In the fourth episode, Professor Marcus du Sautoy concludes his investigation into the history of mathematics with a look at some of the great unsolved problems that confronted mathematicians in the 20th century. After exploring Georg Cantor's work on infinity and Henri Poincare's work on chaos theory, he sees how mathematics was itself thrown into chaos by the discoveries of Kurt Godel and Paul Cohen, before completing his journey by considering some unsolved problems of maths today, including the Riemann Hypothesis.

Professor Simon Schaffer presents the amazing and untold story of automata - extraordinary clockwork machines designed hundreds of years ago to mimic and recreate life. The film brings the past to life in vivid detail as we see how and why these masterpieces were built. Travelling around Europe, Simon uncovers the history of these machines and shows us some of the most spectacular examples, from an entire working automaton city to a small boy who can be programmed to write and even a device that can play chess". All the machines Simon visits show a level of technical sophistication and ambition that still amazes today. As well as the automata, Simon explains in great detail the world in which they were made - the hardship of the workers who built them, their role in global trade and the industrial revolution and the eccentric designers who dreamt them up. Finally, Simon reveals that to us that these long-forgotten marriages of art and engineering are actually the ancestors of many of our most loved modern technologies, from recorded music to the cinema and much of the digital world.

Born in Naples, Bernini was an exceptional talent from an early age and went on to dominate the art world of 17th century Rome. His work epitomised the Baroque style and his sculpture, church interiors and exteriors and town planning could be seen everywhere. Bernini worked under successive Popes; Pope Gregory XV made him a knight and Pope Urban VIII made him as his best friend. He was revered in his time until a jealous rage caused him to have the face of his mistress slashed after discovering her romance with his brother. His reputation fell further after his bell towers for the Cathedral of St Peter's started cracking in 1641. He redeemed himself and kick started his career again with what is arguably his most famous work, The Ecstasy of St Theresa, in 1652.

In the fourth episode of the series, eyewitnesses recall how those in power at Auschwitz lined their pockets with wealth stolen from Jewish inmates while also engaging in illicit affairs.

Enter creator J.R.R. Tolkien's fantastical world of hobbits, orcs and wizards, and uncover the real life influences that shaped his epic fantasy, 'The Lord of the Rings'.

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.