How To Present Algebraic Topology To Non-Mathematicians? I am writing my master thesis in algebraic topology (fundamental groups), and, as a system in my school, students must write one page about their theses explaining for non-mathematicians the purpose of the study (in general) and why it is important in the real life. I don't know actually how shall I start, because I'm not allowed to use some mathematical terminologies like "Topological Space", for instance. My teacher told me it's important to convince the "politicians" to support financially the research in the department of mathematics mainly in algebraic topology to show them that we are doing something useful. Furthermore; it is to make the new students like this kind of mathematics.
So any suggestion or idea will be very appreciated! 

You might consider looking into topological mixing. One studies the optimal way you can mix, for instance, a viscous fluid with n-rods. This applies to such things as taffy pullers. Here are slides from a professor at my institution.
