All open problems
Source labels openChecked July 26, 2026

Millennium ProblemsGeneral topology

Poincare: Smooth Dimension Four

The four dimensional case of the smooth version of the conjecture is still open. See [Wang2017].

Mathematical statement

The four dimensional case of the smooth version of the conjecture is still open. See [Wang2017].

Statement source: Millennium Problems statement material

Statement terms: Source-specific

Source-specific terms. Therefore does not assert reuse rights beyond attributed display.

Statement artifacts, not proofs

These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.

Pinned Lean formulation 1

poincare_conjecture.variants.smooth_dimension_four

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem poincare_conjecture.variants.smooth_dimension_four : SmoothConjectureFor 4 := by  sorry
Statement source
Formal Conjectures
Lean version
v4.27.0
Placeholder
Present; no proof artifact
Source evidence
Pinned source index
Fidelity review
Community formulation

References