In the mathematical theory of knots, a knot is tame if it can be "thickened", that is, if there exists an extension to an embedding of the solid torus into the 3-sphere. A knot is tame if and only if it can be represented as a finite closed polygonal chain. Every closed curve containing a wild arc is a wild knot.[1] Knots that are not tame are called wild and can have pathological behavior. In knot theory and 3-manifold theory, often the adjective "tame" is omitted. Smooth knots, for example, are always tame.
It has been conjectured that every wild knot has infinitely many quadrisecants.[2]
As well as their mathematical study, wild knots have also been studied for their potential for decorative purposes in Celtic-style ornamental knotwork.[3]