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.

In a late Jurassic forest in what is now China, an Epidexipteryx escapes from a juvenile Sinraptor by climbing a tree. It finds a beetle grub in the tree bark, being shown to use its elongated fingers in a similar way to a modern day aye-aye. However, its prey is stolen by another, larger Epidexipteryx, and after a brief bout of posturing, the smaller individual goes to find more food. It drops a second grub to the forest floor, where the other Epidexipteryx retrieves it, only to be killed by the juvenile Sinraptor. The episode then cuts to a desert in late Cretaceous Mongolia, where a Saurornithoides is shown brooding a nest of eggs. When it leaves the nest, an Oviraptor raids it, fleeing when the troodontid returns. The Saurornithoides is suddenly attacked and eaten by a Gigantoraptor, which then heads to compete in a breeding ritual for mates. The males use their feathers for display, a brief fight between two erupting at one point, allowing the females to choose the best suitor. The episode finally cuts to an early Cretaceous forest in China, where a Xianglong is being hunted by a Microraptor, which uses its feathers to pursue the gliding lizard in the air. A Sinornithosaurus attacks it, and after a brief chase the Microraptor manages a lucky escape. The Sinornithosaurus, alongside two other members of its species is then shown hunting a Jeholosaurus and its three young. The group brings down the parent, the narrator explaining that their possibly venomous bite allowed them to tackle animals much larger than themselves. A montage is then shown of the feathered dinosaurs featured in the programme, with the narrator saying that Microraptor not only hints at how flight might have developed, but also that dinosaurs still live amongst us today, as birds.

Frequent security expos feature companies like Megvii and its facial- recognition technology. They show off cameras with A.I. that can track cars, and identify individuals by face, or just by the way they walk. In China it's been projected that over 600 million cameras will be deployed by 2020. Here, they may be used to discourage jaywalking, but they also serve to remind people that the state is watching. Matching with the most advanced artificial intelligence algorithm, they can actually use this data, real-time data, to pick up a face or pick up a action.
A.I. is a technology that can be used for good and for evil. So, how do governments limit themselves in, on the one hand, using this A.I. technology and the database to maintain a safe environment for its citizens, but not to encroach on a individual's rights and privacies?

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.

Michael Wood tells the tale of China's first great international age under the Tang Dynasty (618-907). From the picturesque old city of Luoyang, he travels along the Silk Road to the bazaars of central Asia and into India on the track of the Chinese monk who brought Buddhism back to China. This tale is still loved by the Chinese today and is brought to life by storytellers, films and shadow puppet plays. Then in the backstreets and markets of Xi'an, Michael meets descendants of the traders from central Asia and Persia who came into China on the Silk Road. He talks to Chinese Muslims in the Great Mosque and across town hears the amazing story of the first reception of Christianity in 635. Moving south, Michael sees the beginnings of China as an economic giant. On the Grand Canal, a lock built in 605 still handles 800 barges every day! The film tracks the rise of the silk industry and the world's favourite drink - tea. Michael looks too at the spread of Chinese script, language and culture across east Asia. 'China's influence on the East was as profound as Rome on the Latin West', he says, 'and still is today'. Finally, the film tells the intense drama of the fall of the Tang. Among the eyewitnesses were China's greatest poets. In a secondary school in a dusty village, where the Chinese Shakespeare - Du Fu - is buried in the grounds, the pupils take Michael through one famous poem about loss and longing as the dynasty falls. And in that ordinary classroom, there is a sense of the amazing drama and the deep-rooted continuities of Chinese culture.

Following the Yangtze along Tiger Leaping Gorge into Yunnan in China, Palin reaches the easternmost end of the Himalayas. He gets a medical check-up before exploring medieval Lijiang with the director of the local orchestra. Heading over Myanmar to Nagaland in India he rides the steam train to Tipong Coalmine. In Assam he rides an elephant and then stays in a strange monastery.