History of Knot Theory from Gauss to Jones

In 1867, Lord Kelvin, motivated by Tait’s method of producing vortex smoke rings, came up with the vortex atom theory. He hypothesized that atoms were knotted in a substance called ether. At this time, creating a table of the elements was of significant importance to the scientific community, and this theory encouraged Tait to work on the knot classification problem. In this lecture, the origins of knot theory are examined, taking as a starting point the developments that occurred in Scotland associated with the work of Maxwell, Tait, and Kelvin. Special attention is given to the Tait conjectures and the evolution of the classification of knots. Moreover, we stress how progress in other areas, such as algebraic topology, positively influenced the growth of knot theory. In particular, the Alexander polynomial is discussed. Finally, a historical introduction to the Jones polynomial, a landmark in the theory, is presented.