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.

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 Michael Scott examines the vital role played by the Romans in the preservation of Greek drama and in the history of theatre. He explores how the Romans absorbed Greek theatre and adapted it to their own, very Roman, ends and looks at how this famous empire provides one of the crucial connections between our modern drama and the great plays of the ancient Greeks.

Follow a newborn monkey and its mother as they struggle to survive within the competitive social hierarchy of the Temple Troop, a dynamic group of monkeys who live in ancient ruins found deep in the storied jungles of South Asia. The breathtaking footage of primates in the wild will like animal lovers of all ages". Maya is a toque macaque whose world is changed when her son Kip becomes part of her extended family. Maya’s family has its share of diverse personalities and she wishes her son to have the best advantages for advancing within the family's social strata. When their home is overrun by a neighboring tribe of monkeys, the family has to find a new home. Maya uses her inherent smarts to lead the family to new resources, but it develops that the entire group will have to cooperate in order to reclaim their original home, where Maya wishes to advance her son's future within the family.

In ancient Greece the Asclepian healing temples recognized the power of the primordial spiral which is symbolized by the rod of Asclepius. To this day, this symbol of our evolutionary energy remains as the logo of the American Medical Association and other medical organizations worldwide. The snake, the downward direction, is the manifested spiral, the evolutionary energy of the world.

The series concludes by delving into the world of satirical maps. How did maps take on a new form, not as geographical tools, but as devices for humour, satire or storytelling? Graphic Artist Fred Rose perfectly captured the public mood in 1880 with his General Election maps featuring Gladstone and Disraeli, using the maps to comment upon crucial election issues still familiar to us today. Technology was on the satirist's side with the advent of high-speed printing allowing for larger runs at lower cost. In 1877, when Rose produced his 'Serio Comic Map of Europe at War', maps began to take on a new direction and form, reflecting a changing world. Rose's map exploited these possibilities to the full using a combination of creatures and human figures to represent each European nation. The personification of Russia as a grotesque-looking octopus, extending its tentacles around the surrounding nations, perfectly symbolised the threat the country posed to its neighbours.