Whose paradoxes include Achilles never catching the tortoise?

Zeno of Elea produced perhaps forty arguments in the fifth century BC, of which about nine survive, mostly because Aristotle quoted them in order to disagree. Achilles gives the tortoise a head start; by the time he reaches where it was, it has moved a little; by the time he reaches that point, it has moved again; the sequence never ends, so he never passes it. The Dichotomy makes the same trouble for getting out of your chair, and the Arrow argues that a flying arrow occupies exactly its own length at every instant and is therefore never moving.

He was not, most likely, trying to convince anyone that motion is impossible. He was defending his teacher Parmenides, who held that reality is a single unchanging whole, against people who thought that was absurd. The paradoxes are a counter-attack: your common-sense world of many things moving about generates contradictions of its own, so stop laughing.

The usual modern reply is that an infinite series of intervals can have a finite sum - a half plus a quarter plus an eighth and so on adds up to one, and Achilles passes the tortoise on schedule. That handles the arithmetic, and physicists consider the matter closed. Philosophers tend to note that it explains why the distances add up without quite explaining how infinitely many separate acts get completed, and the argument about whether space and time are infinitely divisible at all is very much still running.