# Interesting “real life” applications of serious theorems [closed]

As student in mathematics, one sometimes encounters exercises which ask you to solve a rather funny “real life problem”, e.g. I recall an exercise on the Krein-Milman theorem which was something like:

“You have a great circular pizza with $n$ toppings. Show that you can divide the pizza equitably among $k$ persons, which means every person gets a piece of pizza with exactly $\frac{1}{k}$ of any of the $n$ topping on it.”

Are there more examples which are particular interesting or instructive?

EDIT: Since this is turning into a list of mathematical jokes or sophisticated proofs for simple facts, I may have to be more precise what I was asking for: a “real life example didactically used to motivate a mathematical theorem” (thanks to Lord_Gestalter for this great wording).

$\sqrt[n]{2}$ is not rational for $n\geq 3$
If $\sqrt[n]{2}=\frac{p}{q}$ then $q^n+q^n=p^n$ contradicting Fermat’s last theorem.