Computationally inspired theorems and conjectures in knot theory

Question

I am collecting examples of theorems and conjectures in knot theory that were originally discovered (or inspired) by computer experiments. Examples include:

• Hoste’s conjecture on zeros of the Alexander polynomials of alternating knots (see discussion in Stoimenow paper).
• The Vol-Det Conjecture of Champanerkar, Kofman, and Purcell (arxiv:1411.7915).
• An AI-discovered conjecture relating the knot signature to a hyperbolic geometry invariants (arXiv:2111.15323).

Are there other notable examples, or survey references/lists that summarize such computationally inspired insights in knot theory?

A related question addresses computer-assisted discoveries in mathematics, though not specifically in knot theory.

Answer 1

The remarkable (and recent!) result by Mark Brittenham and Susan Hermiller that the unknotting number is not additive under connected sum was discovered with computer-assisted help. The two used SnapPy to test millions of knot diagrams. Here is a link to the paper.

Here is a nice excerpt from a Quanta magazine article

“CONNECT SUM BROKEN.” It was a message he and Hermiller had coded into the program — but they’d never expected to actually see it.