Dr Hannah Fry explores a paradox at the heart of modern maths, discovered by Bertrand Russell, which undermines the very foundations of logic that all of maths is built on. These flaws suggest that maths isn't a true part of the universe but might just be a human language - fallible and imprecise. However, Hannah argues that Einstein's theoretical equations, such as E=mc2 and his theory of general relativity, are so good at predicting the universe that they must be reflecting some basic structure in it. This idea is supported by Kurt Godel, who proved that there are parts of maths that we have to take on faith.
Hannah then explores what maths can reveal about the fundamental building blocks of the universe - the subatomic, quantum world. The maths tells us that particles can exist in two states at once, and yet quantum physics is at the core of photosynthesis and therefore fundamental to most of life on earth - more evidence of discovering mathematical rules in nature. But if we accept that maths is part of the structure of the universe, there are two main problems: firstly, the two main theories that predict and describe the universe - quantum physics and general relativity - are actually incompatible; and secondly, most of the maths behind them suggests the likelihood of something even stranger - multiple universes.
We may just have to accept that the world really is weirder than we thought, and Hannah concludes that while we have invented the language of maths, the structure behind it all is something we discover. And beyond that, it is the debate about the origins of maths that has had the most profound consequences: it has truly transformed the human experience, giving us powerful new number systems and an understanding that now underpins the modern world.

In 335 BC Alexander of Macedonia set off on an expedition to conqueror the world. The voyage of Alexander the Great covered more than 22,000 miles in ten years, from Greece to India and back, through some of the most difficult and unforgiving terrain. Michael Wood was hot on his trail, following, as closely as possible, in the footsteps of Alexander and the army that he drove to achieve the impossible. In this programme: the Lebanese city of Tyre, scene of Alexander's most desperate battle; the Palestinian legend of `Two-Horned Alexander'; and the Egyptian oasis of Siwa, where Alexander was proclaimed pharaoh and son of God.

Dr. Thomas Asbridge introduces the epic story of the Crusades – a tale of religious fanaticism and unspeakable brutality, of medieval knights and Jihadi warriors; of castles and kings; of heroism, betrayal, and sacrifice. He explains how, using fresh evidence, eye-witness testimonies and contemporary accounts – from both the Christian and Islamic worlds – we are able to re-examine this epic medieval drama, and how he has retraced the steps of the Crusaders from a small town in France to the magnificent cities of the Holy Land, bringing to life the human experience of the Crusades, and shedding new light on how it was that two of the world’s great religions waged war in the name of God.

At a crucial time in history, when religious violence is impacting peace all over the world, and science is venturing into areas that were once the realms of faith, Morgan Freeman embarks on a journey around the globe and through the centuries to uncover the Story of God. He will explore different cultures and religions on the ultimate quest to uncover the meaning of life, God and all these big questions in between. In the first episode, the actor examines religious belief. He starts by discussing the afterlife with scientists, scholars, a Hindu monk and a man who had a near-death experience.

In the days of the Mayas, cenotes – deep, natural pits on the Yucatan peninsula - provided the only means of obtaining drinking water. But in the mythology of this advanced civilisation, these waterholes and caves were also the entrance to Xibalba – the underworld. All deceased were obliged to pass through Xibalba and wait there until they were called into heaven. It was a place in which one made sacrifices to the gods – objects of daily life, as well as bloody, human sacrifices. To this day, the relics of these acts are still in place preserved underwater for more than a thousand years. The entrance to the underworld begins at a dirty waterhole in the middle of the Mexican jungle overgrown and barely recognisable. But immediately after entry, a hall of breath-taking dimensions and beauty is revealed. As if they were sculptures, stalactites and stalagmites lend the underwater cave an almost sacred ambience. By now, one has succumbed to the fascination emanated by the world’s largest underwater cave system. We accompany four professional research divers to Yucatan – a team of specialists, able to squeeze their bodies through crevices and holes, barely larger than their bodies and who master dives that would push even the most experienced divers to their limits. With them, we penetrate worlds only a few people have ever ventured into. We encounter the remains of human victims, prehistoric fireplaces and primeval animal skeletons and undertake a dive, which takes us from the primeval forest to the open sea. We then enter Xibalba – the place of myths and the dead. In the days of the Mayas - a voyage of no return. Today, this is one of the greatest challenges one can face as a diver – the hidden world of the underwater caves of Yucatan – all filmed in 3D.

With optional Hebrew subtitles. Simon Schama explores the history of the Jewish experience from ancient times to the present day. This programme begins the tale 3,000 years ago, with the emergence of a tribal people in a contested land and their extraordinary book, the Hebrew Bible, a chronicle of their stormy relationship with a faceless, formless, jealous God. It was loyalty to this 'God of Words' that defined the distinct identity of the ancient Jews and preserved it despite all that history could throw their way". The story unfolds with a dazzling cast of historical characters: Sigmund Freud dying in exile in London; Victorian evangelicals and explorers following 'in the footsteps' of Moses; Jewish mercenaries living, prospering and intermarrying in the pagan land of Egypt; Messianic Jews dreaming of the Apocalypse; and a Jewish historian, Josephus, who witnessed first-hand the moment when the apocalypse finally came and the Romans destroyed the Jewish High Temple in Jerusalem.