The Knight’s Tour Problem and Its Beautiful Mathematical Generalizations

A New Video on the Knight’s Tour Problem

A new video just dropped about the knight’s tour problem and a wealth of its beautiful mathematical generalizations.

And today, work is already underway on the next episode — about a topic that is simultaneously simple, universally familiar, and deeply complex. There may be only a few dozen mathematicians in the world who truly understand it, yet every one of us has heard of it or wondered about it at some point.

When One Small Step in Mathematics Opens an Abyss

It is remarkable how in mathematics you can spend centuries living in a well-understood, well-justified world — and then take a single small step sideways and find yourself falling into an abyss of abstraction, an entirely new universe with its own rules and objects.

Infinity, complex numbers, quaternions, uncountable sets, Fermat’s Last Theorem, Galois groups, categories, the axiom of choice — and an endless list of topics and objects beyond those. The knight’s tour problem sits at exactly this kind of threshold: approachable on the surface, yet connected to layers of mathematics that can take a lifetime to explore.