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.

The film looks at the latest understanding of black holes, featuring an interview with Stephen Hawking. Black holes are one of the greatest mysteries in the universe. They behave in a way that is contrary to laws of physics and one has never actually been seen. However, the recent detection of gravitational waves, as predicted by Einstein, proves that black holes exist and provides a way to investigate their remarkable behaviour and properties.

Scientists genuinely don't know what most of our universe is made of. The atoms we're made from only make up four per cent. The rest is dark matter and dark energy (for 'dark', read 'don't know'). The Large Hadron Collider at CERN has been upgraded. When it's switched on in March 2015, its collisions will have twice the energy they did before. The hope is that scientists will discover the identity of dark matter in the debris. The stakes are high - because if dark matter fails to show itself, it might mean that physics itself needs a rethink.

Carl Sagan teaches students in a classroom in his childhood home in Brooklyn, New York, which leads into a history of the different mythologies about stars and the gradual revelation of their true nature. In ancient Greece, some philosophers (Aristarchus of Samos, Thales of Miletus, Anaximander, Theodorus of Samos, Empedocles, Democritus) freely pursue scientific knowledge, while others (Plato, Aristotle, and the Pythagoreans) advocate slavery and epistemic secrecy.

Forget the Big Bang. The real moment of creation was the Cosmic Dawn - the moment of first light. It's the moment the first stars were born, the moment that lit up the Universe, and made the first structure and the first ingredients of life. This is the scientific version of the story of Genesis. The Big Bang gets all the credit for creating our universe. But in fact, the universe it gave was dark and boring. There were no stars, no galaxies, just a vast, black fog of gas - the cosmic dark ages". But, after a hundred million years of nothing, came a dramatic moment of transformation - the Cosmic Dawn. Astronomers are now trying to witness this cosmic dawn. For the first time they have the tools to explore the very first stars of the universe and to tell the scientific story of our creation.

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.