Knots Knotes

Although knots have a long history in Celtic and Islamic art, sailing etc., and were first studied mathematically by Gauss in the 1800s, it was not until the 1870s that there was a serious attempt to produce a knot table. James Clerk Maxwell, William Thompson (Lord Kelvin) and Peter Tait (the Professor of maths at Edinburgh, and inventor of the dimples in a golf ball) began to think that “knotted vortex tubes” might provide an explanation of the periodic table; Tait compiled some tables and gave names to many of the basic properties of knots, and so did Kirkman and Little. It was not until Poincar´e had formalised the modern theory of topology around about 1900 that Reidemeister and Alexander (around about 1930) were able to make significant progress in knot theory. Knot theory was a respectable if not very dynamic branch of topology until the discovery of the Jones polynomial (1984) and its connections with physics (specifically, quantum field theory, via the work of Witten). Since then it has been “trendy” (this is a mixed blessing!) It even has some concrete applications in the study of enzymes acting on DNA strands. See Adams’ “Knot book” for further historical information.