The Signature and Natural Slope of Hyperbolic Knots

Andras Juhasz has explained in his talk how machine learning was used to discover a previously unknown relationship between invariants in knot theory. This relationship is a connection between a classical knot invariant (the signature) and a new knot invariant (the natural slope) derived from hyperbolic geometry. In my talk, I will explain how this conjecture was formulated, verified in millions of cases, and then eventually disproved, and how two more refined conjectures were proved.