I'm working on an educational project about the applications of reasonably 'lofty', high-ish-level mathematical concepts in the real world. I've already scoured these links (1) (2) (3) after exhausting my own knowledge, but I was wondering if anyone here can come up with some additional fun examples very much grounded in everyday life. The intended audience is laypeople - "imaginary numbers are used in electronic engineering" wouldn't impress them! "Gaussian curvature describes the best way to eat pizza" is more the level I'm going for.
I'm also interested in examples where mathematics doesn't necessarily provide the perfect solution to a real-world decision-making problem: for instance, where human intuition arrives at a good solution much more efficiently than a rigorous mathematical analysis. NP-hard problems, the fact that there is no 'equation' to solving the travelling salesman problem, that sort of thing.