Giuseppe Vitali (1875–1932) was an Italian mathematician who spent much of his career teaching in high schools rather than universities, doing research in whatever hours he could find. He constructed one of the most unsettling objects in all of mathematics — a set that simply cannot be assigned a length.

What made the name

The Vitali set is a subset of the number line so strange that no consistent notion of "length" can measure it: try to give it a size and you get a contradiction. It was the first proof that non-measurable sets exist at all — a direct consequence of accepting the axiom of choice — and it drew a firm line around exactly how far ideas like Cantor's infinite sets could be pushed before intuition breaks down completely.