If you teach mathematics to future highschool teachers, you often feel that they are bored because what they learn at university does not have much to do with what they will have to teach in school, and what they will have to teach in school will be boring for their students because it has nothing to do with real life. To remedy this situation, we sometimes offer a course "Mathematics in Real Life" to explain how often mathematics "just happens" in real life, but goes unnoticed. Some sample topics in that course are
GPS as an application of 3d Euclidean geometry,
Existence and meaning of Nash Equilibria as an application of the Brouwer fixpoint theorem
MP3 and the modified discrete cosine transform
Benford's law and accounting fraud detection
I am looking for more examples like those above. They should be accessible to undergraduates (some of the topics above are actually a bit too hard), have some impact on real life, and (ideally) be somewhat surprising for someone who hasn't heard of them yet. Thus, I am neither looking for recreational mathematics as in this question nor for "typical" applications of maths in computer simulation, statistics or finance, which usually involve some deeper mathematics.