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' 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.

The tropical Indian Ocean is home to the Spice Islands. Characterised by beautiful sandy beaches, fringing coral reefs and coastal mangrove forests, this is a vibrant nursery area for marine life, such as whale sharks, crabs, seahorses and a great variety of fish. The coastal areas are where humans have the most direct impact on the ocean's resources.

Welcome to an extreme landscape of rock, ice and snow. We tour the mightiest mountain ranges, starting with the birth of a mountain at one of the lowest places on Earth and ending at the summit of Everest. Find out how some of the most secretive animals rise to the challenge of mountain life. Share one of Earth's rarest phenomena, a lava lake that has been erupting for over 100 years. The same forces built the Simian Mountains where we find troops of gelada baboons nearly a thousand strong. In the Rockies, grizzlies build winter dens inside avalanche-prone slopes and climb the peaks to devour abundant summer moths. In another world first, the programme brings us astounding images of a snow leopard hunting on the Pakistan peaks.

A humpback whale mother and calf embark on an epic journey from tropical coral paradises to storm ravaged polar seas. Newly discovered coral reefs in Indonesia reveal head-butting pygmy seahorses, flashing 'electric' clams and bands of sea kraits, 30-strong, which hunt in packs. Elsewhere plagues of sea urchins fell forests of giant kelp. Huge bull fur seals attack king penguins, who despite their weight disadvantage, put up a spirited defence.