by Student A

Abstract
Mathematicians have been interested in knottheory, orthe study of knots,since the early nineteenth
century. However, despite thisinterest,some basic questionsremain unanswered;for example there
is no effective way to definitively determine whether or not two knots are the same. In this paper,
we will look at a powerful but frequently overlooked knot invariant: the knot quandle. We will
show that the knot quandle is a generalization of several more familiar invariants and that it is a
complete invariant up to orientations. However, as we willsee, determining whether two quandles
are isomorphic is computationally intractable, which limits the utility of this otherwise powerful
invariant