Marcus du Sautoy uncovers the patterns that explain the shape of the world around us. Starting at the hexagonal columns of Northern Ireland's Giant's Causeway, he discovers the code underpinning the extraordinary order found in nature - from rock formations to honeycomb and from salt crystals to soap bubbles. Marcus also reveals the mysterious code that governs the apparent randomness of mountains, clouds and trees and explores how this not only could be the key to Jackson Pollock's success, but has also helped breathe life into hugely successful movie animations.

Professor Brian Cox takes on the story of the force that sculpts the entire universe - gravity. Gravity seems so familiar, and yet it is one of the strangest and most surprising forces in the universe. Starting with a zero gravity flight, Brian experiences the feeling of total weightlessness, and considers how much of an effect gravity has had on the world around us. But gravity also acts over much greater distances. It is the great orchestrator of the cosmos. It dictates our orbit around the sun, our relationship with the other planets in our solar system, and even the way in which our solar system orbits our galaxy. Yet the paradox of gravity is that it is actually a relatively weak force. Brian takes a face distorting trip in a centrifuge to explain how it is that gravity achieves its great power, before looking at the role it plays in one of the most extraordinary phenomena in the universe - a neutron star. Although it is just a few kilometres across, it is so dense that its gravity is 100, 000 million times as strong as on Earth. Over the centuries our quest to understand gravity has allowed us to understand some of the true wonders of the universe, and Brian reveals that it is scientists' continuing search for answers that inspires his own sense of wonder.

Our journey begins with David Attenborough at the North Pole, as the sun returns after six months of darkness. We follow a pair of courting polar bears, which reveal a surprisingly tender side. Next stop is the giant Greenland ice cap, where waterfalls plunge into the heart of the ice and a colossal iceberg carves into the sea. Humpback whales join the largest gathering of seabirds on earth to feast in rich Alaskan waters. Further south, the tree line marks the start of the Taiga forest, containing one third of all trees on earth. Here, 25 of the world's largest wolves take on formidable bison prey. At the other end of our planet, the Antarctic begins in the Southern Ocean where surfing penguins struggle to escape a hungry sea-lion and teams of orcas create giant waves to wash seals from ice floes -a filming first. Diving below the ice, we discover prehistoric giants, including terrifying sea spiders and woodlice the size of dinner plates. Above ground, crystal caverns ring the summit of Erebus, the most southerly volcano on earth. From here we retrace the routes of early explorers across the formidable Antarctic ice-cap - the largest expanse of ice on our planet. Finally, we rejoin David at the South Pole, exactly one hundred years after Amundsen then Scott were the first humans to stand there

Spring arrives in the polar regions, and the sun appears after an absence of five months; warmth and life return to these magical ice worlds - the greatest seasonal transformation on our planet is underway. Male Adelie penguins arrive in Antarctica to build their nests - it takes a good property to attract the best mates and the males will stop at nothing to better their rivals! But these early birds face the fiercest storms on the planet. In the Arctic, a polar bear mother is hunting with her cubs. Inland, the frozen rivers start to break up and billions of tons of ice are swept downstream in the greatest of polar spectacles. This melt-water fertilizes the Arctic Ocean, feeding vast shoals of Arctic cod and narwhal. The influx of freshwater accelerates the breakup of the sea-ice - an area of ice the size of Australia will soon vanish from the Arctic. On land, a woolly bear caterpillar emerges from the snow having spent the winter frozen solid. Caterpillars normally become moths within months of hatching, but life is so harsh here that the woolly bear takes 14 years to reach adulthood. Once mature it has only days to find a mate before it dies! Alongside the caterpillars white Arctic wolves race to raise their adorable cubs before the cold returns.

There is no greater test for life than winter, as temperatures plummet to 70 below and winds reach 200kph. Darkness and ice extend across the polar regions and only a few remarkable survivors gamble on remaining. We join a female polar bear trekking into the Arctic mountains to give birth as the first blizzards arrive. Out on the frozen ocean, the entire world's population of spectacled eider ducks brave the winter in a giant ice hole kept open by ferocious currents. Arctic forests transform into a wonderland of frost and snow - the scene of a desperate and bloody battle between wolf and bison, but also where a remarkable alliance between raven and wolverine is made. Beneath the snow lies a magical world of winter survivors. Here tiny voles dodge the clutches of the great grey owl, but cannot escape the ultimate under-show predator - the least weasel. Midwinter and a male polar bear wanders alone across the dark, empty icescape. Below the snow, polar bear cubs begin life in an icy den while fantastical auroras light the night skies above. In Antarctica, we join male emperor penguins in their darkest hour, battling to protect precious eggs from fierce polar storms. Weddell seals escape to a hidden world of jewel-coloured corals and alien-looking creatures but frozen devastation follows as sinister ice stalactites reach down with deadly effect.

The documentary series reveals the extraordinary riches and wonders of the Polar Regions that have kept people visiting them for thousands of years. Today, their survival relies on a combination of ancient wisdom and cutting-edge science. Most Arctic people live in Siberia, either in cities like Norilsk - the coldest city on earth - or out on the tundra, where tribes like the Dogan survive by herding reindeer, using them to drag their homes behind them. On the coast, traditional people still hunt walrus from open boats - it is dangerous work, but one big walrus will feed a family for weeks. Settlers are drawn to the Arctic by its abundant minerals; the Danish Armed Forces maintain their claim to Greenland's mineral wealth with an epic dog sled patrol, covering 2,000 miles through the winter. Above, the spectacular northern lights can disrupt power supplies so scientists monitor it constantly, firing rockets into it to release a cloud of glowing smoke 100 kilometres high. In contrast, Antarctica is so remote and cold that it was only a century ago that the first people explored the continent. Captain Scott's hut still stands as a memorial to these men. Science is now the only significant human activity allowed; robot submarines are sent deep beneath the ice in search of new life-forms, which may also be found in a labyrinth of ice caves high up on an active volcano. Above, colossal balloons are launched into the purest air on earth to detect cosmic rays. At the South Pole there is a research base designed to withstand the world's most extreme winters. Cut off from the outside world for six months, the base is totally self-sufficient, even boasting a greenhouse.