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.

A compelling, dramatic and stylish cinematic journey into snowboarding's unique history and the wider cultural forces that shaped it. Featuring interviews and archival footage with Todd Richards, Gigi Rüf, Terje Haakonsen, Jake Burton, Tom Sims, Stale Sandbech and Craig Kelly.

With optional Hebrew subtitles. Simon Schama explores the history of the Jewish experience from ancient times to the present day. This programme begins the tale 3,000 years ago, with the emergence of a tribal people in a contested land and their extraordinary book, the Hebrew Bible, a chronicle of their stormy relationship with a faceless, formless, jealous God. It was loyalty to this 'God of Words' that defined the distinct identity of the ancient Jews and preserved it despite all that history could throw their way". The story unfolds with a dazzling cast of historical characters: Sigmund Freud dying in exile in London; Victorian evangelicals and explorers following 'in the footsteps' of Moses; Jewish mercenaries living, prospering and intermarrying in the pagan land of Egypt; Messianic Jews dreaming of the Apocalypse; and a Jewish historian, Josephus, who witnessed first-hand the moment when the apocalypse finally came and the Romans destroyed the Jewish High Temple in Jerusalem.

The enemy gains ground when the massive Tet Offensive catches the Americans by surprise. At Khe Sanh and Pleiku, U.S. troops are under siege. Americans mount a counteroffensive but the shock of the assault ignites anti-war fervour at home.

Arguably the most powerful painting about war ever achieved. It portrays the slaughter of civilians after Napoleonic troops entered Madrid in 1808. The programme reveals the historical truths behind the painting and shows exactly how Goya achieved this masterpiece of protest. he painting's content, presentation, and emotional force secure its status as a groundbreaking, archetypal image of the horrors of war. Although it draws on many sources from both high and popular art, The Third of May 1808 marks a clear break from convention. Diverging from the traditions of Christian art and traditional depictions of war, it has no distinct precedent, and is acknowledged as one of the first paintings of the modern era.
According to the art historian Kenneth Clark, The Third of May 1808 is 'the first great picture which can be called revolutionary in every sense of the word, in style, in subject, and in intention'. Discover how Goya used drawings by authentic witnesses to depict a real firing squad.

Having learned that Vorenus' children are alive, Pullo sets off to find him in Gaul where he is again a serving soldier in Mark Antony's army. He had hoped to arrive before Octavian and Antony's armies meet in battle. Too late however, he is forced to find what is left of Antony's army in the mountains. He finds Vorenus alive and well, if somewhat battle worn, and they set off to find the children.
The victorious Octavian plans his return to Rome. In Western Turkey, Brutus and Cassius amass their own army, now 19 Legions strong.