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.

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.

Go behind the veil of the ancient Greek belief in life after death to explore the myth of their most feared god - Hades - and those mortals who tried to cross his path. It is a chilling collection of tales about Hades and the underworld bearing his name, with eerie links to real world curses, ghosts and secret cults.

Medusa was the most infamous female fiend in Greek mythology, whose look turned every living thing to stone. But what is the true story behind the snake-haired gorgon? Find out about this evil Gorgon's real world connection to human corpses and learn what clues the night sky holds concerning the origins of the tale of Medusa.

More than 2,000 years ago, the thriving city of Petra rose up in the bone-dry desert of what is now Jordan. An oasis of culture and abundance, the city was built by wealthy merchants whose camel caravans transported incense and spices from the Arabian Gulf. They carved spectacular temple-tombs into its soaring cliffs, raised a monumental Great Temple at its heart, and devised an ingenious system that channeled water to vineyards, bathhouses, fountains, and pools. But following a catastrophic earthquake and a slump in its desert trade routes, Petra's unique culture faded and was lost to most of the world for nearly a thousand years. Now, in a daring experiment, an archaeologist and sculptors team up to carve an iconic temple-tomb to find out how the ancient people of Petra built their city of stone. Meanwhile, scientists using remote sensors and hydraulic flumes uncover the vast city and its sophisticated water system. The race is on to discover how these nomads created this oasis of culture in one of the harshest climates on Earth.

The final leg takes him from the Khyber Pass through Pakistan to the Punjab, where Alexander's army mutinied and he was forced to return across the Makran Desert to Babylon, where he died at only 32 years of age.