Editorial standard
Methodology
This is a curated research catalog, not a scrape of famous names. Its 280 stable records were reconciled across 21 fields and checked against 837 bibliography entries as of July 31, 2026.
What enters the catalog
A fixed mathematical assertion or decision problem that is genuinely open, independently recognizable, precisely stateable, and supported by authoritative literature. Canonical finite benchmark cases qualify when they have their own established research identity.
What stays outside
Solved or disproved statements, vague programs, duplicate aliases, arbitrary finite cases, and paper-level questions without broad standing. For an unsettled full-scope proof claim, the underlying problem stays visible as open while the claimed resolution is tracked separately until its scope and acceptance are clear.
Source hierarchy
Final decisions rely on original papers, recognized surveys and monographs, institutional problem lists, and formal-proof archives. Search snippets, encyclopedias, blogs, and generated lists may locate leads but do not determine classification.
Primary-field counting
Each conjecture has exactly one primary field, so headline counts never double-count a cross-disciplinary problem. Secondary fields preserve useful paths between communities and appear in both search and the field index.
Open-source precedent, independent implementation
The information architecture studies the public Erdős Problems repository—stable records, tags, source trails, rendered mathematics, and audit-friendly status boundaries. Math Conjectures uses its own data model, editorial scope, typography, color system, layouts, and components; it is not a visual or source-code copy.
Rendered and source mathematics
Detail pages render every delimited expression with KaTeX and preserve the exact source LaTeX in an expandable view. A failed expression stays visible as source and is flagged by browser tests instead of disappearing silently.
Quality-control pass
Six visible checks, ten enforced questions
Every record receives a second pass for statement, version, symbol definitions, proposal year, current status, remaining gap, prominence, duplicates, sources, and research-agent readiness. The six groups below summarize that review.
Self-contained statement
Every retained record identifies its objects, hypotheses, quantifiers, and conclusion without requiring a nickname to carry the mathematics.
Canonical scope
The catalog fixes one recognized formulation and does not silently substitute a stronger refinement, weaker special case, or broad research program.
Current status
A problem must still be open at the status cutoff. Fresh complete-proof claims receive a separate artifact, scope, and acceptance audit.
Meaningful frontier
The remaining-gap note distinguishes the best-known progress from the exact universal quantifier, endpoint, constant, or construction still missing.
Prominence and deduplication
Every entry carries one of three prominence labels: Iconic for globally recognized defining problems, Landmark for field-defining problems, and Major for established research problems with a narrower specialist reach. Aliases and equivalent formulations are reconciled instead of inflating the catalog.
Reference support
Each record carries two to four checked bibliography keys, favoring primary papers, established surveys, monographs, institutions, and formal archives.
Read the evidence beside the statement.
Stable IDs connect every detail page to its source keys; the bibliography preserves the human-checkable trail behind scope, date, and status decisions.