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We all project images of ourselves online - a curated identity that defines how we want to be perceived. But what temptations exist to embellish and what are the dark implications? In this episode, enter the world of Cyberbanging, where inner city youth are using social media to brag, conspire and incite violence; two African-American women bloggers who have turned the table on the trolls who threaten them; and the creator of Abdullah X, an online character who's trying to keep Muslim kids from falling under the spell of Islamic extremists.

The metaverse is an environment where humans interact socially and economically through a software in cyberspace, which acts as a metaphor for the real world, but without its limitations. The metaverse is generally composed of multiple three-dimensional, shared and persistent virtual spaces linked to a perceived virtual universe. This virtual world is often facilitated by the use of virtual reality (VR) or augmented reality (AR) headsets and avatars. The Metaverse is the successor to the internet. It will change the lives of almost every human on the planet.

Dr Aleks Krotoski concludes her investigation of how the World Wide Web is transforming almost every aspect of our lives. Joined by Facebook founder Mark Zuckerberg, Bill Gates, Al Gore and the neuroscientist Susan Greenfield, Aleks examines the popularity of social networks such as Facebook and asks how they are changing our relationships. And, in a ground-breaking test at University College London, Aleks investigates how the Web may be distracting and overloading our brains.

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.