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

The Hayabusa2 spacecraft has just completed one of the most intricate procedures in space exploration. The first mission to deliver rovers onto an asteroid has now descended to its surface for a sample, before returning back to Earth in 2020.

Plants' solutions to life's challenges are as ingenious and manipulative as any animal's. Innovative time-lapse photography opens up a parallel world where plants act like fly-paper, or spring-loaded traps, to catch insects. Vines develop suckers and claws to haul themselves into the rainforest canopy. Every peculiar shape proves to have a clever purpose. The dragon's blood tree is like an upturned umbrella to capture mist and shade its roots. The seed of a Bornean tree has wings so aerodynamic they inspired the design of early gliders. The barrel-shaped desert rose is full of water. The heliconia plant even enslaves a humming bird and turns it into an addict for its nectar.

Painting became an important means of communication for David since his face was slashed during a sword fight and his speech became impeded by a benign tumour that developed from the wound, leading him to stammer. He was interested in painting in a new classical style that departed from the frivolity of the Rococo period and reflected the moral and austere climate before the French Revolution. David became closely aligned with the republican government and his work was increasingly used as propaganda with the Death of Marat proving his most controversial work.

Journey through the long-vanished corners of prehistoric North America, beginning when man first entered the vast, unspoiled continent some 14,000 years ago, in this appealing BBC documentary. Witness ancient beasts, mammoths, mastodons, giant bears, and sabre-toothed cats, and see the legacies each has passed to their modern successors. Computer animation and digital effects bring to life mammoths, saber-toothed cats, giant ground sloths, short-faced bears, glyptodonts, and a plethora of smaller animals in a lush Ice Age mosaic.

Journey through the long-vanished corners of prehistoric North America, beginning when man first entered the vast, unspoiled continent some 14,000 years ago, in this appealing BBC documentary. Witness ancient beasts, mammoths, mastodons, giant bears, and sabre-toothed cats, and see the legacies each has passed to their modern successors. Computer animation and digital effects bring to life mammoths, saber-toothed cats, giant ground sloths, short-faced bears, glyptodonts, and a plethora of smaller animals in a lush Ice Age mosaic. Discoveries from sites across America are the basis for the reconstructions.