The central problem of knot theory is distinguishing between various
knots. Two knots are considered to be the same if, when they are made out of rope or some other material you can twist one of them around (without cutting) so that each looks exactly like the other one with all the over- and under-crossings in the same place.
Some of the ways that knots are classified is by the arrangement of their crossings, the characteristics of their mirror images, and the braids from which they are formed.
