An [answer](https://mathoverflow.net/questions/48191/how-mathematicians-knowledge-is-organized-closed) of André Henriques' inspired the following closely related CW question. Parts of the following is extracted from his answer and my comments. 



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> I regularly teach a knot theory class. Every time, students ask about applications. What should I say?
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I have two off-the-cuff replies when students ask. The first is that knot theory is a treasure chest of examples for several different branches of topology, geometric group theory, and certain flavours of algebra. The second is a list of engineering and scientific applications: untangling [DNA](http://en.wikipedia.org/wiki/Topoisomerase), mixing [liquids](http://www.math.wisc.edu/~jeanluc/talks/columbia2010a.pdf), and the structure of the Sun's [corona](http://www.suntrek.org/magnetic-sun/tangled-sun/tangled-sun.shtml). I'm interested hearing about other applications. I am *also* interested in hearing your take on the pedagogical issues involved. Thank you! 



Applications of knot theory
If I may steal some thunder from Peter Shor,
his paper, [Quantum money from knots](http://arxiv.org/abs/1004.5127)
(with
Edward Farhi, David Gosset, Avinatan Hassidim, and Andrew Lutomirski)
relies for the security of its "quantum money scheme" on



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> the assumption that given two different looking but equivalent knots, it is difficult to explicitly find a transformation that takes one to the other.
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The Alexander polynomial plays a prominent role in the paper.


