Both men were citizens of the Greek colony of Elea in southern Italy. In approximately 445 B.C., Parmenides and Zeno met with Socrates in Athens to exchange ideas on basic philosophical issues. The event, one of the greatest recorded intellectual encounters (if it really took place), is commemorated in Plato's dialogue "Parmenides." Parmenides, a distinguished thinker nearly 65 years old, presented to the young Socrates a startling thesis: "reality" is an unchanging single entity, seamless in its unity. The physical world, he argued, is monolithic. In particular, motion is not possible. Although the rejection of plurality and change appears idiosyncratic, it has, in general outline, proved attractive to numerous scholars. For example, the "absolute idealism" of the Oxford philosopher F. H. Bradley (1846-1924) has points in common with the Parmenidean outlook.
This portrayal of the world is contrary to our everyday experience and relegates our most fundamental perceptions to the realm of illusion. Parmenides relied on Zeno's powerful arguments, which were later recorded in the writings of Aristotle, to support his case. For two and a half millennia, Zeno's paradoxes have provoked debates and stimulated analyses. At last, using a formulation of calculus that was developed in just the past decade or so, it is possible to resolve Zeno's paradoxes. The resolution depends on the concept of infinitesimals, known since ancient times but until recently viewed by many thinkers with skepticism." from William I. McLaughlin "Solving Zeno's Paradox" SCIENTIFIC AMERICAN November 1994 Volume 271 Number 5 Pages 84-89