Zeno of Elea

Zeno of Elea, who lived around 490 to 430 BC, was a pre-Socratic Greek philosopher from Elea in what is now Southern Italy, a student of Parmenides and one of the Eleatics. Zeno defended his instructor's belief in monism, the idea that only one single entity exists making up all of reality, and rejected the existence of space, time and motion, developing a series of paradoxes to demonstrate why they are impossible; though his original writings are lost, subsequent descriptions by Plato, Aristotle, Diogenes Laertius and Simplicius of Cilicia allow study of his ideas. His arguments divide into two types, those against plurality, holding that anything that exists must be infinitely divisible and so would need to have both infinite mass and no mass simultaneously, and those against motion, holding that any distance must be divisible infinitely so that infinite steps would be required to cross it. Zeno's paradoxes remain debated today and have influenced both philosophy and mathematics, ancient and modern, including atomic theory, mathematical limits and set theory.