In the third programme of the series, Aleks gives the lowdown on how, for better and for worse, commerce has colonized the web - and reveals how web users are paying for what appear to be 'free' sites and services in hidden ways. Joined by some of the most influential business leaders of today's web, including Eric Schmidt (CEO of Google), Chad Hurley (CEO of YouTube), Bill Gates, Martha Lane Fox and Reed Hastings (CEO of Netflix), Aleks traces how business, with varying degrees of success, has attempted to make money on the web. She tells the inside story of the gold rush years of the dotcom bubble and reveals how retailers such as Amazon learned the lessons. She also charts how, out of the ashes, Google forged the business model that has come to dominate today's web, offering a plethora of highly attractive, overtly free web services, including search, maps and video, that are in fact funded through a sophisticated and highly lucrative advertising system which trades on what we users look for. Aleks explores how web advertising is evolving further to become more targeted and relevant to individual consumers. Recommendation engines, pioneered by retailers such as Amazon, are also breaking down the barriers between commerce and consumer by marketing future purchases to us based on our previous choices. On the surface, the web appears to have brought about a revolution in convenience. But, as companies start to build up databases on our online habits and preferences, Aleks questions what this may mean for our notions of privacy and personal space in the 21st century

Austrian director Michael Glawogger travels to five countries to focus on some of the worst jobs imaginable: Ukrainian miners crawl into tiny cracks in old coal pits to scratch out a few bags of winter fuel; Indonesian workers trudge long distances carrying baskets with hundreds of pounds of sulfur chunks extracted from a steaming mountain; Pakistanis risk explosions and burial under tons of scrap iron as they dismantle huge carrier ships. The visuals are everything here. Despite the hardships depicted, many sequences have a dreamlike beauty. In addition, the director has a bone-dry sense of irony; during the Ukraine scenes, he frequently cuts away to a statue of Stakhanov, the "hero" lauded by the Soviets for his superhuman work habits. He also shows us an old German smelting works that's been converted into a theme park.

A feature length documentary about humanity's absolute dependence on animals (for pets, food, clothing, entertainment, and scientific research) but also illustrates our complete disrespect for these so-called 'non-human providers'. With an in-depth study into pet stores, puppy mills and animals shelters, as well as factory farms, the leather and fur trades, sports and entertainment industries, and finally the medical and scientific profession, the film uses hidden cameras and never before seen footage to chronicle the day-to-day practices of some of the largest industries in the world, all of which rely entirely on animals for profit. Powerful, informative and thought-provoking, EARTHLINGS is by far the most comprehensive documentary ever produced on the correlation between nature, animals, and human economic interests. There are many worthy animal rights films available, but this one transcends the setting.

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.

Our lifespan is increasing by 2.5 years every decade - and a third of all babies born today can expect to live to 100. But living longer can come at a cost. Old age itself brings with it a range of debilitating illnesses, many of which are the result of accumulating damage during our lifetime. Three diseases in particular have become the main killers in the developed world - cancer, heart disease and dementia. But a revolution in bio-medicine is now offering new hope for the treatment of these ailments, and the potential to extend our lives still further. Methods such as gene editing and stem cell therapies are transforming the way medicine can conquer disease today. "How to Live Longer" counts with the guide of the Nobel laureate Sir Paul Nurse, for whom the big question isn't just what science can do to fix our bodies and extend our lives, but whether it's right to use all the tools and techniques available.

Travelling forward in time to 30,000 years ago, it's the middle of an ice age. The landscape is dominated by mighty mammoths, living side-by-side with woolly rhinos, giant deer and two separate species of human. The programme follows the fate of a herd of mammoths in their annual struggle against the harsh ice-age conditions. Every summer they spend on the grassy plains of what will one day become the bottom of the North Sea, but every winter they are forced to head for the less exposed valleys further south. It is a journey fraught with danger: mammoths can get trapped in frozen bogs, and the herd must run the gauntlet of hunters like cave lions and the deadly Neanderthals.