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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.

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.

Richard Dawkins examines the growing suspicion the public has for science-based medicine, despite its track record of successes like the germ theory of disease, vaccines, antibiotics and increased lifespan. He notes a fifth of British children are currently not immunised against measles, mumps and rubella, attributing it to fears arising from a highly controversial report linking the vaccine with autism. Dawkins criticizes the growing field of alternative medicine which does not pass the same objective and statistical rigour as scientifically derived treatments using controlled double-blind studies. Without verifiable evidence, alternative therapies must rely on biased anecdotes and word of mouth to perpetuate. Dawkins observes these treatments have fanciful rationales and rituals behind them, with many alternative treatments employing pseudoscientific jargon such as "energy", "vibration" or "quantum theory" to give themselves greater credence to patients.

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.