A Greek philosopher called Zeno thought up a paradox involving the idea of infinity.

A man called Achilles challenges a tortoise to a race. Suppose Achilles can run ten times faster than the tortoise, but he gives the tortoise a 10 metre head-start. When Achilles has run 10 metres, the tortoise has run 1 metre and is still in the lead.

When Achilles has covered that 1 metre, the tortoise has moved another tenth of a metre forward. Each time Achilles tries to catch up, the tortoise has gone a bit further still.

This can continue forever, the tortoise moving forward by even smaller increments. So it seems logical that Achilles can never overtake the tortoise - yet common sense tells us that anyone can overtake a tortoise in a race!

The puzzle baffled the Greeks because they didn't understand the idea of infinity. They thought an infinite number of values, however tiny, must add up to an infinite amount.

The problem wasn't fully solved until the 1600s, when a Scottish mathematician, James Gregory, showed that an infinite number of ever-decreasing values can add up to a finite amount.