Dr Hannah Fry travels down the fastest zip wire in the world to learn more about Newton's ideas on gravity. His discoveries revealed the movement of the planets was regular and predictable. James Clerk Maxwell unified the ideas of electricity and magnetism, and explained what light was. As if that wasn't enough, he also predicted the existence of radio waves. His tools of the trade were nothing more than pure mathematics. All strong evidence for maths being discovered.

But in the 19th century, maths is turned on its head when new types of geometry are invented. No longer is the kind of geometry we learned in school the final say on the subject. If maths is more like a game, albeit a complicated one, where we can change the rules, surely this points to maths being something we invent - a product of the human mind. To try and answer this question, Hannah travels to Halle in Germany on the trail of perhaps one of the greatest mathematicians of the 20th century, Georg Cantor. He showed that infinity, far from being infinitely big, actually comes in different sizes, some bigger than others. This increasingly weird world is feeling more and more like something we've invented. But if that's the case, why is maths so uncannily good at predicting the world around us? Invented or discovered, this question just got a lot harder to answer.

But in the 19th century, maths is turned on its head when new types of geometry are invented. No longer is the kind of geometry we learned in school the final say on the subject. If maths is more like a game, albeit a complicated one, where we can change the rules, surely this points to maths being something we invent - a product of the human mind. To try and answer this question, Hannah travels to Halle in Germany on the trail of perhaps one of the greatest mathematicians of the 20th century, Georg Cantor. He showed that infinity, far from being infinitely big, actually comes in different sizes, some bigger than others. This increasingly weird world is feeling more and more like something we've invented. But if that's the case, why is maths so uncannily good at predicting the world around us? Invented or discovered, this question just got a lot harder to answer.

Professor Jim Al-Khalili investigates the amazing science of gravity. A fundamental force of nature, gravity shapes our entire universe. It sculpts galaxies and warps space and time. But gravity’s strange powers also affect our daily lives in the most unexpected ways. This is a story with surprises in store for Jim himself. In telling the story of gravity, his own understanding of the nature of reality comes to be challenged. Finally, Jim discovers that, despite incredible progress, gravity still has many secrets to unveil.

For centuries, the precise workings of gravity have confounded the greatest scientific minds - from Newton to Faraday and Einstein - and the idea of controlling gravity has been seen as little more than a fanciful dream. Yet in the mid 1990s, UK defence manufacturer BAE Systems began a ground-breaking project code-named Greenglow. Nasa was simultaneously running its own Breakthrough Propulsion Physics Project". It was concerned with potential space applications of new physics, including concepts like 'faster-than-light travel' and 'warp drives'. Looking into the past and projecting into the future, Horizon explores science's long-standing obsession with the idea of gravity control. It looks at recent breakthroughs in the search for loopholes in conventional physics and examines how the groundwork carried out by Project Greenglow has helped change our understanding of the universe. Gravity control may sound like science fiction, but the research that began with Project Greenglow is very much ongoing, and the dream of flying cars and journeys to the stars no longer seems quite so distant.

On November 25th, 1915, Einstein published his greatest work: General Relativity. The theory transformed our understanding of nature’s laws and the entire history of the cosmos, reaching back to the origin of time itself. Now, in celebration of the 100th anniversary of Einstein’s achievement, discover the inside story of Einstein’s masterpiece". The story begins with the intuitive thought experiments that set Einstein off on his quest and traces the revolution in cosmology that is still playing out in today’s labs and observatories. Discover the simple but powerful ideas at the heart of relativity, illuminating the theory—and Einstein’s brilliance—as never before. From the first spark of an idea to the discovery of the expanding universe, the Big Bang, black holes, and dark energy, NOVA uncovers the inspired insights and brilliant breakthroughs of “the perfect theory.”

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