In the third episode we will see Europe by the 17th century taking over from the Middle East as the powerhouse of mathematical ideas. Great strides had been made in understanding the geometry of objects fixed in time and space. The race was on to discover the mathematics to describe objects in motion. This programme explores the work of Rene Descartes, Pierre Fermat, Isaac Newton, Leonard Euler and Carl Friedrich Gauss. Du Sautoy proceeds to describes René Descartes realisation that it was possible to describe curved lines as equations and thus link algebra and geometry. He talks with Henk J. M. Bos about Descartes. He shows how one of Pierre de Fermat’s theorems is now the basis for the codes that protect credit card transactions on the internet. He describes Isaac Newton’s development of math and physics crucial to understanding the behaviour of moving objects in engineering. He covers the Leibniz and Newton calculus controversy and the Bernoulli family. He further covers Leonhard Euler, the father of topology, and Gauss' invention of a new way of handling equations, modular arithmetic. The further contribution of Gauss to our understanding of how prime numbers are distributed is covered thus providing the platform for Bernhard Riemann's theories on prime numbers. In addition Riemann worked on the properties of objects, which he saw as manifolds that could exist in multi-dimensional space.

Washington, D.C. is in many ways a city of extremes. Starland Vocal Band, Marvin Gaye, Duke Ellington, Nils Lofgren, Chuck Brown, Henry Rollins, Fugazi and Trouble Funk all hail from D.C. In the early '70s, the music style go-go originated here, and has remained a local craze ever since. Dave Grohl sits down with Trouble Funk's Big Tony Fisher to talk about go-go, and explores its origins with Chuck Brown, the genre's undisputed godfather.
He also chats with Don Zientara, owner of Inner Ear Studios, which the Virginia-raised Grohl says 'produced the entire soundtrack of my youth,' as well as with members of the harDCore band Bad Brains and Ian MacKaye of Teen Idles, Minor Threat and Fugazi, who all recorded at Inner Ear over the decades. The song 'The Feast and the Famine' is recorded during this episode.

What if we could travel not just through space, but through time itself? If you could travel through time, would you change the past or the future? What if you found it couldn’t be changed? What price does the time traveller -- and the people they are closest to -- pay? This is a journey from H. G. Wells' The Time Machine through ideas like The Grandfather Paradox and The Butterfly Effect to the professional time traveller that is the ever popular Doctor Who. Steven Moffat, David Tennant, Karen Gillan, and Neil Gaiman offer a unique perspective on the Doctor. Edward James Olmos reveals the hidden meaning of the language he created for the vision of the future that is Blade Runner. Bob Gale and Christopher Lloyd take us behind the scenes of Back to the Future, while Ed Solomon describes the joy of solving a time travel conundrum for Bill & Ted’s Excellent Adventure. But what would be the physical and emotional cost to the time traveller? Audrey Niffenegger explains what inspired her novel The Time Traveller’s Wife. And what if someone from the future tried to travel back in time to warn us? Would we believe them? From the apocalyptic tones of 12 Monkeys to the drama of Quantum Leap and the comedy of Groundhog Day, time travel is a subject that has been irresistible to the creators of every type of science fiction.

Dr Nigel Spivey explores how art influences life by tracing the development of the image from cave paintings to our modern obsession with images. Dr. Spivey begins his investigation by travelling to the Cave of Altamira near the town of Santillana del Mar in Cantabria, Spain, where in 1879 a young girls exclamation of 'Papa, look, oxen!' to her father, local amateur archaeologist Marcelino Sanz de Sautuola, is explained to have meant that Maria had just become the first modern human to set eyes on the first gallery of prehistoric paintings ever to be discovered.

Nathan and Angela accelerate their parenting rehearsal with three-year-old, then six-year-old actors portraying their fake son, 'Adam'. Angela refuses to participate in Halloween due to her belief in Satanic conspiracies.
Nathan balances parenting duties with a rehearsal for Patrick, a man who wants to confront his brother over their late grandfather's will, which bans Patrick from inheriting money if he is dating a 'gold digger'. The rehearsal occurs in a replica Raising Cane's restaurant in a warehouse next to the relocated Alligator Lounge. To introduce real emotions to the rehearsal, Nathan stages a scenario to convince Patrick that he could inherit buried gold from the grandfather of Isaac, the actor who plays Patrick's brother. After Patrick has an emotional breakthrough during a rehearsal, he leaves the production and never returns. Nathan narrates that he is envious that self-deception is easy for some people as he ponders his fake family.

From steamy jungles to dry deserts, amphibians have taken their first footsteps onto land using their bizarre life histories to break their ties with the water and invade the earth.
This episode delves into the extraordinary and intimate lives of the soft skinned amphibians. This includes the marsupial frogs, a peculiar species where the father carries his young in pouches and then gives birth. It also features warring giant salamanders over a metre long and show-off newts that offer displays just like underwater birds of paradise.