Invariants should be well-formed formulas, that is, they should be logical statements (with a truth-value--true, of course), in the predicate calculus or rigorous English. A good invariant is a ...

Knot theory, a branch of topology, examines the intricate properties of closed curves embedded in three-dimensional space. At its core is the study of knot invariants—quantitative measures that remain ...

When Lisa Piccirillo solved a decades-old mystery about the “Conway knot,” she had to overcome the knot’s uncanny ability to hoodwink some of the most powerful tools mathematicians have devised. Known ...