AI, technology, education, and ideas about what comes next.
Mathematics uses human-made symbols to reveal relationships that may exist independently of us. From invariant structures and physics to quantum interpretation, engineering and AI-assisted discovery, this essay asks what we invent—and what we discover.
Superintelligence may discover extraordinary solutions—and reveal why some problems have no solution under their defining constraints. Explore physical, mathematical and epistemic limits on solvability.
AI companies may be better served by building the world’s best intellectual tools than by claiming ownership of the discoveries their customers make with them.
If AI begins discovering mathematics beyond human invention, does that mean humans will be unable to understand it? Discovery, verification, explanation and understanding are different abilities.
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.
When AI enters mathematics, the challenge is not only whether machines can solve difficult problems, but what happens to discovery, attribution, provenance, and the human mathematical ecosystem.
If AI can solve mathematical problems that have resisted humanity for decades, should we slow the machine—or rethink what mathematical discovery is for?
In 2026, the Clay Mathematics Institute’s Millennium Prize Problems remain strikingly open: one has been solved and six remain unsolved. Here is what has changed, what has not, and why these problems still matter.
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.
AI is entering mathematics at unprecedented speed. The real question is not whether machines can solve problems, but who gets the credit—and whether AI enriches mathematics or turns it into a leaderboard.
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 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.
Learn how interleaving mathematics topics and switching between related concepts can strengthen understanding and make practice more effective.