In the 5th century BC the Greek philosopher Zeno of Elea formulated some paradoxes that undermined the idea of motion: Achilles would never catch the tortoise, the arrow would never reach the target. The paradox arises from summing infinitely many terms; its solution is that such a sum can have a finite value. This is exactly the substance of the concept of the limit, which the Greeks intuited (geometric series, method of exhaustion) but which received rigorous language only with Cauchy and Weierstrass in the nineteenth century.