The article seems to be implying that mathematicians study knots because there's lots of fun to be had. This is partly true, but there's other more profound reasons. For example: higher dimensional algebra. The "usual" algebra is just one dimensional, but people have noticed that in many cases this is just a projection (shadow) of higher dimensional systems, where the symbols can interact in more than just a linear direction. And once you get to three dimensions hey presto your algebra can get knotted!