The discovery of a link between apparently unrelated fields is always
a particular highlight in the development of natural sciences. An enti
re wave of such discoveries was triggered in 1984 and is still rolling
. It all started with a bridge between knot theory and the theory of v
on Neumann algebras: the Jones polynomials. Within one year mathematic
ians discovered a most remarkable connection between statistical mecha
nics and knot theory. Again, the mathematician and physicist Vaughan J
ones played a central role. In 1988 Ed Witten successfully used techni
ques of quantum field theory and gauge theory to arrive at the Jones p
olynomial.