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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.

Bitcoin, the beautiful anonymity of cash, but cash that wasn't printed by governments. Instead, it was made by a bit of code, powered by citizens of the internet, and you could trust it. Today, anyone can buy cryptocurrency. A few signups, type in your credit card number, and trade in your money for digital cash. And with a few more steps, you can use Bitcoin to buy what the majority of Bitcoin is spent on: Illegal services. Virtual currencies can pose challenges for law enforcement, given the appeal they have among those seeking to conceal.
Is digital cash the next revolution? Learn about this anonymous currency and why it's so coveted.

Technology is opening up new possibilities for physical, sexual and romantic relationships with astonishing speed. But is seeking human connection virtually a positive step forward or are we stunting our intimate lives? In the first episode of this series, meet a cyber BDSM couple who use tracking technology to fulfill their master slave relationship; an eligible bachelor in Japan who has fallen in love with a virtual girlfriend; and a revenge porn victim whose life was upended when her private naked photos were published online.

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.

the rise and fall of a tech industry prodigy. Interviews with his friends and loved ones paint a portrait of Swartz as a martyr of freedom of information and hail his fight for the public's right to access tax-funded academic and scientific research, culminating in a personally devastating two-year Federal lawsuit." An avid researcher who had previously accessed otherwise private databases, Swartz, acting "in the grand tradition of civil disobedience to declare... opposition to this private theft of public culture" used MIT computers to access tax-funded research that would otherwise be held privately by for-profit publishers, an incident many viewers may remember from national headlines just a few year ago. Though neither MIT nor the digital repository Swartz accessed pressed charges, a US Attorney stepped in and filed a 13-count felony charge against Swartz, threatening him with over $1 million in fines and up to 35 years of jail time. Despite the defense of his peers, these events launched Swartz into a two-year long downward spiral of withdrawal and depression. Aaron Swartz's untimely death at the age of 26.

In this second episode, a woman recounts her journey to becoming a mouthpiece for white nationalist hate speech, work that culminates in high-profile violence and murder. Samantha confesses how she became a spokesperson on the Internet for the hate speech of one of the many white nationalist groups that swarm the United States. And this fact ended in racist violence and death during an event.
'I had to start to realize what I was supporting. Was I the victim or was I also a villain?' says Samantha, looking into the camera. Hand in hand with xenophobia, digital true crime seems to have no respite, and so it will be shown how those supremacists work with good Wi-Fi.