Mathematically the knot is defined as the mapping of a closed curve S1 ("circle") in a three-dimensinal space. This embedding can have non-trivial linking so the linking number does not change in any smooth deformation of the curve(s) and is thus a topological invariant... as we seem to have been convinced, the world seems to be constructed from invariants.

We often deal with curves; velocity curve, electric current, and magnetic flux which when closed may have non-vanishing linking number that do not change (i.e., is conserved- topological invariants).

The knot appears everywhere: Maxwell’s electro dynamics, Skyrme theory, QCD, fluid dynamics, atomic physics, plasma physics, polymer physics, condensed matter physics, Einstein’s theory.

Here is a review..