Having explained the science behind global warming, and addressed the arguments of the climate change sceptics earlier in the series, Dr Iain Stewart concludes the series by looking at the biggest challenge now facing climate scientists - Just how can they predict exactly what changes global warming will bring?
It's a journey that takes him from early attempts to model the climate system with dishpans, to supercomputers, and to the frontline of climate research today: Greenland. Most worryingly he discovers that scientists are becoming increasingly concerned that their models are actually underestimating the speed of changes already underway.

The story of the British Library's Royal Manuscripts collection reaches its end with the last great flowering of illumination, in the magnificent courts of the Tudors. Dr Janina Ramirez investigates astrological texts created for Henry VII, and unwraps his will - still in its original, extravagantly-decorated velvet and gold cover. She hears music written for Henry VIII, which went unperformed for centuries; and reads love notes between the king and Anne Boleyn, written in the margins of a prayer book. Nina also visits Bruges, the source of many of the greatest manuscripts, where this medieval art form collided with the artistic innovations of the Renaissance.

Every year grizzly bear families in North America depend for their survival on a spectacular natural event: the return of hundreds of millions of salmon from the Pacific Ocean to the mountain streams where they were born. The salmon travel thousands of miles to spawn and then die. The great run not only provides food for bears, but for killer whales, wolves, bald eagles, and even the forest itself. The question is: will the salmon return in time to keep hungry bears alive?
A mother grizzly and her cubs emerge from their den high in snowy Alaskan mountains. Filming from the air the team capture a TV first, following the bears as they negotiate a near vertical slope on their journey to the coast where they await the return of the salmon. Meanwhile, the salmon are making their way to the to river mouths where they must swim upstream and against the current. The programme reveals how they tackle the torrents and leap over waterfalls, a feat equivalent to a human jumping over a house. Dozens of hungry bears eagerly await the salmon that make it up river. In another TV first, underwater cameras record the ingenuity and fancy footwork they use to collect dead salmon from the bottom of deep pools.

Each year more than one million wildebeest and zebra invade the Serengeti grasslands, making it a paradise for the predators that live there. But what happens when the herds move off again? We follow the moving story of one lion family's struggle to survive until the return of the great migration. Nature's Great Events tells the story of the epic trek of herds that follow the rains to fresh pastures, and the tale of the predators they leave behind.
The crew captures the desperate plight of a single pride of lions, revealing a different side to the Serengeti. Rather than being a predators' paradise, it is a land in constant change, with wildebeest following the rains and leaving the lions to tough it out. The Ntudu pride has seven cubs, and is already suffering as the wildebeest leave to find fresh pastures. The four pride females struggle to find enough food for their hungry offspring. As weeks turn to months, the pride members become more emaciated and frailer, and the number of cubs dwindles to just two. As the herds begin to return, the plains reveal one final secret. For the first time since 1967 the Serengeti's only active volcano, Ol Doinyo Lengai, begins to billow ash and smoke. Filmed from the air, the team captures the exciting action. Fertilised by the volcanic ash over millions of years, these short grass plains are among the most productive grasslands in the world. After months of hardship, the pride's tragic story, through sickness, drought and fire, is over as the herds return, providing plentiful food.

A mighty army of dolphins, sharks, whales, seals and gannets hunt down the billions of sardines along South Africa's east coast each winter. This is the Sardine Run: an underwater Armageddon, the greatest gathering of predators anywhere on the planet, and the most spectacular event in the world's oceans. From intimate moments of the creatures caught up in the run, to the dramatic finale of this spectacular event, The Great Tide is an action-packed feeding-frenzy, filmed underwater, on the ocean's surface, and in the air.
However, in recent years the sardine run has become less predictable, perhaps due to the warming effects of climate change. If the sardine run does not happen, the lives of the animals caught up in the drama hang in the balance. Pioneering a unique boat stabilised camera mount for surface filming, Nature's Great Events crew capture all the high octane action as the predators compete for sardines, filmed with aerial, underwater and above water cameras. Super slow motion cameras also capture the very moment gannets plunge into the water, hitting it at sixty miles an hour.
A violent winter storm is the trigger for the sardines to begin their desperate dash. They are followed by a super-pod of 5,000 dolphins and further up the coast more predators gather. A shoal of sardines 15 miles long is pushed into the shallows and aerial shots show thousands of sharks gathering to feed on them. The climax to the sardine run is a spectacular feeding frenzy as the dolphins round the sardines up into balls on which all the predators feast. Gannets rain down in their thousands, sharks pile in scattering the fish and a Bryde's whale lunges in taking great mouthfuls of sardines.

Dr Hannah Fry travels down the fastest zip wire in the world to learn more about Newton's ideas on gravity. His discoveries revealed the movement of the planets was regular and predictable. James Clerk Maxwell unified the ideas of electricity and magnetism, and explained what light was. As if that wasn't enough, he also predicted the existence of radio waves. His tools of the trade were nothing more than pure mathematics. All strong evidence for maths being discovered.
But in the 19th century, maths is turned on its head when new types of geometry are invented. No longer is the kind of geometry we learned in school the final say on the subject. If maths is more like a game, albeit a complicated one, where we can change the rules, surely this points to maths being something we invent - a product of the human mind. To try and answer this question, Hannah travels to Halle in Germany on the trail of perhaps one of the greatest mathematicians of the 20th century, Georg Cantor. He showed that infinity, far from being infinitely big, actually comes in different sizes, some bigger than others. This increasingly weird world is feeling more and more like something we've invented. But if that's the case, why is maths so uncannily good at predicting the world around us? Invented or discovered, this question just got a lot harder to answer.