P vs NP: A 25-Year Journey from an Old Idea to a New Struggle
A personal research journey from the first P vs NP exploration in 2001, through the 2006 Elsevier setback and a long pause, to a renewed AI-assisted investigation in 2026.
Tag
Algorithm Design
4 Posts
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 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.