Zeno of Elea conceived a number of "paradoxes". Zeno conceived these not as mathematical amusement, but as an attempt to support the doctrine of his teacher, the ancient Greek philosopher Parmenides, that all evidence of the senses is illusory, particularly the illusion of "motion".

One of Zeno's most famous paradoxes posited a race between the popular Greek hero Achilles, and a tortoise.

Zeno set out to logically show that, with the tortoise given a head start, Achilles, speedy as he might be, could, in fact, never overtake the plodding reptile.

Zeno reasoned that when Achilles reached the starting point of the tortoise, the tortoise would have advanced incrementally further. Achilles would continually reach a point the tortoise had already reached, while the tortoise would at the same time have reached a slightly further point. Thus, Zeno reasoned, the tortoise could never be overtaken by Achilles.

Zeno's paradox provided an early entree into the science and mathematics of limits.

Zeno's paradox is resolved with the insight that a sum of infinitely many terms can nevertheless yield a finite result, an insight of calculus. It was not until Cantor's development of the theory of infinite sets in the mid-nineteenth century that, after more than two millennia, Zeno's Paradoxes could be fully resolved.

Zeno's portrait is depicted in the style of an ancient Grecian amphora vase.

Overlaying Zeno is a graphical depiction of 'limits'.