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In the third episode we will see Europe by the 17th century taking over from the Middle East as the powerhouse of mathematical ideas. Great strides had been made in understanding the geometry of objects fixed in time and space. The race was on to discover the mathematics to describe objects in motion. This programme explores the work of Rene Descartes, Pierre Fermat, Isaac Newton, Leonard Euler and Carl Friedrich Gauss. Du Sautoy proceeds to describes René Descartes realisation that it was possible to describe curved lines as equations and thus link algebra and geometry. He talks with Henk J. M. Bos about Descartes. He shows how one of Pierre de Fermat’s theorems is now the basis for the codes that protect credit card transactions on the internet. He describes Isaac Newton’s development of math and physics crucial to understanding the behaviour of moving objects in engineering. He covers the Leibniz and Newton calculus controversy and the Bernoulli family. He further covers Leonhard Euler, the father of topology, and Gauss' invention of a new way of handling equations, modular arithmetic. The further contribution of Gauss to our understanding of how prime numbers are distributed is covered thus providing the platform for Bernhard Riemann's theories on prime numbers. In addition Riemann worked on the properties of objects, which he saw as manifolds that could exist in multi-dimensional space.

In the fourth episode, Professor Marcus du Sautoy concludes his investigation into the history of mathematics with a look at some of the great unsolved problems that confronted mathematicians in the 20th century. After exploring Georg Cantor's work on infinity and Henri Poincare's work on chaos theory, he sees how mathematics was itself thrown into chaos by the discoveries of Kurt Godel and Paul Cohen, before completing his journey by considering some unsolved problems of maths today, including the Riemann Hypothesis.

Author and nuclear physicist Professor Jim Al-Khalili looks at what led to the discovery that everything is made of atoms. The programme looks at how the discovery affected the scientific world including the atomic energy theories of Albert Einstein and Werner Heisenberg and quantum mechanics

In the last in the series Professor Jim Al-Khalili explores how studying the atom forced us to rethink the nature of reality itself. He discovers that there might be parallel universes in which different versions of us exist, finds out that empty space isn't empty at all, and investigates the differences in our perception of the world in the universe and the reality.

A humpback whale mother and calf embark on an epic journey from tropical coral paradises to storm ravaged polar seas. Newly discovered coral reefs in Indonesia reveal head-butting pygmy seahorses, flashing 'electric' clams and bands of sea kraits, 30-strong, which hunt in packs. Elsewhere plagues of sea urchins fell forests of giant kelp. Huge bull fur seals attack king penguins, who despite their weight disadvantage, put up a spirited defence.

Through ancient manuscripts and oral tales Michael Wood charts the first human migrations out of Africa. He travels from the tropical backwaters of South India through lost ancient cities in Pakistan to the vibrant landscapes of the Ganges plain. In Turkmenistan dramatic archaeological discoveries cast new light on India’s past.