In mathematics, "compactification" refers to a process of adding points to a space to make it compact. In other words, it's a way of making a space "smaller" in some sense by adding points to it, so that it becomes easier to work with or understand.

In the context of the joke, "compactifying his sense of humor" is a play on words. The mathematician is studying the Heine-Borel Theorem to make his sense of humor more compact and easy to understand, like adding points to a space to make it compact.

So the joke is a play on the mathematical concept of compactification, and by understanding the joke you can also enjoy its humor.
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