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.

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.

Of all the objects in the cosmos, planets, stars, galaxies, none are as strange, mysterious, or powerful as black holes. Black holes are the most mind-blowing things in the universe. They can swallow a star completely intact. Black holes have these powerful jets that just spew matter out.

First discovered on paper, on the back of an envelope, some squiggles of the pen. The bizarre solution to a seemingly unsolvable equation, a mathematical enigma. Einstein himself could not accept black holes as real. People didn't even believe for many years that they existed. Nature doesn't work that way. Yet slowly, as scientists investigate black holes by observing the effect they have on their surroundings, evidence begins to mount.

First discovered on paper, on the back of an envelope, some squiggles of the pen. The bizarre solution to a seemingly unsolvable equation, a mathematical enigma. Einstein himself could not accept black holes as real. People didn't even believe for many years that they existed. Nature doesn't work that way. Yet slowly, as scientists investigate black holes by observing the effect they have on their surroundings, evidence begins to mount.

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.

The film follows a ground-breaking experiment in the Canary Islands to use quasars at opposite ends of the universe to once and for all settle remaining questions.