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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.

Just under 200 years ago scientists discovered something profound, that electricity is connected to another of nature's most fundamental forces - magnetism. In the second episode, Jim discovers how harnessing the link between magnetism and electricity would completely transform the world, allowing us to generate a seemingly limitless amount of electric power which we could utilise to drive machines, communicate across continents and light our homes. This is the story of how scientists and engineers unlocked the nature of electricity in an extraordinary century of innovation and invention.

In astronomy, we've been looking at different kinds of light and opening up the universe a little bit more of the time. But then in 2015, the roof came off. Something happened that changed everything, the ability to see waves in space and time itself. Gravitational waves help us roll back the clock to the dawn of time, discover epic cosmic collisions, on make Earth-shaking discoveries. Gravitational waves are the biggest game changer since the invention of the telescope. We have a completely new universe to view now. A new exploration of space is just beginning.

In changing seas and oceans, cephalopods like the cuttlefish and the giant Pacific octopus must rely on their remarkable intelligence to survive. Their alien appearance comes with astonishing resources, independence, and invention. And there's still so much to learn about these rarely seen legends of the deep.