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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.

Visit the ghostly villages surrounding Chernobyl (abandoned by humans after the 1986 nuclear disaster), travel to remote islands off the coast of Maine to search for abandoned towns that have vanished from view in only a few decades, then head beneath the streets of New York to see how subway tunnels may become watery canals. A visual journey, LIFE AFTER PEOPLE is a thought provoking adventure that combines movie-quality visual effects with insights from experts in the fields of engineering, botany, ecology, biology, geology, climatology, and archaeology to demonstrate how the very landscape of our planet will change in our absence.

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.

Scientists investigate the way the Sun builds its power -- through fusion -- hoping to find a way to use fusion as a less dangerous and less radioactive waste-producing path to energy than fission. But there are some major difficulties along the way. Fusion really is the perfect way to make energy. We have millions of years worth of fuel. It produces no long-lived radioactive waste. If we can solve the engineering challenges, energy will become cheaper, more available for everybody.

Millions of tourists photograph the ancient monuments of Rome every year. But is there more to them than people guess? There's new evidence that these ruins were once machines, designed by Rome's emperors to connect their power with the sun. Did Roman emperors harness the power of the universe to awe and terrify the people of Rome? We uncover the last, great mysteries of the ancient world's greatest empire.

Over the last years, the world has experienced an energy revolution, driven by an urgent need to green the grid and save life on Earth as we know it. 50 years ago, a devastating oil crisis kicked off an energy revolution. The world set course to cut the costly habit of burning fossil fuels. With the urgent new threat of a changing climate, the drive to unleash the power of the sun, earth and wind has accelerated into a race for humanity's survival. Change is taken place but, is it happening fast enough to secure our future? Technologies are right here, right now, and they will enable the transition to 100% renewables, because winning the energy race means a win for the entire world.