Philosopher Zeno of Elea was an ancient Greek philosopher who lived in the 5th century BCE. He is best known for his paradoxes, which were used to challenge accepted ideas about space and time. He was a member of the Eleatic school of philosophy, which was founded by Parmenides. Zeno's most famous paradox is known as 'Achilles and the Tortoise, ' which states that Achilles can never catch up to a tortoise if the tortoise is given a head start.