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.

Washington, D.C. is in many ways a city of extremes. Starland Vocal Band, Marvin Gaye, Duke Ellington, Nils Lofgren, Chuck Brown, Henry Rollins, Fugazi and Trouble Funk all hail from D.C. In the early '70s, the music style go-go originated here, and has remained a local craze ever since. Dave Grohl sits down with Trouble Funk's Big Tony Fisher to talk about go-go, and explores its origins with Chuck Brown, the genre's undisputed godfather.
He also chats with Don Zientara, owner of Inner Ear Studios, which the Virginia-raised Grohl says 'produced the entire soundtrack of my youth,' as well as with members of the harDCore band Bad Brains and Ian MacKaye of Teen Idles, Minor Threat and Fugazi, who all recorded at Inner Ear over the decades. The song 'The Feast and the Famine' is recorded during this episode.

Filmmaker and artist Yann Arthus-Bertrand spent 3 years collecting real-life emotional stories from more than 2,000 women and men in 60 countries. Those emotions, those tears and smiles, those struggles and those laughs are the ones uniting us all. A combination of testimonies and exclusive aerial images, HUMAN is a unique documentary. This sensitive experience is an introspection into whom we are today as a community but also and most importantly as an individual. Through wars, inequalities, discriminations, HUMAN confronts us with the realities and the diversity of our human conditions. Beyond this darker side, testimonies show the empathy and the solidarities which we are capable of. All these contradictions are ours and HUMAN leads us to reflect about the future we wish to give to people and the planet today.

This episode covers the European refugee crisis, the largest refugee migration since World War II. Following the refugees on their journey, Vice sets out to cover not only the trials of those seeking asylum from the Syrian conflict, but the reactions from the Western world and the countries that have sought to take them in. Unfortunately, but perhaps not surprisingly, the response in many regions has been oppositional, especially in the aftermath of the Paris and Brussels ISIS attacks. In addressing this modern world crisis, Vice depicts the severe trials and tribulations faced by the desperate refugees, and the consequences, noticed or unnoticed, of turning them away.

In the 1960s, US President John F Kennedy proposed landing a man on the moon before the decade was finished. This film has interviews with most of the surviving astronauts of the Apollo program who were making ready to make that great voyage with an army of experts determined to make the endeavour possible. Through training, tragedy and triumph, we follow the greatest moments of one of Humanity's great achievements. The documentary reviews both the footage and media available to the public at the time of the missions, as well as NASA films and materials which had not been opened in over 30 years.

Filmmaker Daniel McNicoll explores the emerging movement to reclaim the ancient medieval and renaissance martial arts in this documentary narrated by Welsh actor John Rhys-Davies, and produced on corroboration with Lord of the Rings director Peter Jackson. The Medieval and Renaissance blade was a remarkable weapon crafted with the utmost attention to detail. Though the history of the sword remains largely shrouded in mystery for younger moviegoers, their presence on the big screen can still be felt in the Star Wars saga, as well as films like Chronicles of Narnia and The Pirates of the Caribbean. Join host Davies as he traces the history of this remarkable weapon throughout the ages, in the process giving us a better understanding of the sword's unique role in both history, and films.