Proof index Open problems Projects Researchers Packages MCP

Search Lean proofs

Sign in Sign up

Open navigation

Search Lean proofs

Proof index Open problems Research projects Researchers Lean packages Connect MCP Search Mathlib Check Lean code

Research proofs Open problems Mathlib Type and shape search

Questions, not proof records

Open-problem statements, with their sources attached.

Each statement record keeps the mathematical question, a dated status source, accessible references, and any pinned Lean formulation separate from proof verification.

“Open” is a dated source assertion. In these pinned sources, sorry marks an admitted statement, not a proof. Source indexing does not mean the formulation has been independently built or certified by Therefore.

Search open problemsFilter by mathematical fieldFilter by source collection

All topics

Search topics

Additive combinatoricsAlgebraic geometryAlgorithmsAMS 11AMS 12AMS 13AMS 14AMS 15AMS 16AMS 18AMS 20AMS 22AMS 26AMS 28AMS 3AMS 30AMS 32AMS 33AMS 35AMS 37AMS 40AMS 41AMS 42AMS 46AMS 47AMS 49AMS 5AMS 51AMS 52AMS 54AMS 57AMS 58AMS 6AMS 60AMS 68AMS 8AMS 81AMS 91AMS 94AnalysisArithmetic geometryAssociative algebrasAutomata theoryCalculus of variationsCategory theoryCombinatoricsCommutative algebraComplex analysisComplexity theoryComputationComputer scienceConvex geometryDesign theoryDiophantine approximationDiophantine equationsDiscrete dynamicsDivisorsDynamical systemsDynamicsElliptic curvesExponential equationsExtremal set theoryField theory and polynomialsFluid mechanicsFunctional analysisGeneral topologyGeometryGraph labelingGraph theoryGroup theoryHarmonic analysisHodge theoryJordan curvesLinear algebraMathematical logicMathematical physicsMathematicsMatrix theoryMeasure and integrationNormal numbersNumber theoryOperator theoryPartial differential equationsPerfect numbersPrime gapsPrime numbersProbabilityQuantum field theoryReal functionsSequences and seriesSet systemsSeveral complex variablesSieve theorySpecial functionsTheoretical computer scienceTopological groupsTopology

1 of 1194 statement records

17 source collections · 43 mathematical fields

Open problemEditorial · Automata theory

Černý Conjecture

Every synchronizing deterministic finite automaton with $n$ states has a synchronizing word of length at most $(n-1)^2$ .

Source checked Jul 24, 20261 pinned Lean statementInspect problem

Search complete Lean declarations, inspect their provenance, and check code in a live Lean environment.

Research

Research proofs Open problems Search Mathlib Type and shape search Projects Researchers

Use Therefore

Check a proof Packages MCP, API, and editor Verification model

Built for the Lean community.Verification, provenance, and authorship stay separate.