With a little imagination, could a few terrorists sabotage a mighty nation? Perhaps even tear down modern civilization? The stability of the US, Europe, China, or any global power depends on high-speed digital communication. Our increasing dependence on digital devices and global interactivity may be placing us in grave danger. Scientists around the world are dealing with new threats such as body hacking, Trojan horse viruses, and brain-damaging Internet addiction. But what if the ultimate threat isn’t an attack on technology, but the technology? Could the final superpower be the disembodied mind of the Internet itself?

Helen Czerski ventures beyond the visible spectrum in the final (and best) episode in this vibrant series, showing how electromagnetic radiation is so much broader than the narrow slice of reality we see with our eyes. Before delving into the details of UV, infrared and x-rays, Dr Czerski explores colour subjectivity by trying on a dress that recently divided the internet — to some it appeared blue and black, to others white and gold. It's a perfect fit. It's also a neat analogy of how people can have opposing views but both swear blind that their perspective is correct. The series ends with some amazing imaging techniques that show our bodies in a whole new light.

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.

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.

Can we find a way to distribute power so that everyone has their say? A U.S. president explains the challenges of making decisions that affect hundreds of millions of lives, and Freeman learns about an African woman who has created a society without men. He explores how the rise of the internet may fundamentally change how democracy works.