P vs NP problem

Determine whether the complexity classes P and NP are equal; equivalently, establish whether every decision problem whose solutions can be verified in polynomial time also admits a polynomial-time algorithm that constructs such solutions.

Background

The essay situates computational complexity as an epistemic framework and explicitly cites the canonical open problem of whether P equals NP. This question is used to frame the broader philosophical dichotomy between constructive procedures and recognitional verification that the paper explores through the historical development of quantum mechanics.

By invoking P vs NP as the central open problem, the author connects the asymmetry between generation and verification in computation to the epistemic divide between matrix and wave mechanics, without claiming a formal reduction of physical theories to complexity classes.