This paper is a remembrance of the work and influence of Vaughan Jones. This is a commentary on the remarkable breakthroughs in knot theory and low-dimensional topology catalyzed by his work. This paper recalls the beginnings of the Jones polynomials and the author’s discovery of the bracket polynomial model of the Jones polynomials. We then describe the development of knot theory, inspired by the Jones polynomials, with variations and generalizations of this invariant. This paper is written in the form of a personal adventure and aims to demonstrate various mathematical themes that arise in connection with Jones polynomials. This invariant can be interpreted in relation to combinatorial topology, statistical mechanics, Lie algebras, Hopf algebras, quantum field theory, category theory, etc. In any case, Jones invariants appear as important examples of patterns and connections in these mathematical and physical contexts. It is worth noting that Vaughan-Jones’ discovery of polynomials influenced mathematics, physics, the natural sciences, and much of our mathematical life.
