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"If you are walking between two policemen going to the same station, you will end up there, too."

This encodes the familiar Squeeze Theorem: If $a_n,b_n, c_n$ are sequences of real numbers such that $a_n \leq b_n \leq c_n$ and $\lim_{n \to \infty}a_n =\lim_{n \to \infty} c_n$, then $\lim_{n \to \infty}a_n =\lim_{n \to \infty} c_n= \lim_{n \to \infty}b_n$.

I am not sure whether the Squeeze Theorem it counts as "serious mathematics", but this is how I learned it as a high school student in Communist-ruled Poland.