Du Sautoy commences in Egypt where recording the patterns of the seasons and in particular the flooding of the Nile was essential to their economy. There was a need to solve practical problems such as land area for taxation purposes. Du Sautoy discovers the use of a decimal system based on the fingers on the hands, the unusual method for multiplication and division. He examines the Rhind Papyrus, the Moscow Papyrus and explores their understanding of binary numbers, fractions and solid shapes.

He then travels to Babylon and discovered that the way we tell the time today is based on the Babylonian 60 base number system. So because of the Babylonians we have 60 seconds in a minute, and 60 minutes in an hour. He then shows how the Babylonians used quadratic equations to measure their land. He deals briefly with Plimpton 322.

In Greece, the home of ancient Greek mathematics, he looks at the contributions of some of its greatest and well known mathematicians including Pythagoras, Plato, Euclid, and Archimedes, who are some of the people who are 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 social outcasts and a little be strange and not in the norm. There is a legend going around that one of his followers, Hippasus, was drowned when he announced his discovery of irrational numbers. As well as his work on the properties of right angled triangles, Pythagoras developed another important theory after observing musical instruments. He discovered that the intervals between harmonious musical notes are always in whole number intervals.a It deals briefly with Hypatia of Alexandria.