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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.

Dr Thomas Dixon delves into the BBC's archive to explore the troubled relationship between religion and science. From the creationists of America to the physicists of the Large Hadron Collider, he traces the expansion of scientific knowledge and asks whether there is still room for God in the modern world. He looks at what happens when new scientific discoveries start to explain events that were once seen as the workings of God, and explains how some of our most famous scientists have seen God in the grandest laws of the universe. Finally, he finds intriguing evidence from brain science which hints that belief in God is here to stay.

Over a person's lifetime they are likely to be prescribed more than 14,000 pills. Antibiotics, cholesterol lowering tablets, anti-depressants, painkillers, even tablets to extend youth and improve performance in bed. These drugs perform minor miracles day after day, but how much is really known about them? Drug discovery often owes as much to serendipity as to science, and that means much is learnt about how medicines work, or even what they do, when they're taken. By investigating some of the most popular pills people pop, Horizon asks, how much can they be trusted to do what they are supposed to?

Horizon explores the strange and wonderful world of illusions – and reveals the tricks they play on our senses and why they fool us. We show how easy it is to trick your sense of taste by changing the colours of food and drink, explain how what you see can change what you hear, and see just how unreliable our sense of colour can be. But all this trickery has a serious purpose. It’s helping scientists to create a new understanding of how our senses work – not as individual senses, but connected together. It holds the intriguing possibility that one sense could be mapped into another.

Born in Groot-Zundert, The Netherlands, Van Gogh spent his early life as an art dealer, teacher and preacher in England, Holland and Belgium. His period as an artist began in 1881 when he chose to study art in Brussels, starting with watercolours and moving quickly on to oils. The French countryside was a major influence on his life and his early work was dominated by sombre, earthy colours depicting peasant workers, the most famous of which is The Potato Eaters, 1885. It was during Van Gogh's studies in Paris (1886-8) that he developed the individual style of brushwork and use of colour that made his name. In 1888 he moved to Arles where the Provençal landscape provided his best-known subject matter. However, it also marked the start of his mental crisis following an argument with his contemporary Paul Gauguin. Van Gogh was committed to a mental asylum in 1889 where he continued to paint, but he committed suicide in 1890.

This documentary details the root causes of the systemic value disorders and detrimental symptoms caused by our current established system. This video presentation advocates a new socio-economic system, which is updated to present-day knowledge, featuring the life-long work of Social Engineer, Futurist, Inventor and Industrial Designer Jacque Fresco, which he calls a Resource-Based Economics.