MATHEMATICIAN

Life
Zeno was born in Elea, in Magna Graecia (south Italy). He was a disciple of Parmenides, the founder of the Eleatic School, whom he later succeeded as its head. His pupils included Pericles and later, in Athens, where he and Parmenides both went to teach, Socrates. He is cited by Plato, Heraclides Ponticus, Hermippus, Antisthenes, Stobaeus, Aristotle, Plutarch, Eudemus, Philo and Suidas.


Work
Zeno taught that there is no movement, and he proved it by 4 arguments, which are quoted by Aristotle in his "Physics". The first holds that, in order to cover a distance one must first cover half the distance, but in order to do that one must first cover half of that first half, and so on ad infinitum. This demonstrates that one can, therefore, never reach the goal, and in fact that there is no movement at all. The second is the example of Achilles, who can never catch up with the tortoise because he must first reach the point the tortoise started from, by which time the tortoise has moved on, and so forth. The third is the example of the arrow released from the bow, which is "proven" not to move at all, because each moment of time is made up of an infinite number of instants, indivisible and infinitely small. The fourth is the example of the two rows of bodies in the stadium, which he proposed as a mathematical proof of the non-existence of motion.

Aristotle refuted Zeno's arguments, pointing out that "time is not made up of indivisible instants, any more than is any other magnitude".

Zeno overturned the whole structure of mathematics, for in his view, all human knowledge was based on an unprovable hypothesis, and the same applied to the science of mathematics.

Principal work:

"On nature": 4 fragments extant, 3 in Simplicius and 1 in Diogenes Laertius.