Five Moves, Not Six: Knot Theory and Low-Dimensional Topology

Deep End Era. Engineering with Sankalp · Oct 28, 2026 · 59m

For nearly a century, mathematicians assumed that if one knot takes three crossing changes to undo, two of them tied together take six. In 2025, two Nebraska mathematicians found a pair that takes five. Episode one hundred and fifty three uses that surprise to tour knot theory: how you prove knots are different, the polynomials that came out of quantum physics, a graduate student's week-long proof about the Conway knot, Perelman's solution of the Poincaré conjecture, and knots in DNA and water. A fictional doctoral student, Mireille, checks the new result with a length of rope. Mireille is…