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.

Written and presented by Robert Hughes, one of the world’s most prominent art commentators, this program explores the life and work of Francisco Goya—focusing on the painter’s subversive, often gruesome outlook. The video provides in-depth visual and intellectual analysis of dark Goya masterpieces, including The Dream of Reason, Witches in the Air, and The Third of May, as well as examples of his portraiture and early work—such as The Duchess of Alba, both Majas, and a gratuitously violent tapestry painting. Links between Goya’s work, deafness, and political stance are explored in detail, while observations from painter Leon Golub highlight Goya’s continuing relevance.

'Dinosaurs: Giants of Patagonia' Following Pr Rodolfo Coria, a world-reknown Argentinian paleontologist, we visit sites of major discoveries he has contributed to in Patagonia and travel back in time to see these amazing beasts come to life in 3D. Patagonia has given us the largest living animal to ever walk the Earth: the titanesque plant-eating Argentinosaur, and its nemesis, the Giganotosaur, a bipedal carnivore that could easily challenge the famous T-Rex.

The honey badger looks like something you might buy in pet shop and give to children, but turns out to be one of the most violent and determined creatures ever to scuttle across the face of the earth. Nothing in the badger’s world-not even the badgers themselves-are safe from its remarkable ability to create havoc and cause harm. Like a meter long skunk with the brain of a shark the Honey Badger’s metabolism compels it to eat constantly and live on the run. Its diet is admirably inclusive ranging from insects to its own young. If an animal is too big to eat then the badger will fight it anyway, indeed it is this almost supernatural tenacity that compels you respect it, as well as yielding some of the most spectacular sequences in the film. Five foot long cobra sleeping in the top of tree? No problem, the badger scoots up and bites its head off. When an ailing badger is attacked by a full size leopard it takes the leopard over an hour to finish it off. When one is bitten in the face by a snake that can kill a man, it just lies down for a while and sleeps it off.

Welcome to an extreme landscape of rock, ice and snow. We tour the mightiest mountain ranges, starting with the birth of a mountain at one of the lowest places on Earth and ending at the summit of Everest. Find out how some of the most secretive animals rise to the challenge of mountain life. Share one of Earth's rarest phenomena, a lava lake that has been erupting for over 100 years. The same forces built the Simian Mountains where we find troops of gelada baboons nearly a thousand strong. In the Rockies, grizzlies build winter dens inside avalanche-prone slopes and climb the peaks to devour abundant summer moths. In another world first, the programme brings us astounding images of a snow leopard hunting on the Pakistan peaks.

Open your eyes to the bizarre, ferocious and surprisingly beautiful world of the invertebrates, a ground-breaking exploration into a spectacular miniature universe never normally seen but teeming all around us. In the first episode, the story of the land-living invertebrates. Discover the private life of Europe's dramatic leopard slug, a common garden resident with a truly bizarre end to its marathon mating ritual; watches the courtship ballet of tiny springtails on the underside of a leaf; sees swarms of bright red South African millipedes find partners, and in the caves of Venezuela meets the giant bat-eating centipede.