brilliant mathematicians whose genius has profoundly affected us, but which tragically drove them insane and eventually led to them all committing suicide. Kurt Gödel, the introverted confidant of Einstein, proved that there would always be problems which were outside human logic. His life ended in a sanatorium where he starved himself to death. Finally, Alan Turing, the great Bletchley Park code breaker, father of computer science and homosexual, died trying to prove that some things are fundamentally unprovable.

The fantastical tale of King Arthur, the hero warrior, is one of the great themes of British literature. But was it just invented to restore British pride after the Norman invasion? Michael Wood puts the king in the spotlight.

Mammals dominate the planet. They do it through having warm blood and by the care they lavish on their young. Weeks of filming in the bitter Antarctic winter reveal how a mother Weddell seal wears her teeth down keeping open a hole in the ice so she can catch fish for her pup. A powered hot air balloon produces stunning images of millions of migrating bats as they converge on fruiting trees in Zambia, and slow-motion cameras reveal how a mother rufous sengi exhausts a chasing lizard. A gyroscopically stabilised camera moves alongside migrating caribou, and a diving team swim among the planet's biggest fight as male humpback whales battle for a female.

Mammals' ability to learn new tricks is the key to survival in the knife-edge world of hunters and hunted. In a TV first, a killer whale off the Falklands does something unique: it sneaks into a pool where elephant seal pups learn to swim and snatches them, saving itself the trouble of hunting in the open sea. Slow-motion cameras reveal the star-nosed mole's newly-discovered technique for smelling prey underwater: it exhales then inhales a bubble of air ten times per second. Young ibex soon learn the only way to escape a fox - run up an almost vertical cliff face - and young stoats fight mock battles, learning the skills that make them one of the world's most efficient predators.

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.

The Red Sea is one of the youngest oceans in the world and one of the warmest. The northern region, with its diverse array of marine life, is one of the most visited dive locations on earth while the southern end remains virtually unexplored. It's a global hotspot for marine biology and an important trade route throughout human history, linking the trade goods of India and the Far East with the markets of Egypt and Europe.