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The Pythagorean Theorem is simple: x2 + y2 = z2. In this form, the equation can be solved. But what if the 2 is replaced with any positive integer greater than 2? Would the equation still be solvable? More than 300 years ago, amateur mathematician Pierre de Fermat said no, and claimed he could prove it. Unfortunately, the book margin in which he left this prophecy was too small to contain his thinking. Fermat's Last Theorem has since baffled mathematicians armed with the most advanced calculators and computers. Andrew Wiles methodically worked in near isolation to determine the proof for this seemingly simple equation.

Humans are so clever they’ve built their own habitat, designed to keep wild nature out. Yet as we discover the urban environment is totally dependant on the natural world. Over the three years of filming for Human Planet, the teams have spent time with over seventy different communities in countries across the planet. Despite seeing many different ways of living, there are some aspects of family life that remain the same whether you live in a tree house in West Papua, or a brick house in Bolton. These similarities became very clear when the urban team went to film on a rubbish dump in Kenya. Here on the Kibarani dump on the outskirts of Mombasa, Ali, Ashe and their family live and survive amongst the rubbish, and even here, just like anywhere on the planet, everything stops for a nice cup of tea!

The episode, devoted to the planet Mars, begins with scientific and fictional speculation about the Red Planet during the late nineteenth and early twentieth centuries (H. G. Wells' The War of the Worlds, Edgar Rice Burroughs' science fiction books, and Percival Lowell's false vision of canals on Mars). It then moves to Robert Goddard's early experiments in rocket-building, inspired by reading science fiction, and the work by Mars probes, including the Viking, searching for life on Mars. The episode ends with the possibility of the terraforming and colonization of Mars and a Cosmos Update on the relevance of Mars' environment to Earth's and the possibility of a manned mission to Mars.

Since the dawn of civilization, humans have wondered who or what created the universe. Religion offers a spiritual answer, but do the latest discoveries in physics show evidence of a transcendent intelligence, or simply that the laws of physics by themselves could have led to the universe in which we live? This episode embarks on a mind-bending scientific search for God, asking physicists and theologians if the seemingly miraculous way the universe has been calibrated to support life is evidence of a creator...whether string theory will eventually be able to rule out the existence of God...why Stephen Hawking says the universe could have been created spontaneously...and how an advanced civilization in another universe could have conceivably created our own.

After filming for three years, Planet Earth finally captures the shy Mongolian gazelle. Only a handful of people have witnessed its annual migration. Don't miss the bizarre-looking Tibetan fox, captured on film for the first time. Over six weeks the team follow a pride of 30 lions as they attempt to hunt elephants. Using the latest night vision equipment, the crew film the chaotic battles that ensue at close quarters.

The extraordinary wildlife, culture and history of this immense, fascinating ocean and its myriad islands are revealed in stunning detail. With its coral reefs, turquoise lagoons and dramatic oceanic atolls, the South Pacific is the archetypal paradise. It is still relatively healthy and teeming with fish, but it is a fragile paradise. International fishing fleets are taking a serious toll on the sharks, albatross and tuna, and there are other insidious threats to these bountiful seas. We look at what is being done to preserve the ocean and its wildlife.