This documentary looks at the remarkable genius of Orson Welles on his centenary - the enigma of his career as a Hollywood star, a Hollywood director (for some a Hollywood failure), and a crucially important independent filmmaker. Orson Welles's life was magical: a musical prodigy at age 10, a director of Shakespeare at 14, a painter at 16, a star of stage and radio at 20, romances with some of the most beautiful women in the world, including Rita Hayworth. His work was similarly extraordinary, most notably Citizen Kane, (considered by many to be the most important movie ever made), created by Welles when he was only 25. In the years following Citizen Kane, Welles's career continued to change as he made film after film (some never finished, many dismissed) and acted in other projects often to earn money in order to keep making his own films. Magician features scenes from almost every existing Welles film, from Hearts of Age, (which he made in a day when he was only 18 years old) to rarely-seen clips from his final unfinished works like The Other Side of the Dream, The Deep, and Don Quixote, as well as his television and commercial work.

The film chronicles Allen's career - from teen writer to Sid Caesar's TV scribe, from stand-up comedian to award-winning writer-director averaging one film-per-year for more than 40 years. Exploring Allen's writing habits, casting, directing, and relationship with his actors first-hand, new interviews with A-listers, writing partners, family and friends provide insight and backstory to the usually inscrutable filmmaker.

Mathematician Dr Hannah Fry explores the mystery of maths. It underpins so much of our modern world that it's hard to imagine life without its technological advances, but where exactly does maths come from? Is it invented like a language or is it something discovered and part of the fabric of the universe? It's a question that some of the most eminent mathematical minds have been wrestling with. To investigate this question, Hannah goes head first down the fastest zip wire in the world to learn more about Newton's law of gravity, she paraglides to understand where the theory of maths and its practice application collide, and she travels to infinity and beyond to discover that some infinities are bigger than others.
In this episode, Hannah goes back to the time of the ancient Greeks to find out why they were so fascinated by the connection between beautiful music and maths. The patterns our ancestors found in music are all around us, from the way a sunflower stores its seeds to the number of petals in a flower. Even the shapes of some of the smallest structures in nature, such as viruses, seem to follow the rules of maths. All strong evidence for maths being discovered. But there are those who claim maths is all in our heads and something we invented. To find out if this is true, Hannah has her brain scanned. It turns out there is a place in all our brains where we do maths, but that doesn't prove its invented.
Experiments with infants, who have never had a maths lesson in their lives, suggests we all come hardwired to do maths. Far from being a creation of the human mind, this is evidence for maths being something we discover. Then along comes the invention of zero to help make counting more convenient and the creation of imaginary numbers, and the balance is tilted in the direction of maths being something we invented. The question of whether maths is invented or discovered just got a whole lot more difficult to answer

Mind reading might sound like pseudoscientific, but its scientific counterpart, thought identification, is very much a real thing. It's based in neuroimaging and machine learning, and what's really cool is that experiments in mind reading aren't just about spying on what someone is thinking. They're about figuring out what thoughts are even made of.
When you think of something, what does that mental picture actually look like? What resolution is it in? How high fidelity is a memory, and how do they change over time? In this episode, we are going to look at how reading people's minds can help us answer these questions.

Horizon uncovers the secret world of our dreams. In a series of cutting-edge experiments and personal stories, we go in search of the science behind this most enduring mystery and ask: where do dreams come from? Do they have meaning? And ultimately, why do we dream? What the film reveals is that much of what we thought we knew no longer stands true. Dreams are not simply wild imaginings but play a significant part in all our lives as they have an impact on our memories, the ability to learn, and our mental health. Most surprisingly, we find nightmares, too, are beneficial and may even explain the survival of our species.

Stephen Hawking is the most famous scientist on the planet. But behind the public face lies an argument that has been raging for almost 30 years. Has he been wrong for the last 30 years? Hawking shot to fame in the world of physics when he provided a mathematical proof for the Big Bang theory. This theory showed that the entire universe exploded from a singularity, an infinitely small point with infinite density and infinite gravity. Hawking was able to come to his proof using mathematical techniques that had been developed by Roger Penrose. These techniques were however developed to deal not with the beginning of the Universe but with black holes". Science had long predicted that if a sufficiently large star collapsed at the end of its life, all the matter left in the star would be crushed into an infinitely small point with infinite gravity and infinite density – a singularity. Hawking realised that the Universe was, in effect, a black hole in reverse. Instead of matter being crushed into a singularity, the Universe began when a singularity expanded to form everything we see around us today, from stars to planets to people. Hawking realised that to come to a complete understanding of the Universe he would have to unravel the mysteries of the black hole and its paradoxes