Why P vs NP Is Equally Hard for AI and Computers
Why P vs NP may resist increasingly powerful AI and computation: the deeper challenge may be discovering structural principles that eliminate exponential search rather than merely searching faster.
Tag
Computational Complexity
6 Posts
P vs NP: The Government Clerk, the Wine Tester, and the People Who Couldn’t Find the Answer
A humorous explanation of P vs NP through government clerks and wine testers: verifying a proposed solution can be easy, but finding the solution efficiently is the real mystery.
New Design of P Vs NP Problem in Modern Terminology (2026) — © Hemant Pandey
A formal research framework reframing the P Vs NP question through Euclidean TSP, clustering, relative separation, convex-hull hierarchy, controlled addition, and elementary tour transformations.
Ongoing Research: New Frontiers (P Vs NP) — From Human Clustering to a Possible Structural Invariant
An archival record of an ongoing investigation: whether the human ability to see clusters, relative distance, convex hulls and nested geometric structure can be converted into formal rules that reduce combinatorial search in Euclidean TSP—and eventually illuminate the deeper P Vs NP question.
P vs. NP: From the 2006 Geometric Seed to a Hierarchical Proof Framework
A sequel to the 2006 Euclidean TSP manuscript: reconstructing the geometric argument through one-to-one mapping, triangle inequality, four-city closure, recursive stitching, clusters, and a precise list of what is proved, what is evidence, and what still requires proof.
P vs. NP: From a 2006 Geometric Seed to a Formal 2026 Research Program
A 2026 formal expansion of Hemant Pandey’s 2006 P vs. NP manuscript, returning to its geometric seed—Hamiltonian paths, convex polygons and topology—and identifying the proof obligations needed to turn that intuition into a rigorous polynomial-time result.