  We give a brief historical overview of the Tait conjectures, made 120 years
ago in the course of his pioneering work in tabulating the simplest knots, and
solved a century later using the Jones polynomial. We announce the solution,
again based on a substantial study of the Jones polynomial, of one (possibly
his last remaining?) problem of Tait, with the construction of amphicheiral
knots of almost all odd crossing numbers. An application to the non-triviality
problem for the Jones polynomial is also outlined.
