Knot tabulation

Ever since Sir William Thomson's vortex theory, mathematicians have tried to classify and tabulate all possible knots.

In the 19th century, Sir William Thomson made a hypothesis that the chemical elements were based upon knotted vortices in the aether.

The resulting ambiguity has continued to the present day, and has been further compounded by mistaken attempts to correct errors caused by this that were themselves incorrect.

For example, Wolfram Web's Perko Pair page erroneously compares two different knots (due to the renumbering by mathematicians such as Burde and Bar-Natan).

Jim Hoste, Jeff Weeks, and Morwen Thistlethwaite used computer searches to count all knots with 16 or fewer crossings.