Editing Knot polynomial (section)

==History==
The first knot polynomial, the [[Alexander polynomial]], was introduced by [[James Waddell Alexander II]] in 1923. Other knot polynomials were not found until almost 60 years later.

In the 1960s, [[John Horton Conway|John Conway]] came up with a [[skein relation]] for a version of the Alexander polynomial, usually referred to as the [[Alexander–Conway polynomial]]. The significance of this skein relation was not realized until the early 1980s, when [[Vaughan Jones]] discovered the [[Jones polynomial]]. This led to the discovery of more knot polynomials, such as the so-called [[HOMFLY polynomial]].

Soon after Jones' discovery, [[Louis Kauffman]] noticed the Jones polynomial could be computed by means of a [[Partition function (statistical mechanics)|partition function]] (state-sum model), which involved the [[bracket polynomial]], an invariant of [[Framed knot|framed knots]]. This opened up avenues of research linking knot theory and [[statistical mechanics]].

In the late 1980s, two related breakthroughs were made. [[Edward Witten]] demonstrated that the Jones polynomial, and similar Jones-type invariants, had an interpretation in [[Chern–Simons theory]]. [[Victor Anatolyevich Vasilyev|Viktor Vasilyev]] and [[Mikhail Goussarov]] started the theory of [[finite type invariant]]s of knots.  The coefficients of the previously named polynomials are known to be of finite type (after perhaps a suitable "change of variables").

In recent years, the Alexander polynomial has been shown to be related to [[Floer homology]]. The graded [[Euler characteristic]] of the [[Heegaard Floer homology|knot Floer homology]] of [[Peter Ozsváth]] and [[Zoltán Szabó (mathematician)|Zoltan Szabó]] is the Alexander polynomial.