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 summer in the seas off Alaska humpback whales, sea lions and killer whales depend on an explosion of plant life, the plankton bloom. It transforms these seas into the richest on Earth. But will these animals survive to enjoy the great feast? The summer sun sparks the growth of phytoplankton, microscopic floating plants which can bloom in such vast numbers that they eclipse even the Amazon rainforest in sheer abundance of plant life. Remarkably, it is these minute plants that are the basis of all life here. But both whales and sea lions have obstacles to overcome before they can enjoy the feast. Humpback whales migrate 3,000 miles from Hawaii, and during their 3 month voyage lose a third of their body weight. In a heart-rending scene a mother sea lion loses her pup in a violent summer storm, while another dramatic sequence shows a group of killer whales working together to kill a huge male sea lion.
In late summer the plankton bloom is at its height. Vast shoals of herring gather to feed on it, diving birds round the fish up into a bait ball and then a humpback whale roars in to scoop up the entire ball of herring in one huge mouthful. When a dozen whales work together they employ the ultimate method of co-operative fishing - bubble net feeding. One whale blows a ring of bubbles to engulf the fish and then they charge in as one. Filmed from the surface, underwater and, for the first time, from the air, we reveal how these giant hunters can catch a tonne of fish every day.

Arguably the most powerful painting about war ever achieved. It portrays the slaughter of civilians after Napoleonic troops entered Madrid in 1808. The programme reveals the historical truths behind the painting and shows exactly how Goya achieved this masterpiece of protest. he painting's content, presentation, and emotional force secure its status as a groundbreaking, archetypal image of the horrors of war. Although it draws on many sources from both high and popular art, The Third of May 1808 marks a clear break from convention. Diverging from the traditions of Christian art and traditional depictions of war, it has no distinct precedent, and is acknowledged as one of the first paintings of the modern era.
According to the art historian Kenneth Clark, The Third of May 1808 is 'the first great picture which can be called revolutionary in every sense of the word, in style, in subject, and in intention'. Discover how Goya used drawings by authentic witnesses to depict a real firing squad.

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.

The film uses drones, hidden and handheld cameras to expose the dark underbelly of modern animal agriculture, questioning the morality and validity of humankind's dominion over the animal kingdom. While mainly focusing on animals used for food, it also explores other ways animals are exploited and abused by humans, including clothing, entertainment and research.
In words of its writer & director, Chris Delforce, 'Dominion to me is the idea of one group or entity exercising control, power or authority over another, under the belief that they have the right to do so. Often this belief seems to stem from the perception of self-superiority and that might equals right. Through this film I challenge both the notion that animals are inferior, and that we as humans have the right to use and treat them as we please for our own ends – and I briefly examine how this superiority complex has and continues to complement some of humanity's darkest ideologies, asking viewers to consider the similarities between racism, sexism and speciesism.'

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