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.

Two thousand years ago one of history's most notorious individuals was born. Professor Mary Beard embarks on an investigative journey to explore the life and times of Gaius Julius Caesar Augustus Germanicus - better known to us as Caligula. Caligula has now become known as Rome's most capricious tyrant, and the stories told about him are some of the most extraordinary told about any Roman emperor. He was said to have made his horse a consul, proclaimed himself a living God, and indulged in scandalous orgies - even with his own three sisters - and that's before you mention building vast bridges across land and sea, prostituting senators' wives and killing half the Roman elite seemingly on a whim. All that in just four short years in power before a violent and speedy assassination in a back alley of his own palace at just 28-years-old." But how much of his story is true? Travelling across the Roman world - from Germany and Capri in the bay of Naples to the astonishing luxury of his life in imperial Rome - Mary attempts to peel away the myths. Some stories are difficult to get to the bottom of as they were written by hacks long after his death, but there is plenty of surviving evidence where the 'real' Caligula can be glimpsed. Such as in the extraordinary luxury of his private yachts outside Rome; in the designs he chose for his coins when he became Emperor; in an eye-witness account of Caligula's withering humour written in 41AD; the trial documents covering the mysterious death of his father when he was just seven-years-old; and even in a record of his imperial slaves - from the palace spy to his personal trainer. Piecing together the evidence, Mary puts Caligula back into the context of his times to reveal an astonishing story of murder, intrigue and dynastic family power. Above all, she explains why Caligula has ended up with such a seemingly unredeemable reputation. In the process, she reveals a more intriguing portrait of not just the monster, but the man.

An intimate and heart-warming look at the man behind the legend - as we've never seen Ali before. Told through exclusive, unprecedented access to Ali's personal archive of 'audio journals' combined with touching interviews and testimonials from his inner circle of family and friends, including his daughters, son, brother and former wife, plus legends of the boxing community including Mike Tyson, George Foreman and Gene Kilroy

This new feature-length biographical film tells the extraordinary and dramatic story of the planet's most famous living scientist, told for the first time in his own words and by those closest to him. Made with unique access to his private life, this is an intimate and moving journey into Stephen Hawking's past and present. Interviewees include Stephen Hawking's sister Mary, his ex-wife Jane, carers and students, as well as colleagues such as Roger Penrose, plus Apollo astronaut Buzz Aldrin, actors Benedict Cumberbatch and Jim Carrey, and Sir Richard Branson This inspirational portrait of an iconic figure relates Hawking's incredible personal journey from boyhood underachiever to scientific genius and multi-million-selling author. And it charts how he overcame being diagnosed with motor neurone disease - and being given just two years to live - to make amazing scientific discoveries and become a symbol of triumph over adversity. Born exactly 300 years after the death of Galileo, Hawking grew up in a family some regarded as eccentric. Always asking questions, he was nicknamed 'Einstein' at school. Hawking blossomed at Oxford, although he only spent an hour a day studying. He noticed that he was becoming clumsy and fell over for no apparent reason. He was diagnosed with motor neurone disease, but nevertheless started a family and embarked on his academic career, finding himself at the heart of a searing scientific debate about the origins of the universe. And as he lost the use of his body, Hawking had to find new ways to think. He went on to write the huge bestseller A Brief History of Time, and the film reveals the high and lows of his resulting fame and fortune.

Andrew Graham-Dixon reveals how the Medici family transformed Florence through sculpture, painting and architecture and created a world where masterpieces fetch millions today. Without the money and patronage of the Medici we might never have heard of artists such as Donatello, Michelangelo or Botticelli, and Graham-Dixon examines how a family of shadowy, corrupt businessmen, driven by greed and ambition, became the financial engine behind the Italian Renaissance.

Four years in the making, Life will set a new benchmark in family entertainment and natural history epics. Many animals and plants go to extremes to give themselves a chance. Aerial photography reveals how bottle-nosed dolphins trap fish in a ring of mud, and time-lapse cameras show how the Venus flytrap ensnares insect victims. The strawberry frog carries a tadpole high into a tree and drops it in a water-filled bromeliad. Fledgling chinstrap penguins undertake a heroic and tragic journey through the broken ice to get out to sea. Many can barely swim and the formidable leopard seal lies in wait