All open problems
Source labels openChecked July 26, 2026

WikipediaCombinatorics

Ramsey numbers

The open problem: determine the Ramsey number R(5,5)R(5,5).

Mathematical statement

The open problem: determine the Ramsey number R(5,5)R(5,5).

It is known that 43R(5,5)4643 \le R(5,5) \le 46.

Statement source: Wikipedia statement material

Statement terms: CC-BY-SA-4.0

Attributed source material. Reuse must follow the linked attribution and share-alike terms.

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

ramsey_number_five_five

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem ramsey_number_five_five :    R(5, 5) = answer(sorry) := 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