I was literally just reading about this (see in particular "arguments in favor of")

https://webhomes.maths.ed.ac.uk/~v1ranick/papers/mfaknot.pdf ("Geometry and Physics of Knots" by Atiyah)

It's interesting that the mathematical theory of knots was initially developed in response to Kelvin's proposal (i.e. Tait's work), because people were motivated trying to work out its implications for atomic theory. A branch of mathematics created by wrong physics.