Zeno of Elea's Paradox (or rather Paradoxes, as there are four of them and they each argue different things) are preserved for us by Aristotle, and Zeno's arguments against plurality are quoted by Simplicius. Plato also refers to Zeno's arguments about plurality. Zeno's arguments are not called paradoxes by any ancient author, but simply arguments (λόγοι), and technically speaking they are not paradoxes, they're what are called antinomies, from ἀντί-νόμος, against the law. The idea of an antinomy is to produce an argument whose constituent parts are true but which, when placed together, appear to create a circumstance which is no longer true. The purpose of using antinomy is not to prove that the result is true, because it generally isn't (and in Zeno's case, as Aristotle points out, it certainly is not). The purpose is to force an inquiry of the constituent parts. Zeno's four arguments against motion, commonly called Zeno's Paradox, all argue slightly different things. The Achilles argument and the Dichotomy postulate that motion is an infinite series of tasks and that therefore it can never be completed. The Arrow argues that an object that occupies a space exactly equivalent to its size is at rest, and that since an object in motion is, at any moment, occupying a space equivalent to its size it is at rest--basically the argument is that time is divided into finite, indivisible units and that therefore motion is really just a series of periods of rest placed next to each other sequentially. The Stadium argues that if two runners run down a track, one beginning at the start and the other halfway to the finish, since the first runner reaches the midway point at the same time that the runner who started at the midpoint finishes the total distance is equal to half.

That these arguments are preposterous was obvious to observers--Aristotle lays out in his discussion why each of them is easily disproven and why a number of them rest on false assumptions. Zeno's arguments against motion were not intended to be mathematically sound, our texts are in universal agreement about that. Nor were his arguments against plurality, that essentially argued that if plurality exists then things are simultaneously similar and dissimilar and are therefore impossible--Zeno gave as an example the sound that a bushel of millet makes when it hits the ground, which, if we accept that plurality exists, must be the sum of many non-existent sounds, since a single grain of millet hitting the ground makes no sound. Zeno's arguments against plurality, which appear to have been the majority of his major work, are really considered more important than his arguments against motion, and they indicate what exactly Zeno was trying to show. Aristotle describes Zeno's arguments as being ἀπορία, a word that "paradox" is a pretty terrible translation for. It means something like "being at a loss, without resources" (from πόρος, "a passage, way through"). It's the word that Socrates was accused of making people, and Aristotle rightly considered Zeno to be the founder of dialectic, which Socrates perfected--Zeno's methods are very similar to Socrates' system of getting his interlocutor to agree to his postulates but then proving the interlocutor's argument to be false by means of the very statements to which he has agreed. Like Socrates' dialectic the point seems to have been to force the questioning of basic, seemingly obvious principles--Plato considers Zeno to be attacking the concept of common sense and the truth of the information given to us by our senses. I'm going to stress that: Zeno's arguments against motion and plurality were intentionally absurd and without good resolution, and they were pretty certainly not supposed to be good mathematics, those arguments that actually used mathematics. In particular Zeno's arguments were aimed at the Atomists and at Anaxagoras, both of whom argued in favor of the subdivision of parts--the common theme throughout Zeno's arguments is that if we assume that things can be divided up into finite or indivisible parts then things that we can perceive with our senses to be quite obviously true of the sum of those parts become apparently contradictory.

So the short version is that Zeno's actual mathematics were not particularly mindblowing to much of anybody, the actual work was disproven pretty easily and Aristotle dismisses them without all that much thought. Nor were the mathematics, or the arguments in general, intended to have all that much value--their value lies, as was quickly understood to Zeno's contemporaries, in their use as a tool to be applied in dialectic. The point is not that they make sense, the point is that they don't make sense and are obviously disproven by our senses--so either our senses are wrong or the assumptions about divisibility that the arguments rest on, and that the Atomists in particular clung to, are wrong