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.

Psychopaths have long captured the public imagination. Painted as charismatic, violent predators lacking in all empathy, they provide intrigue and horror in equal measure. But what precisely is a psychopath? What is it that drives them to cause harm, even kill? And can they ever be cured? The film also features a series of candid interviews with prison inmates who not only describe their crimes but why they think they committed them.
'What Makes a Psychopath?' explores not only how each individual's crimes were shaped by their own life experiences, but also gives an insight into how these people think and behave. Working with the world's experts in the field, the film sheds light on the biological, psychological and environmental influences that shape a psychopath. And it looks to the future, with ground-breaking research that suggests a lifetime of incarceration is not the only option to manage violent and dangerous psychopaths.