An answer of André Henriques' inspired the following closely related CW question. Parts of the following is extracted from his answer and my comments.
I regularly teach a knot theory class. Every time, students ask about applications. What should I say?
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, mixing liquids, and the structure of the Sun's corona. I'm interested hearing about other applications. I am also interested in hearing your take on the pedagogical issues and also other applicationsinvolved. Thank you!
