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.

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.

Fish dominate the planet's waters through their astonishing variety of shape and behaviour. The beautiful weedy sea dragon looks like a creature from a fairytale, and the male protects their eggs by carrying them on his tail for months. The sarcastic fringehead, meanwhile, appears to turn its head inside out when it fights. Slow-motion cameras show the flying fish gliding through the air like a flock of birds and capture the world's fastest swimmer, the sailfish, plucking sardines from a shoal at 70 mph. And the tiny Hawaiian goby undertakes one of nature's most daunting journeys, climbing a massive waterfall to find safe pools for breeding.

Birds owe their global success to feathers - something no other animal has. They allow birds to do extraordinary things. For the first time, a slow-motion camera captures the unique flight of the marvellous spatuletail hummingbird as he flashes long, iridescent tail feathers in the gloomy undergrowth. Aerial photography takes us into the sky with an Ethiopian lammergeier dropping bones to smash them into edible-sized bits. Thousands of pink flamingoes promenade in one of nature's greatest spectacles. The sage grouse rubs his feathers against his chest in a comic display to make popping noises that attract females. The Vogelkop bowerbird makes up for his dull colour by building an intricate structure and decorating it with colourful beetles and snails.

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 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.