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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.

In part 2, we take a look at Odysseus, whom Homer made famous in "The Odyssey," including his adventures in light of astronomical and geographical evidence which bases the story on accurate real events.

Between 1850 and 1950, three cataclysmic revolutions shook China to the core, but out of them, today's China emerged. The film begins in Canton with the meeting of a US missionary and a Chinese student. Inspired by the Christian story and calling himself God's second son, Hong unleashed the bloodiest war of the 19th century, the Taiping Rebellion.
As imperial China weakened, foreign influence grew. Treaty ports expanded, bringing growth and wealth, trams, railways and western sensibilities. But this provoked another surge of violence, the Boxer Rebellion, an attack against the foreigners, which was crushed by those same foreigners, who extorted a huge indemnity - $60 billion in today's money.
Then in 1912, the empire fell, and many groups contested China's future. In World War I, China sent 100,000 men to the western front, only to be humiliated at Versailles when German colonies in China were handed to Japan. Between the two world wars, the disparity between rich and poor, city and countryside increased. We visit Hong Kong's Peninsular Hotel in the jazz age and then follow Mao on the Long March to Yan'an, the heartland of revolution.
World War II came to China two years earlier than it did in the west. Wood talks to a survivor of the Japanese massacre of Nanjing in 1937 and then charts the triumph of the communists, before ending the story with Mao's death and the boom time of the last 30 years. The series ends with the warmth of the Chinese family and, at Beijing's Altar of Heaven, a final haunting glimpse of eternal China.

Mathematician Dr Hannah Fry explores the mystery of maths. It underpins so much of our modern world that it's hard to imagine life without its technological advances, but where exactly does maths come from? Is it invented like a language or is it something discovered and part of the fabric of the universe? It's a question that some of the most eminent mathematical minds have been wrestling with. To investigate this question, Hannah goes head first down the fastest zip wire in the world to learn more about Newton's law of gravity, she paraglides to understand where the theory of maths and its practice application collide, and she travels to infinity and beyond to discover that some infinities are bigger than others.
In this episode, Hannah goes back to the time of the ancient Greeks to find out why they were so fascinated by the connection between beautiful music and maths. The patterns our ancestors found in music are all around us, from the way a sunflower stores its seeds to the number of petals in a flower. Even the shapes of some of the smallest structures in nature, such as viruses, seem to follow the rules of maths. All strong evidence for maths being discovered. But there are those who claim maths is all in our heads and something we invented. To find out if this is true, Hannah has her brain scanned. It turns out there is a place in all our brains where we do maths, but that doesn't prove its invented.
Experiments with infants, who have never had a maths lesson in their lives, suggests we all come hardwired to do maths. Far from being a creation of the human mind, this is evidence for maths being something we discover. Then along comes the invention of zero to help make counting more convenient and the creation of imaginary numbers, and the balance is tilted in the direction of maths being something we invented. The question of whether maths is invented or discovered just got a whole lot more difficult to answer

Idolized in ancient Norse mythology as the protector god, Thor battles evil ogres and a giant serpent bent on destroying mankind. It's the quintessential fight for survival that culminates in a final showdown between good and evil. But was the rise and fall of the hero Thor ancient code for something greater? Today, new discoveries unlock the hidden truth behind the Norse god of Thunder. Able to wield thunder from his hammer, Thor was the most revered of the Norse gods, from fending humanity from the giants that brought calamity, to his pursuit of the Midgard Serpent. Though, his fate is told to sealed during Ragnarok, it is actually the invasion of Christianity that proves far more damning to this mighty god.

This programme focuses on Nero, charting his obsession with becoming a god, how his plans to turn Rome into a glorious city bankrupted the Empire, how he married his slaveboy and killed his beloved wife in a frenzy, and how he was finally overthrown.