Mathematical aphorisms: theorems captured in everyday analogies

Question

What are some popular mathematical aphorisms or sayings that capture the intuition behind a theorem?

Statements such as A drunk man will find his way home, but a drunk bird may get lost forever help popularize mathematics through everyday analogies that spark curiosity about the underlying concepts.

For contrast, there are many quote non-examples. Although arguably true, they may not refer to a mathematical result: In mathematics, the art of proposing a question must be held of higher value than solving it - George Cantor

For this question, the statements should also not oversimplify in a way that it would make the corresponding mathematical statement incorrect or too ambiguous.

Answer 1

I once wrote a paper that might qualify, except for the "popular": it's titled "Stronger players need not win more knockout tournaments". Journal of the American Statistical Association 76 (1981) 950-951: https://doi.org/10.1080/01621459.1981.10477747

Answer 2

A drunk man will find his way home, but a drunk bird may get lost forever. (about)

You can't comb a hairy ball flat without creating a cowlick. (about)

A map of a city placed over the same city will always have a point lying directly over its location. (about)

You can always cut a ham sandwich with a single straight slice so that the bread, ham, and cheese are divided equally. (about)(video)

The real number line is not longer than the coastline of Britain. (about)

You can't hear the shape of a drum. (about)