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.

Technology is evolving from an external tool we wield when needed to an always-there presence that is with us, on us, even inside of us. As we become more and more wired, are we becoming digital devices ourselves? In this episode meet a Swedish mom who implanted an RFID chip as a lifestyle choice; a filmmaker who lost his eye in a gun accident and replaced it with a camera; and the so-called "world most connected man," who uses between 300-700 tracking and life logging systems to monitor every aspect of his life.

The Internet promises us escape from reality. We can go places we never thought possible and express ourselves as never before. But as we sit in our homes surrounded by screens, are we free... and safe? In this episode meet a woman pulled into an online cult from the safety of her bedroom; a former pilot who suffers from Electromagnetic Hypersensitivity and can only find relief in the absence of electricity and wifi; plus, a quadriplegic who uses cutting-edge adaptive robotics and virtual reality to transcend his body's limitations.

The Internet enables us to connect with people, images and information in ways that were unimaginable 30 years ago. But with every click we are re-wiring the physical structure of our brains. Are we evolving or actively de-evolving down a dopamine-laced click-hole? In this episode meet a 17-year-old boy struggling with an addiction to online pornography; autistic technologists in Silicon Valley who are turning their genetic variation to an advantage; plus, Nootropics, a class of cognition-enhancing supplements that claims to rewire the brain.

The human eye is a remarkable piece of precision engineering, but it is also extremely limited. Beyond the narrow range of light that makes up the familiar colours of the rainbow is a vast spectrum of light, entirely unseen. Richard Hammond does just that, using ground-breaking new imaging technologies to take the viewer on a breath-taking journey of discovery beyond the visible spectrum, seeing the world, quite literally, in a whole new light. From death-defying aerial repairmen in the United States using ultraviolet cameras to seek out an invisible force that lurks unseen on power lines, to German scientists unlocking the secrets of animal locomotion with the world's most powerful moving x-ray camera, to infrared cameras that can finally reveal the secrets within a humble beehive, he shows how new technologies are letting us see our world anew.

Inspired by the Southern Sky as he travels Australia, Brian reveals our very latest understanding about how the Universe began & how it will end.