In the fourth episode, Professor Marcus du Sautoy concludes his investigation into the history of mathematics with a look at some of the great unsolved problems that confronted mathematicians in the 20th century. After exploring Georg Cantor's work on infinity and Henri Poincare's work on chaos theory, he sees how mathematics was itself thrown into chaos by the discoveries of Kurt Godel and Paul Cohen, before completing his journey by considering some unsolved problems of maths today, including the Riemann Hypothesis.

Professor Simon Schaffer presents the amazing and untold story of automata - extraordinary clockwork machines designed hundreds of years ago to mimic and recreate life. The film brings the past to life in vivid detail as we see how and why these masterpieces were built. Travelling around Europe, Simon uncovers the history of these machines and shows us some of the most spectacular examples, from an entire working automaton city to a small boy who can be programmed to write and even a device that can play chess". All the machines Simon visits show a level of technical sophistication and ambition that still amazes today. As well as the automata, Simon explains in great detail the world in which they were made - the hardship of the workers who built them, their role in global trade and the industrial revolution and the eccentric designers who dreamt them up. Finally, Simon reveals that to us that these long-forgotten marriages of art and engineering are actually the ancestors of many of our most loved modern technologies, from recorded music to the cinema and much of the digital world.

In the fourth episode of the series, eyewitnesses recall how those in power at Auschwitz lined their pockets with wealth stolen from Jewish inmates while also engaging in illicit affairs.

Dr Michael Scott examines the vital role played by the Romans in the preservation of Greek drama and in the history of theatre. He explores how the Romans absorbed Greek theatre and adapted it to their own, very Roman, ends and looks at how this famous empire provides one of the crucial connections between our modern drama and the great plays of the ancient Greeks.

Homer's The Odyssey ranks amongst the most famous epics ever written. Follow its archetypal hero, Odysseus, as he sets sail on a twenty-year journey to return home from battle to reclaim his wife and kingdom. It's a timeless tale of adventure, filled with mythological beasts, vengeful gods, and enchanting seductresses. But could it have actually happened? Underwater divers have uncovered remains that date back thousands of years and may be a direct link to the story of Odysseus.

It was the bloodiest war in history, yet Hitler's brutal invasion of the Soviet Union and Stalin's subsequent fight back is surprisingly little known in the West. More than 30 million people died during Hitler and Stalin's terrible war in the East - more than in any other single war in history. With direct testimony from people who perpetrated atrocities and the victims who suffered on both sides, we bring the unspeakable to the screen and allowing victims and aggressors to tell the truth as they see it. In the first episode, we will look at Hitler's plans to invade the Soviet Union and the horror of the first months of conflict.