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.

It was 1985. Guns N' Roses were soon to be known as the last mammoth rock entity to come out of LA after selling over 100 million albums. Jon Brewer brings alive never-before-seen video footage of Guns N' Roses in their earliest days as a fledgling band, filmed and meticulously archived over the years by their close friend. They became known as 'the most dangerous band in the world' and retained the title for reasons this film portrays, via interviews with band members and those who were there on, and off, tour. Venture down seedy Sunset Strip to the Whiskey, the Rainbow and the Roxy, all known as 'the Jungle'.

The big blue is the world's greatest wilderness, far from shore and many kilometres deep. It's a vast marine desert where there is little to eat and nowhere to hide. Yet it's home to some of the biggest and most spectacular creatures on earth. This episode reveals what it takes to survive in this savage and forbidding world. We witness feats of incredible endurance, moments of high drama and extraordinary acts of heart-wrenching self-sacrifice. Every animal in the big blue must find their own unique way to survive. Sperm whales have the largest brains in the world. They live for 80 years, and we are only now beginning to learn the extraordinary complexity of their language of clicks - thought to coordinate the whole family in everything from childcare to hunting. With special pressure-proof cameras, we witness record-breaking feats of endurance as they hunt for squid a kilometre down into the abyss. Only recently have we begun to solve the mystery of where baby turtles disappear to in their early years. They leave the crowded waters of the coast and head to the open ocean, where they use floating debris like logs as life rafts. Here they remain until adulthood, adrift on the high seas in relative safety away from coastal predators. Over half of all animals in the open ocean drift in currents. Jellyfish cross entire oceans feeding on whatever happens to tangle with their tentacles. The jelly-like Portuguese man-of-war can harness sail power to fish with its deadly tentacles. Sometimes there is a brief explosion of food in this marine desert, but ocean hunters must be fast to make the best of this bonanza. We witness super pods of up to 5,000 spinner dolphins racing to herd vast shoals of lanternfish, briefly caught at the surface where it is thought they spawn. New aerial footage reveals, for the first time, the truth to a centuries-old sailors' legend of the 'boiling seas' - the spectacular feeding frenzy of 90kg tuna and dolphins smashing through the lantern fish shoals turning the sea white with foam.

Where is everyone? We have been listening for messages from outer space for more than half a century, and so far... silence, why? Are we truly alone in the universe? Or is everyone else acting like us and just doing a lot of listening? Maybe we need to be louder. Maybe we need to send more messages out there. But how do you write a letter to an extraterrestrial whose language and culture and biology and mind we have no concept of? And what do you say?
Given all of the unknowns about what they might behave, should we say anything at all?

To survive Mars, our species will need to evolve how we eat, drink, and build our homes. Will we need our genes to evolve as well? Sometime in the future humans will leave Earth to colonize Mars, and in doing so will begin to adapt to life on another planet in surprising ways. Evolutionary biologist Dr. Scott Solomon foresees a series of changes to our species from the size of our hearts and heads to the pigments in our skin.

There is one miniature fierce queen, hardly bigger than a grain of rice. Enter the fascinating, and sometimes brutal world of honey ants, struggling not just for survival, but power - all in service of their fearless leader, the queen. Her story has it all-- ambition, murder, and a great army of female warriors on the rampage.