both be true. Since Conjecture A (the prime k-tuples conjecture) is considered more likely to be true bas... | 5 | open | null | null | 1 | 7 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 5,
"level": 5,
"name": "L5: Millennium Prize",
"description": "Millennium Prize Problems and problems of equivalent difficulty.",
"color_class": "text-purple-600 bg-purple-50 border-purple-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,519 | HL-F | Hardy-Littlewood Conjecture F (Primes in Quadratic Polynomials) | For a polynomial $f(x) = ax^2 + bx + c$ with $a > 0$, $\gcd(a,b,c) = 1$, and discriminant $\Delta = b^2 - 4ac$ not a perfect square, the polynomial takes infinitely many prime values. Furthermore, the number $P(n)$ of primes of the form $f(x) \leq n$ satisfies an asymptotic formula $P(n) \sim A \cdot \frac{\sqrt{n}}{\l... | Conjecture F is a special case of the Bateman-Horn conjecture and concerns primes represented by quadratic polynomials. It predicts not only the infinitude of such primes but also their asymptotic density. The constant A can take values larger or smaller than 1, meaning some polynomials are especially rich in primes wh... | 4 | partially_solved | null | null | 1 | 7 | 0 | 0 | 2024-01-01T00:00:00 | 2026-09-27T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 4,
"level": 4,
"name": "L4: Expert",
"description": "Very challenging problems at the frontier of mathematical research.",
"color_class": "text-red-600 bg-red-50 border-red-200"
} | null | The polynomial x^2+x+2 refutes the wording because it has a fixed prime divisor. With the usual local-obstruction condition, the Hardy–Littlewood/Bateman–Horn question remains open.
**What remains.** The earlier solved label is not accepted for the intended or insufficiently specified problem. The cited partial result... | [
{
"url": "https://arxiv.org/abs/math/0703284",
"label": "Stephan Baier and Liangyi Zhao, On primes represented by quadratic polynomials, Anatomy of Integers, CRM Proceedings & Lecture Notes 46 (2008), 159-174; arXiv:math/0703284."
},
{
"url": "https://doi.org/10.1090/S0025-5718-1962-0148632-7",
... | 2026-09-27T00:00:00 | null | {
"source_url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"checked_at": "2026-09-27T00:00:00",
"kind": "scope_correction",
"evidence": "scope_review"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,855 | GUY-A4 | The Prime Number Race | Let $\pi(n; a, b)$ be the number of primes $p \le n$ with $p \equiv a \pmod b$. For every $a$ and $b$ with $a \perp b$, are there infinitely many values of $n$ for which $\pi(n; a, b) > \pi(n; a_1, b)$ for every $a_1 \not\equiv a \pmod b$? | Turán was particularly interested in the prime number race. Knapowski & Turán settled special cases, but the general problem is wide open. Chebyshev noted that $\pi(n; 1, 3) < \pi(n; 2, 3)$ for small values of $n$, but this inequality is reversed for very large $n$. From Richard Guy's "Unsolved Problems in Number Theor... | 4 | partially_solved | null | null | 1 | 9 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 4,
"level": 4,
"name": "L4: Expert",
"description": "Very challenging problems at the frontier of mathematical research.",
"color_class": "text-red-600 bg-red-50 border-red-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,857 | GUY-A5b | Erdős $3000 Conjecture on Arithmetic Progressions | Let $\{a_i\}$ be any infinite sequence of integers for which $\sum 1/a_i$ is divergent. Does the sequence contain arbitrarily long arithmetic progressions? | Erdős offered $3000.00 for a proof or disproof of this conjecture. This is a generalization of the arithmetic progressions of primes problem. From Richard Guy's "Unsolved Problems in Number Theory", Section A5.
<!-- LITERATURE-TRIAGE:BEGIN -->
## Literature review (checked 2026-08-17)
**Status:** partially_solved
*... | 4 | partially_solved | null | null | 1 | 9 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 4,
"level": 4,
"name": "L4: Expert",
"description": "Very challenging problems at the frontier of mathematical research.",
"color_class": "text-red-600 bg-red-50 border-red-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,858 | GUY-A6 | Consecutive Primes in Arithmetic Progression | Are there arbitrarily long arithmetic progressions of consecutive primes? That is, for any positive integer $k$, do there exist $k$ consecutive primes $p_n, p_{n+1}, \ldots, p_{n+k-1}$ in arithmetic progression? | Known examples include the 4-term sequences 251, 257, 263, 269 and 1741, 1747, 1753, 1759. Dubner, Forbes, Lygeros, Mizony & Zimmermann found 10 consecutive primes in arithmetic progression in 1998. It is not known if there are infinitely many sets of three consecutive primes in arithmetic progression. From Richard Guy... | 4 | open | null | null | 1 | 9 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 4,
"level": 4,
"name": "L4: Expert",
"description": "Very challenging problems at the frontier of mathematical research.",
"color_class": "text-red-600 bg-red-50 border-red-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,859 | GUY-A7a | Infinitude of Sophie Germain Primes | Are there infinitely many Sophie Germain primes? A prime $p$ is called a Sophie Germain prime if $2p + 1$ is also prime. | It is believed, but not known, that there are infinitely many Sophie Germain primes. Dubner has found many large examples. The largest known Sophie Germain prime has over 24000 decimal digits. From Richard Guy's "Unsolved Problems in Number Theory", Section A7.
<!-- LITERATURE-TRIAGE:BEGIN -->
## Literature review (ch... | 4 | open | null | null | 1 | 9 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 4,
"level": 4,
"name": "L4: Expert",
"description": "Very challenging problems at the frontier of mathematical research.",
"color_class": "text-red-600 bg-red-50 border-red-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,860 | GUY-A7b | Shanks Chains of Length 7 | Are there any Shanks chains of length 7 with $p_{i+1} = 4p_i^2 - 17$? | Shanks chains are quadratic chains of primes. The recurrence $p_{i+1} = 4p_i^2 - 17$ yields a 4-chain if $p_1 = 3$ and a 5-chain if $p_1 = 303593$, but it can be seen (mod 59) that no such chain has length 17. It seems certain that such chains cannot be of arbitrary length. From Richard Guy's "Unsolved Problems in Numb... | 3 | open | null | null | 1 | 9 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,861 | GUY-A8a | Erdős $5000 Problem on Prime Gaps | Is it true that for infinitely many $n$, $d_n = p_{n+1} - p_n > c \ln n \ln \ln n \ln \ln \ln \ln n / (\ln \ln \ln n)^2$ for arbitrarily large constant $c$? | Erdős offers $5,000 for a proof or disproof that the constant $c$ can be taken arbitrarily large. Rankin showed this holds for $c = e^\gamma$, and Pintz improved it to $c = 2e^\gamma > 3.562$. From Richard Guy's "Unsolved Problems in Number Theory", Section A8.
<!-- LITERATURE-TRIAGE:BEGIN -->
## Literature review (ch... | 4 | solved | null | null | 1 | 9 | 0 | 0 | 2024-01-01T00:00:00 | 2026-09-27T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 4,
"level": 4,
"name": "L4: Expert",
"description": "Very challenging problems at the frontier of mathematical research.",
"color_class": "text-red-600 bg-red-50 border-red-200"
} | null | Reconciled with the existing literature review of 2026-08-17: The requested arbitrary-constant lower bound for large consecutive prime gaps was proved in 2014. This is a consistency correction based on that cited review; the discussion does not independently re-verify its proof claims.
**What remains.** No work remain... | [
{
"url": "https://arxiv.org/abs/1408.4505",
"label": "K. Ford, B. Green, S. Konyagin and T. Tao, Large gaps between consecutive prime numbers, Ann. of Math. 183 (2016), 935--974; arXiv:1408.4505."
},
{
"url": "https://arxiv.org/abs/1412.5029",
"label": "K. Ford, B. Green, S. Konyagin, J. Maynard... | 2026-09-27T00:00:00 | K. Ford, B. Green, S. Konyagin and T. Tao, Large gaps between consecutive prime numbers, Ann. of Math. 183 (2016), 935--974; arXiv:1408.4505.: https://arxiv.org/abs/1408.4505
K. Ford, B. Green, S. Konyagin, J. Maynard and T. Tao, Long gaps between primes, J. Amer. Math. Soc. 31 (2018), 65--105; arXiv:1412.5029.: https:... | {
"source_url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"checked_at": "2026-09-27T00:00:00",
"kind": "triage_reconciliation",
"evidence": "existing_literature_review"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,862 | GUY-A8b | Twin Prime Conjecture | Are there infinitely many twin primes? That is, are there infinitely many primes $p$ such that $p + 2$ is also prime? | A very famous conjecture. Hardy and Littlewood conjectured that $P_2(n)$, the number of twin prime pairs less than $n$, is asymptotically $2cn/(\ln n)^2$ where $2c \approx 1.32032$. Brun showed that the sum of the reciprocals of twin primes is convergent. From Richard Guy's "Unsolved Problems in Number Theory", Section... | 4 | open | null | null | 1 | 9 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 4,
"level": 4,
"name": "L4: Expert",
"description": "Very challenging problems at the frontier of mathematical research.",
"color_class": "text-red-600 bg-red-50 border-red-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,863 | GUY-A9 | General Patterns of Consecutive Primes | For any given pattern of primes with no congruence obstructions, are there infinitely many sets of consecutive primes with this pattern? | This conjecture is more general than Chowla's conjecture. It seems likely that there are infinitely many triples of primes $\{6k - 1, 6k + 1, 6k + 5\}$ and $\{6k + 1, 6k + 5, 6k + 7\}$. Hensley & Richards showed this is incompatible with the conjecture $\pi(x + y) \le \pi(x) + \pi(y)$ for all integers $x, y \ge 2$. Fro... | 4 | partially_solved | null | null | 1 | 9 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 4,
"level": 4,
"name": "L4: Expert",
"description": "Very challenging problems at the frontier of mathematical research.",
"color_class": "text-red-600 bg-red-50 border-red-200"
} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.