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.

Widespread immigration to the U.S. from Latin countries begins – first with a small group from Cuba, then a larger one from Mexico. Both flee chaos and violence in their home country and are attracted by opportunities in the United States. In 1898, the U.S. helps liberate Cuba and Puerto Rico from Spain but then seizes Puerto Rico as its colony. The first Puerto Rican arrivals (now U.S. citizens) establish a network in New York.

The story of how the secret of life has been examined through the prism of the most complex organism known - the human body. It begins with attempts to save the lives of gladiators in Ancient Rome, unfolds with the macabre work and near-perfect drawings of Leonardo in the Renaissance, through the idea of the 'life force' of electricity, to the microscopic world of the cell. It reveals how a moral crisis unleashed by work on the nuclear bomb helped trigger a great breakthrough in biology - understanding the structure and workings of DNA.

Audrey Hepburn was a film and fashion icon of the twentieth century and one of the most beloved actresses of all time. She enchanted the world with elegance and innocent charm, and portrayed some of the most memorable characters in film. Although she was one of the few actresses to win an Emmy, Tony, Grammy, and Academy Award, Audrey was modest about her talents, often claiming she had no acting technique. She redefined glamour with elfin features and a waif-like figure that inspired timeless designs by Hubert de Givenchy.Raised in the Netherlands during World War II, Audrey never forgot her own struggles during the German occupation and dedicated her later years to helping needy children around the world, becoming an International Goodwill Ambassador for UNICEF and traveling around the world to provide aid. Audrey Hepburn is remembered as a natural talent, a timeless beauty and a great humanitarian.

Northern Africa is home to the greatest desert on Earth, the Sahara. On the fringes, huge zebras battle over dwindling resources and naked mole rats avoid the heat by living a bizarre underground existence. Within the desert, where the sand dunes 'sing', camels seek out water with the help of their herders and tiny swallows navigate across thousands of square miles to find a solitary oasis. This is a story of an apocalypse and how, when nature is overrun, some are forced to flee, some endure, but a few seize the opportunity to establish a new order.