Zeno was born at Elea (now Velia in Italy) and in about 450 bc accompanied his teacher, Parmenides, to Athens. There he propounded the theories of the Eleatic school and became famous for his series of paradoxes and his invention of dialectic.

Little survives of Zeno's written work and this only in other authors' writings. He proposed that motion and multiplicity are unreal (thus supporting Parmenides's theories) since assumption of their existence gave rise to contradictory propositions. One of the most famous arguments against plurality and motion is that of Achilles and the tortoise: if the tortoise is given a start in a race against Achilles, when Achilles reaches the tortoise's starting position, the tortoise will have advanced a small way to a new position. Endless repetition of this argument means that Achilles can never overtake the tortoise.

Zeno's paradoxes remained unresolved for about 20 centuries, in fact until the advances in rigor of mathematical analysis (to the development of which these paradoxes may be said to have contributed). These advances included the study of convergent series (infinite series with a finite sum), the invention by Gottfried Leibniz and Isaac Newton of calculus, and Georg Cantor's theory of the infinite in the 19th century.

Following his return to Elea Zeno died while joining a coup against the tyrant Nearchus.