Egyptian hieroglyphics Copyrighted image Credit: OU In this opening programme Marcus du Sautoy looks at how fundamental mathematics is to our lives before exploring the mathematics of ancient Egypt, Mesopotamia, and Greece.

In Egypt he uncovers use of a decimal system based on ten fingers of the hand, the Egyptians’ unusual method of multiplication and division, and their understanding of binary numbers, fractions, and solids such as the pyramid.

He discovers that the way we tell the time today is based on the Babylonian Base 60 number system - so it is thanks to the Babylonians that we have 60 seconds in a minute, and 60 minutes in an hour - and shows how the Babylonians used quadratic equations to measure their land.

In Greece, he looks at the contributions of some of the giants of mathematics including Plato, Euclid, Archimedes, and Pythagoras, who is credited with beginning the transformation of mathematics from a tool for counting into the analytical subject we know today.

A controversial figure, Pythagoras’ teachings were considered suspect and his followers seen as a bizarre sect. Legend has it that one of his followers, Hippasus, was drowned when he announced his discovery of irrational numbers - a discovery that upset those who had held faith with the Pythagorean world view.

As well as his ground-breaking work on the properties of right-angled triangles, Pythagoras developed another important theory after observing the properties of musical instruments: he discovered that the intervals between harmonious musical notes are always in whole number ratios to each other.

First broadcast: Monday 13 Oct 2008 on BBC FOUR; the programme can be seen again on Tuesday 12th July at 8.00pm. Further broadcast information and iPlayers links can be found on bbc.co.uk

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