When our species first arrived in Europe, the peak of the Ice Age was approaching and the continent was already crawling with a rival: stronger, at home in the cold and even (contrary to their popular image) brainier than us. So how did the European pioneers survive first the Neanderthals and then the deep freeze as they pushed across the continent? Alice Roberts reconstructs the head of the 'first European' to come face to face with one of our ancestors; she discovers how art became crucial for survival in the face of Neanderthal competition; and what happened to change the skin colour of these European pioneers from black to white.

The Red Sea is one of the youngest oceans in the world and one of the warmest. The northern region, with its diverse array of marine life, is one of the most visited dive locations on earth while the southern end remains virtually unexplored. It's a global hotspot for marine biology and an important trade route throughout human history, linking the trade goods of India and the Far East with the markets of Egypt and Europe.

Dr Alice Roberts looks at our ancestors' seemingly impossible journey to Australia. Miraculously preserved footprints and very old human fossils buried in the outback suggest a mystery: that humans reached Australia almost before anywhere else. How could they have travelled so far from Africa, crossing the open sea on the way, and do it thousands of years before they made it to Europe? The evidence trail is faint and difficult to pick up, but Alice takes on the challenge. In India, new discoveries among the debris of a super volcano hint that our species started the journey much earlier than previously thought, while in Malaysia, genetics points to an ancient trail still detectable in the DNA of tribes today. Alice travels deep into the Asian rainforests in search of the first cavemen of Borneo and tests out a Stone Age raft to see whether sea travel would have been possible thousands of years ago, before coming to a powerful conclusion.

When ancient Greece fell into decline, mathematical progress stagnated as Europe entered the Dark Ages, but in the East mathematics reached new heights. In the second episode, Du Sautoy explores how maths helped build imperial China and discovers how the symbol for the number zero was invented in India. He also looks at the Middle Eastern invention of algebra and how mathematicians such as Fibonacci spread Eastern knowledge to the West.

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.

What was the Wehrmacht? A group of obedient yeasayers? A murdering band of thugs? An army of millions of abused young men? This series in 5 parts provides differentiated and conclusive answers based on the latest historical and comprehensive investigative research, bringing many new facts to light – among them documents proving for the first time ever, what many among the officers actually thought. Blitzkrieg, the lightning war, in German incorporate modern weapons and vehicles as a method to help avoid the stalemate of trench warfare and linear warfare in future conflicts. The first practical implementations of these concepts coupled with modern technology were instituted by the Wehrmacht in the opening theatres of World War II. The strategy was particularly effective to Germany in the invasions of Western Europe and initial operations in the Soviet Union. These operations were dependent on surprise penetrations, general enemy unpreparedness and an inability to react swiftly enough to German offensive operations.