In the first episode, <strong>The Language of the Universe</strong>, after showing how fundamental mathematics is to our lives, du Sautoy explores the mathematics of ancient Egypt, Mesopotamia and Greece. In Egypt, he uncovers use of a decimal system based on ten fingers of the hand, while in former Mesopotamia he discovers that the way we tell the time today is based on the Babylonian Base 60 number system. 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.

The second episode, <strong>The Genius of the East</strong>, sees du Sautoy leaving the ancient world. When ancient Greece fell into decline, mathematical progress stagnated as Europe entered the Dark Ages, but in the East mathematics reached new heights. Du Sautoy visits China and explores how maths helped build imperial China and was at the heart of such amazing feats of engineering as the Great Wall. In India, he discovers how the symbol for the number zero was invented and Indian mathematicians’ understanding of the new concepts of infinity and negative numbers. In the Middle East, he looks at the invention of the new language of algebra and the spread of Eastern knowledge to the West through mathematicians such as Leonardo Fibonacci, creator of the Fibonacci Sequence.

<strong>The Frontiers of Space</strong>. By the 17th century, Europe had taken over from the Middle East as the world’s powerhouse of mathematical ideas. Great strides had been made in understanding the geometry of objects fixed in time and space. The race was now on to discover the mathematics to describe objects in motion. In the third part of the series, Marcus du Sautoy explores the work of René Descartes and Pierre Fermat, whose famous Last Theorem would puzzle mathematicians for more than 350 years. He also examines Isaac Newton’s development of the calculus, and goes in search of Leonard Euler, the father of topology or ‘bendy geometry’ and Carl Friedrich Gauss, who, at the age of 24, was responsible for inventing a new way of handling equations: modular arithmetic.

The fourth episode, <strong>To Infinity and Beyond</strong>, concludes the series. After exploring Georg Cantor’s work on infinity and Henri Poincare’s work on chaos theory, he looks at how mathematics was itself thrown into chaos by the discoveries of Kurt Godel, who showed that the unknowable is an integral part of maths, and Paul Cohen, who established that there were several different sorts of mathematics in which conflicting answers to the same question were possible. He concludes his journey by considering the great unsolved problems of mathematics today, including the Riemann Hypothesis, a conjecture about the distribution of prime numbers. A million dollar prize and a place in the history books await anyone who can prove Riemann’s theorem.

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