What’s the physical significance of a knot? William Thomson (who later became Lord Kelvin) must have asked himself that question in 1867 when he proposed his “vortex atom” hypothesis—the idea that different knotted configurations of swirling vortex lines in the ether are manifest in nature as different atoms. Earlier that year he’d witnessed Peter Guthrie Tait’s intriguing experiments on smoke rings. And based on earlier work by Hermann von Helmholtz, he knew that lines of vorticity are topologically conserved quantities. The closed loop and knotted configurations Thomson envisioned would thus be discrete and immutable—ideal traits for a theory of atoms.
Although initially skeptical, Tait came to believe that one could account for the rich variety of atoms in the periodic table by systematically building a classification system for all types of knots. For the catalog he produced, Tait is now viewed as the father of knot theory. Thomson, for his...
