Dr George McGavin and Dr Zoe Laughlin set up base camp at one of the UK's biggest sewage works to investigate the revolutionary science finding vital renewable resources and undiscovered life in human waste.
Teaming up with world-class scientists, they search for biological entities in sewage with potentially lifesaving medical properties, find out how pee can generate electricity, how gas from poo can fuel a car and how nutrients in waste can help solve the soil crisis. They follow each stage of the sewage treatment process, revealing what the stuff we flush can tell us about how we live today, and the mind boggling biotechnology being harnessed to clean it, making the wastewater safe enough to return to the environment.

It's a timeless classic of children's literature and the third most-quoted book in English after the Bible and Shakespeare. But what lies behind the extraordinary appeal of Alice's Adventures in Wonderland to generations of adults and children alike? To mark the 150th anniversary of its publication, this documentary explores the life and imagination of the man who wrote it, the Reverend Charles Dodgson, better known as Lewis Carroll." Broadcaster and journalist Martha Kearney delves into the biographies of both Carroll himself and of the young girl, Alice Liddell, who inspired his most famous creation. Kearney's lifelong passion for Carroll's work began as a young girl, when she starred as Carroll's heroine Alice in her local village play. She discusses the book with a range of experts, biographers and distinguished cultural figures - from the actor Richard E Grant to children's author Philip Pullman - and explores with them the mystery of how a retiring, buttoned-up and meticulous mathematics don, who spent almost his entire life within the cloistered confines of Christ Church Oxford, was able to capture the world of childhood in such a captivating way

Silk is the invertebrates' great invention, used in a range of ways from from the protective stalks of lacewing eggs to the amazing hanging threads of New Zealand's 'glow worms'. Spiders, though, have taken silk-spinning to extremes. The common wolf spider has no web, but the female is a gentle parent, encasing her eggs in silk and carrying the precious bundle wherever she goes. The bolas spider uses a ball of sticky silk soaked in a copy of moth pheromone to lure its prey. Millions of communal spiders live and feed together in a vast, towering web - an arachnophobe's nightmare.

The Southern Ocean, which circles the globe without being blocked by land, is home to the Antarctic Circumpolar Current (ACC), the longest of the world's ocean currents. Also known as the "channel", it connects the Indian, Atlantic and Pacific Ocean basins and exerts a powerful influence over the Earth's climate. The ACC carries 150 times more water around Antarctica than the flow of all the world's rivers combined.

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.

In the fourth episode, Professor Marcus du Sautoy concludes his investigation into the history of mathematics with a look at some of the great unsolved problems that confronted mathematicians in the 20th century. After exploring Georg Cantor's work on infinity and Henri Poincare's work on chaos theory, he sees how mathematics was itself thrown into chaos by the discoveries of Kurt Godel and Paul Cohen, before completing his journey by considering some unsolved problems of maths today, including the Riemann Hypothesis.