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

With optional Hebrew subtitles. This episode explores how the spread of the Enlightenment brought ghetto walls around Europe crashing down and allowed Jews to join the wider fabric of modern life in Europe in unprecedented ways. This Jewish renaissance saw Giacomo Meyerbeer and Felix Mendelssohn to establish the enduring tradition for Jewish musical prodigies. However the integration of Jewish talent into the mainstream of European culture and commerce eventually stirred up ancient prejudice, expressed in the new fashion of Romantic nationalism and the pseudo-science of anti-semitism.

The film is the inside track on the World's most influential weapon. For over a thousand years this weapon dominated the battlefields of Japan, instilled fear and terror into every enemy it faced, and created a new spiritual way of life that lasts through to the present day. The Samurai sword – a weapon so technologically perfect in structure, so formidable in strength and so beautiful in creation. For the first time unique access has been granted and we travel into the core of the ancient foundries, sword-smiths and fighting schools to reveal what makes the so-called perfect sword. This is a no holds barred look at one of the most iconic man-made objects ever forged.

Lucy Worsley travels to Russia to tell the extraordinary story of the dynasty that ruled the country for more than three centuries. It's an epic tale that includes giant figures such as Peter the Great and Catherine the Great, the devastating struggle against Napoleon in 1812, and the political murders of Nicholas II and his family in 1918 which brought the dynasty to a brutal end.
In this first episode, Lucy investigates the beginning of the Romanovs' 300-year reign in Russia. In 1613, when Russia was leaderless, 16-year-old Mikhail Romanov was plucked from obscurity and offered the crown of Russia. Lucy also charts the story of Peter the Great, the ruthless and ambitious tsar who was determined to modernise Russia at the end of the 17th century.

In this episode, Michael demonstrates how our society is built on our search to find the answer to what makes up everything in the material world. This is a story that moves from the secret labs of the alchemists and their search for gold by the stone of the philosophers to the creation of the world's first synthetic dye - Purple - and onto the invention of the transistor. This quest may seem abstract and highly theoretical. Yet it has delivered the greatest impact on humanity. By trying to answer this question, scientists have created theories from elements to atoms, and the strange concepts of quantum physics that underpin our modern, technological world.

In the fourth part of the series, Diarmaid MacCulloch makes sense of the Reformation, and of how a faith based on obedience and authority gave birth to one based on individual conscience. He shows how Martin Luther wrote hymns to teach people the message of the Bible, and how a tasty sausage became the rallying cry for Swiss Reformer Ulrich Zwingli to tear down statues of saints, allow married clergy and deny that communion bread and wine were the body and blood of Christ.