Alain Goriely, Gresham Professor of Geometry, traces knot theory from its origins in Lord Kelvin and Peter Tait's vortex atom theory to its modern reach across science. He defines what makes a knot mathematically, explains ambient isotopy, crossing numbers, and Reidemeister moves, and shows how knots compose and classify into prime knots cataloged by the billions. The lecture covers chirality through the figure-eight knot and the unresolved Gordian Knot problem of unknotting numbers. Goriely then turns to applications: enzymes that untangle DNA topology, transposons studied through gel electrophoresis, and the physics of how umbilical cords knot during pregnancy. Recorded at Barnard's Inn Hall in London, the talk moves from Helmholtz's vortex rings and solar flares to shoestrings, building a case that knot theory connects geometry, topology, biology, and physics in ways few branches of mathematics do.