Knots and physics: Old wine in new bottles

The history of the interplay between physics and mathematics in the theory of knots is briefly reviewed. In particular, Gauss’ original definition of the linking number in the context of electromagnetism is presented, along with analytical, algebraical, and geometrical derivations. In a modern context, the linking number appears in the first-order term in the perturbation expansion of a Wilson loop in Chern–Simons quantum field theory. New knot invariants, the Vassiliev numbers, arise in higher-order terms of the expansion, and can be written in a form which shows them to be generalizations of the linking number.