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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.

Super quick computers and advanced mathematical formulas have taken over trading on the financial markets from human beings -algorithms- which seem to have a life of their own. The only ones who understand the system in any way are its architects, the algorithm developers. Haim Bodek is one such algo-developer. After finding some strange wrongdoings he set out on a personal crusade against this elusive system". The machinery behind our financial markets, consisting of mathematical models, data centers and miles and miles of fiber optic cables, is disguised by technological complexity and secrecy. The builders of this financial system are a new breed of Wall Street employees -quants- mathematicians and physicists who are responsible for a technological revolution. Haim Bodek is a quant; he specialized in artificial intelligence and worked for Goldman Sachs. He knows the system from the inside, he helped build it. Haim Bodek was invited to tell his story at the "Battle of the Quants" - a recurring event where quants discuss high-frequency trading, amongst other things. Bodek wrote an algorithm for trading machines that would generate guaranteed income - a money machine that weathered the financial meltdown of 2008. But then from one day to the next the algorithm stopped working.

Alex Winter explores the downloading revolution; the kids that created it, the bands and the businesses that were affected by it, and its impact on the world at large. He focuses on the advent of digital media sharing, including the rise of game-changing company Napster and controversial pioneers Shawn Fanning and Sean Parker. The digital revolution ultimately created a technology paradigm shift and upended the music industry. Audiences will hear insight from well known music artists and figures within the music industry including: The Beastie Boys' Mike D, Noel Gallagher, Henry Rollins, former Sony Music Chairman, Don Ienner, former record producer and Island Records founder Chris Blackwell and Hilary Rosen, former CEO of the Recording Industry Association of America.

Scientific advancements are challenging the concept of what it means to be human. Technology embedded in our bodies is fairly common: artificial limbs, pacemakers. But new research is taking us beyond replacement parts and into a new realm that is changing the nature of the human body and the human mind. Will the fusion of biology and technology change how we think, how we feel, how we experience the world?

Painted over five centuries ago, Filippo Lippi's nativity is like none other: it shows the birth of Christ in a dark, wooded wilderness. There are no shepherds, kings, ox, ass – there is no Joseph. Its beauty inspired Michelangelo, Leonardo da Vinci and Botticelli. But it also conceals a deeply personal story. It was painted for Cosimo de Medici, a wealthy banker who feared that his money was dragging him straight to hell. The artist's life was equally surprising. One of the most celebrated painters of his day, Filippo Lippi was also a Carmelite friar, but he was no stranger to the temptations of the flesh, to which he frequently yielded. Shortly before painting his Adoration, he caused uproar by seducing a twenty year-old nun. His paintings rejoice not only in divine beauty, but in the beauty of women. In later times, the Adoration's history was interwoven with that of rulers and dictators. It became a bargaining chip after Napoleon's allies seized twenty merchant ships. And in the 20th century, it was hidden by the Nazis in a potassium mine, where specialist american officers, known as Monuments Men, stumbled upon it. they were now told to get it ready to be shipped out. In an unprecedented turn of events they refused. This is the only known case in the whole of the Second World War of American officers refusing an order. It was sent to the National Gallery of Art, but in 1949 Lippi's Adoration was returned to Germany.

The rock revolution of the 1960s seen through the life and music of Jimi Hendrix. We see how he became the first, ultimately doomed, icon of rock. The Birth Of Rock also explores the influence of rhythm & blues on a generation of British musicians such as The Rolling Stones, Cream and The Who, and how the song-writing of Bob Dylan and studio developments of The Beatles transformed the possibilities and ambitions of rock.