AI, technology, education, and ideas about what comes next.
A concise exploration of the central P vs NP distinction: efficiently verifying a proposed solution is not the same as efficiently finding one, and what that distinction may mean for mathematics and AI.
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.
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.
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.
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.
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.
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.
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.
A historical record of Hemant Pandey’s 2006 P vs. NP manuscript, “P Vs NP… Are they same?”, including its submission history, withdrawal, Zenodo archive, and GitHub archival record.
I asked ChatGPT to estimate my intellectual percentile based on our conversations. Its answer revealed both unusual strengths—and a weakness that may matter more than the score.