ABSTRACT
Using his growing familiarity with topological concepts, Leonhard Euler liked to challenge his colleagues with problems that require topological solutions. The most famous of these is known as the 'Bridges of Konigsberg' problem. The Konigsberg that Euler knew had its town center on an island that was connected to the surrounding 'suburbs' by seven bridges over the Pregel river. The primary interest of physicists and chemists in knot theory is in terms of its rapidly developing connection with the science of polymer chemistry. Both chemists and biochemists have been able to synthesize polymeric rings which are knotted in complex ways. Ring lengths of up to several thousand polymer bonds have been analysed and knots with up to ten crossing points identified. It seems only a matter of time before linked polymers and polymer glasses can also be analysed to clarify the role played by knots in determining the properties of these even more complicated materials as well.
