Mathematician Dr Hannah Fry explores the mystery of maths. It underpins so much of our modern world that it's hard to imagine life without its technological advances, but where exactly does maths come from? Is it invented like a language or is it something discovered and part of the fabric of the universe? It's a question that some of the most eminent mathematical minds have been wrestling with. To investigate this question, Hannah goes head first down the fastest zip wire in the world to learn more about Newton's law of gravity, she paraglides to understand where the theory of maths and its practice application collide, and she travels to infinity and beyond to discover that some infinities are bigger than others.
In this episode, Hannah goes back to the time of the ancient Greeks to find out why they were so fascinated by the connection between beautiful music and maths. The patterns our ancestors found in music are all around us, from the way a sunflower stores its seeds to the number of petals in a flower. Even the shapes of some of the smallest structures in nature, such as viruses, seem to follow the rules of maths. All strong evidence for maths being discovered. But there are those who claim maths is all in our heads and something we invented. To find out if this is true, Hannah has her brain scanned. It turns out there is a place in all our brains where we do maths, but that doesn't prove its invented.
Experiments with infants, who have never had a maths lesson in their lives, suggests we all come hardwired to do maths. Far from being a creation of the human mind, this is evidence for maths being something we discover. Then along comes the invention of zero to help make counting more convenient and the creation of imaginary numbers, and the balance is tilted in the direction of maths being something we invented. The question of whether maths is invented or discovered just got a whole lot more difficult to answer

Predictions underlie nearly every aspect of our lives, from sports, politics, and medical decisions to the morning commute. With the explosion of digital technology, the internet, and 'big data,' the science of forecasting is flourishing. But why do some predictions succeed spectacularly while others fail abysmally? And how can we find meaningful patterns amidst chaos and uncertainty? From the glitz of casinos and TV game shows to the life-and-death stakes of storm forecasts and the flaws of opinion polls that can swing an election, 'Prediction by the Numbers' explores stories of statistics in action. Yet advances in machine learning and big data models that increasingly rule our lives are also posing big, disturbing questions. How much should we trust predictions made by algorithms when we don't understand how they arrive at them? And how far ahead can we really forecast?

In Los Angeles, a remarkable experiment is underway; the police are trying to predict crime, before it even happens. At the heart of the city of London, one trader believes that he has found the secret of making billions with math. In South Africa, astronomers are attempting to catalogue the entire cosmos. These very different worlds are united by one thing - an extraordinary explosion in data. Meet the people at the forefront of the data revolution, and reveals the possibilities and the promise of the age of big data.

Sir Roger Penrose is more than just a fan of MC Escher's mind-bending art. During the course of a long creative collaboration, the British mathematician and the Dutch artist exchanged ideas and inspirations. Some of Escher's most iconic images have their origin in Penrose's mathematical sketches - while the artist's work has served as a starting point for the professor's own explorations of new scientific ideas". To coincide with the first ever Escher retrospective in the UK, Penrose takes us on a personal journey through Escher's greatest masterpieces - marvelling at his intuitive brilliance and the penetrating light it still sheds on complex mathematical concepts.

Marcus du Sautoy uncovers the patterns that explain the shape of the world around us. Starting at the hexagonal columns of Northern Ireland's Giant's Causeway, he discovers the code underpinning the extraordinary order found in nature - from rock formations to honeycomb and from salt crystals to soap bubbles. Marcus also reveals the mysterious code that governs the apparent randomness of mountains, clouds and trees and explores how this not only could be the key to Jackson Pollock's success, but has also helped breathe life into hugely successful movie animations.

Al-Khalili travels to northern Syria to discover how, a thousand years ago, the great astronomer and mathematician Al-Biruni estimated the size of the earth to within a few hundred miles of the correct figure. He discovers how medieval Islamic scholars helped turn the magical and occult practice of alchemy into modern chemistry. In Cairo, he tells the story of the extraordinary physicist Ibn al-Haytham, who helped establish the modern science of optics and proved one of the most fundamental principles in physics - that light travels in straight lines. Prof Al-Khalili argues that these scholars are among the first people to insist that all scientific theories are backed up by careful experimental observation, bringing a rigour to science that didn't really exist before.