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.

Irena Salina's award-winning documentary investigation into what experts label the most important political and environmental issue of the 21st Century - The World Water Crisis. Salina builds a case against the growing privatization of the world's dwindling fresh water supply with an unflinching focus on politics, pollution, human rights, and the emergence of a domineering world water cartel. Interviews with scientists and activists intelligently reveal the rapidly building crisis, at both the global and human scale, and the film introduces many of the governmental and corporate culprits behind the water grab, while begging the question "CAN ANYONE REALLY OWN WATER?" Beyond identifying the problem, FLOW also gives viewers a look at the people and institutions providing practical solutions to the water crisis and those developing new technologies, which are fast becoming blueprints for a successful global and economic turnaround.

David Attenborough reveals the surprising truth about the cold-blooded lives of reptiles and amphibians. These animals are as dramatic in combat, as colourful in their communication and as tender in their parental care as any other animals. Join giant courting crocodiles, jousting tortoises and bright red sumo-wrestling frogs in their sophisticated, solar-powered lives.

From steamy jungles to dry deserts, amphibians have taken their first footsteps onto land using their bizarre life histories to break their ties with the water and invade the earth.
This episode delves into the extraordinary and intimate lives of the soft skinned amphibians. This includes the marsupial frogs, a peculiar species where the father carries his young in pouches and then gives birth. It also features warring giant salamanders over a metre long and show-off newts that offer displays just like underwater birds of paradise.

The Taiga forest, on the edge of the Arctic, is a silent world of stunted conifers. The trees may be small but filming from the air reveals its true scale. A third of all trees on Earth grow here and during the short summer they produce enough oxygen to change the atmosphere. In California General Sherman, a giant sequoia, is the largest living thing on the planet, ten times the size of a blue whale. The oldest organisms alive are bristlecone pines. At more than 4,000 years old they pre-date the pyramids. But the baobab forests of Madagascar are perhaps the strangest of all.