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.

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.

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.

In less than two years, Al Capone has risen from a humble bookkeeper to second-in-command of Johnny Torrio's criminal empire in Chicago. The empire is worth the modern-day equivalent of $35 million. Capone purchases a home for his family and moves them from New York to Chicago. Torrio and Capone expand their empire from Chicago's South Side to the North Side, which is controlled by Chicago's second largest gang, the Irish. Violence erupts as ruthless Irish gang leader Dean O'Banion protects his territory and bootlegging business from Torrio and Capone.

Zeitgeist Addendum attempts to locate the root causes of this pervasive social corruption, while offering a solution. This solution is not based on politics, morality, laws, or any other 'establishment' notions of human affairs, but rather on a modern, non-superstitious based understanding of what we are and how we align with nature, to which we are a part. The work advocates a new social system which is updated to present day knowledge, highly influenced by the life long work of Jacque Fresco and The Venus Project.

In the fourth part of the series, Diarmaid MacCulloch makes sense of the Reformation, and of how a faith based on obedience and authority gave birth to one based on individual conscience. He shows how Martin Luther wrote hymns to teach people the message of the Bible, and how a tasty sausage became the rallying cry for Swiss Reformer Ulrich Zwingli to tear down statues of saints, allow married clergy and deny that communion bread and wine were the body and blood of Christ.