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.

Music, art and chaos in the wild West-Berlin of the 1980s. The walled-in city became the creative melting pot for sub- and pop-culture. Before the iron curtain fell, everything and anything seemed possible. B-Movie is a fast-paced collage of mostly unreleased film and TV footage from a frenzied but creative decade, starting with punk and ending with the Love Parade, in a city where the days are short and the nights are endless. Where it was not about long-term success, but about living for the moment - the here and now. (Click CC for closed captions)

Join us on an unforgettable voyage through one of the most desolate periods in human history as the rulers, conflicts, and cataclysmic societal breakdown of Early Middle Ages are brought to light. At its height in the second century A.D., the Roman Empire was the beacon of learning, trade, power and prosperity in the western world. But the once-powerful Rome--rotten to the core by the fifth century--lay open to barbarian warriors who came in wave after wave of invasion, slaughtering, stealing, and ultimately, settling. As chaos replaced culture, Europe was beset by famine, plague, persecutions, and a state of war that was so persistent it was only rarely interrupted by peace.
The documentary profiles those who battled to shape the future, from the warlords whose armies threatened to case the demise of European society, like Alaric, Charles the Hammer, and Clovis; to the men and women who valiantly tended the flames of justice, knowledge, and innovation including Charlemagne, St. Benedict, Empress Theodora, and other brave souls who fought for peace and enlightenment. It was in the shadows of this turbulent millennium that the seeds of modern civilization were sown.