P versus NP
The central question about the gap between efficiently checking and efficiently finding solutions.
Mathematical statement
Determine whether : can every decision problem whose solutions are verifiable in polynomial time also be solved in polynomial time?
Statement source: Therefore editorial statement
Statement terms: Source-specific
Editorial wording by Therefore. No statement reuse license is granted.
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
Millennium.clay_prize_p_versus_np
def clay_prize_p_versus_np : ClayPVersusNPResolution := by sorry- Statement source
- Lean Millennium Prize Problems
- Lean version
- v4.31.0
- Placeholder
- Present; no proof artifact
- Source evidence
- Pinned source index
- Fidelity review
- Community formulation
References