Watson, Andrew, Twists, tangles, and topology, New Scientist (5 October 1991) 42 46.
Describes recent progress in the mathematical theory of knots in non-technical language. Notes the connection of knots and links with braids, and that Vaughan Jones (now at UC Berkeley, winner of 1990 Fields Medal) unexpectedly discovered a system to index braid generators and thus label knots and links, using a new polynomial. The article goes on to describe the role of the braid group in statistical physics, that of knot theory in the attempt to classify three-dimensional manifolds, and the connection between knot complements and three-manifolds.
This review was reprinted with permission from Mathematics Magazine, February 1992 issue.