There is a tendency to deny German culture the equal reverence of Italy or Spain, and this enlightening new series provides a wonderful opportunity to explore a great, yet often neglected, artistic tradition whose influence has been just as profound. Andrew Graham-Dixon concludes his exploration of German art by investigating the dark and difficult times of the 20th century. Dominating the landscape is the figure of Adolf Hitler, failed artist, would-be architect and obsessed with the aesthetics of his 1,000-year Reich". In a series of extraordinary building projects and exhibitions, Hitler waged a propaganda war against every form of modern art as a prelude to unleashing total war on the whole of Europe. After the war the shadow of the Third Reich persisted, Germany remained divided and traumatised. How would artists deal with a past that everybody wanted to forget? Journeying through the work of Otto Dix and George Grosz and the age of the Bauhaus to the post-war painters Georg Baselitz, Hilla Becher and the conceptual artist Joseph Beuys is a long and strange journey, but the signs that art has a place at the heart of the new reunited Germany are clearly visible.

Drazen Petrovic and Vlade Divac were two friends who grew up together sharing the common bond of basketball. Together, they lifted the Yugoslavian National team to unimaginable heights. After conquering Europe, they both went to America where they became the first two foreign players to attain NBA stardom. But with the fall of the Soviet Union on Christmas Day 1991, Yugoslavia split up. A war broke out between Petrovic's Croatia and Divac's Serbia. Long buried ethnic tensions surfaced. And these two men, once brothers, were now on opposite sides of a deadly civil war. As Petrovic and Divac continued to face each other on the basketball courts of the NBA, no words passed between the two. Then, on the fateful night of June 7, 1993, Drazen Petrovic was killed in an auto accident. "Once Brothers" will tell the gripping tale of these two men, how circumstances beyond their control tore apart their friendship, and whether Divac has ever come to terms with the death of a friend before they had a chance to reconcile.

When our species first arrived in Europe, the peak of the Ice Age was approaching and the continent was already crawling with a rival: stronger, at home in the cold and even (contrary to their popular image) brainier than us. So how did the European pioneers survive first the Neanderthals and then the deep freeze as they pushed across the continent? Alice Roberts reconstructs the head of the 'first European' to come face to face with one of our ancestors; she discovers how art became crucial for survival in the face of Neanderthal competition; and what happened to change the skin colour of these European pioneers from black to white.

The Red Sea is one of the youngest oceans in the world and one of the warmest. The northern region, with its diverse array of marine life, is one of the most visited dive locations on earth while the southern end remains virtually unexplored. It's a global hotspot for marine biology and an important trade route throughout human history, linking the trade goods of India and the Far East with the markets of Egypt and Europe.

Dr Alice Roberts looks at our ancestors' seemingly impossible journey to Australia. Miraculously preserved footprints and very old human fossils buried in the outback suggest a mystery: that humans reached Australia almost before anywhere else. How could they have travelled so far from Africa, crossing the open sea on the way, and do it thousands of years before they made it to Europe? The evidence trail is faint and difficult to pick up, but Alice takes on the challenge. In India, new discoveries among the debris of a super volcano hint that our species started the journey much earlier than previously thought, while in Malaysia, genetics points to an ancient trail still detectable in the DNA of tribes today. Alice travels deep into the Asian rainforests in search of the first cavemen of Borneo and tests out a Stone Age raft to see whether sea travel would have been possible thousands of years ago, before coming to a powerful conclusion.

When ancient Greece fell into decline, mathematical progress stagnated as Europe entered the Dark Ages, but in the East mathematics reached new heights. In the second episode, Du Sautoy explores how maths helped build imperial China and discovers how the symbol for the number zero was invented in India. He also looks at the Middle Eastern invention of algebra and how mathematicians such as Fibonacci spread Eastern knowledge to the West.