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.

Every year, around the world, seasonal changes transform entire landscapes and draw in millions of creatures as these great events unfold. This fantastic series combines the epic scale of Planet Earth and the intimate, emotional stories of charismatic animals as they struggle to survive. Using state of the art technology, these programmes capture the Earth's most dramatic and epic wildlife spectacles and the intimate stories of the animals caught up in them.
The Great Melt: The summer melt of Arctic ice, opening up nearly three million square miles of ocean and land, provides opportunities for millions of animals, including beluga whales, families of Arctic foxes, vast colonies of seabirds, and the fabled Arctic unicorn, the narwhal. For polar bears, however, it is the toughest time of year. Why? How will they survive? A mother polar bear and her cub make their first journey together onto the sea ice. They are looking for ringed seals, their favourite prey. It is a serious business but the cub just wants to play. The melting ice makes it harder for them to hunt and threatens their survival. In a unique aerial sequence, the migration of narwhal with their distinctive unicorn-like tusks is filmed for the first time. The whales' journey is risky as they travel along giant cracks in the ice. If the ice were to close above them, they would drown. Hundreds of beluga whales gather in the river shallows. They rub themselves on smooth pebbles in one of the most bizarre summer spectacles. Guillemot chicks take their first flights from precipitous sea cliff nests to the sea 300 metres below. They attempt to glide to safety but many miss their target. Their loss is a bonus for the hungry Arctic fox family waiting below. As the melt comes to an end the bears gather, waiting for the sea to freeze again. Two 400kg males square up to each other to spar.

Trade, and in particular trade in luxury goods, drove the commerce economies of the Bronze Age. This is the time when the first super powers in history, Egypt and Mesopotamia, emerge and dominate the 'world' stage of the Mediterranean and Aegean seas and surrounding areas.

The film follows the dramatic journey of three whistleblowers who are determined to break the silence around one of the most controversial current affairs issues of our time: the secret U.S. drone war. At the center of the film are three U.S. military veterans. Plagued by guilt over participating in the killing of faceless people in foreign countries, they decide to speak out publicly, despite the possible consequences. Their stories take dramatic turns, leading one of the protagonists to Afghanistan where she learns about a horrendous incident. But her journey also gives hope for peace and redemption. National Bird gives rare insight into the U.S. drone program through the eyes of veterans and survivors, connecting their stories as never seen before in a documentary. Its images haunt the audience and bring a faraway issue close to home.

Every day of our lives, we are bombarded by thousands of different images, images which affect us in countless different ways. But of all these there's one particular kind of image whose power is uniquely mesmerising, because while it terrifies us somehow it also comforts. But although it can manipulate us, it also reassures, It's the image of death.

What if we could explore the vastness of Space? Science fiction has always fed upon our need to explore – to wonder what is out there. Space journeys from Jules Verne’s earliest ideas about attempts to leave our planet, to the Star Wars far away galaxy through to Nichelle Nichols revealing how her groundbreaking role as Lt. Uhura in Star Trek led to her participation in the recruitment of NASA’s astronauts. It explores the deep sea inspiration for Avatar, finds out why Ursula K Le Guin wrote The Left Hand of Darkness and discovers how Stanley Kubrick was able to make 2001: A Space Odyssey seem so believable. In addition, the program looks at the way Dune and The Mars Trilogy embraced the challenge of world building and discusses the appeal of the beaten up ‘dirty space’ of Dark Star and Firefly. From the horrifying scenes of Alien, to the epic spectacle of Star Wars, this is a journey to the stars and the alien encounters that await us there.