In the third episode we will see Europe by the 17th century taking over from the Middle East as the powerhouse of mathematical ideas. Great strides had been made in understanding the geometry of objects fixed in time and space. The race was on to discover the mathematics to describe objects in motion. This programme explores the work of Rene Descartes, Pierre Fermat, Isaac Newton, Leonard Euler and Carl Friedrich Gauss. Du Sautoy proceeds to describes René Descartes realisation that it was possible to describe curved lines as equations and thus link algebra and geometry. He talks with Henk J. M. Bos about Descartes. He shows how one of Pierre de Fermat’s theorems is now the basis for the codes that protect credit card transactions on the internet. He describes Isaac Newton’s development of math and physics crucial to understanding the behaviour of moving objects in engineering. He covers the Leibniz and Newton calculus controversy and the Bernoulli family. He further covers Leonhard Euler, the father of topology, and Gauss' invention of a new way of handling equations, modular arithmetic. The further contribution of Gauss to our understanding of how prime numbers are distributed is covered thus providing the platform for Bernhard Riemann's theories on prime numbers. In addition Riemann worked on the properties of objects, which he saw as manifolds that could exist in multi-dimensional space.

Last year, just before Thanksgiving, I approached my dad, Leonard Nimoy, about the possibility of working together on a film about Mr. Spock. I had skimmed through some of the books on the making of Star Trek and felt there was so much more to explore about the creation and development of Mr. Spock. And the timing seemed right, as the 50th anniversary of Star Trek the original series was not that far away. Dad agreed that now was the right time, and that he was 100% committed to collaborating with me on this project. He also reminded me that we were (then) just days away from the 50th anniversary of the start of production on 'The Cage,' the original pilot for Star Trek in which dad first appeared as Mr. Spock.

The photographer of the second episode of the series is Richard I'Anson, who documents a fire rite, attempts to photograph the elusive Himalayan snow leopard and captures the colorful Festival of Holi.

Lucy Worsley continues her journey through Russia in the footsteps of the Romanovs, the most powerful royal dynasty in modern European history. In this episode she examines the extraordinary reign of Catherine the Great, and the traumatic conflict with napoleonic France that provides the setting for the novel War and Peace. At the magnificent palace of Peterhof near St Petersburg, Lucy charts the meteoric rise of Catherine the Great, who seized the Russian throne from her husband Peter III in 1762 and became the most powerful woman in the world. Catherine was a woman of huge passions - for art, for her adopted country (she was German by birth) and for her many lovers.
Catherine expanded her empire through military victories overseas, while at home she encouraged education and introduced smallpox inoculation to Russia. But Catherine struggled to introduce deeper reforms, and the institution of serfdom remained largely unchanged. Lucy explains how this injustice fuelled a violent rebellion. Nevertheless, Catherine left Russia more powerful on the world stage than ever. But all she had achieved looked set to be undone when Napoleon invaded Russia in 1812. Lucy relives the pivotal battle of Borodino, when the Russian army finally confronted the French forces; the traumatic destruction of Moscow; and, under Catherine's grandson Alexander, the eventual victory over the French that provided the Romanov dynasty with its most glorious hour.

In Egypt, Caesar rebukes the advisers of the boy king, Ptolemy XIII, for their presumption in eliminating Pompey and demands the man who killed him. Caesar decides to intervene in the dispute between Ptolemy and his sister-wife, Cleopatra, to ensure both Rome's grain supply and his own access to Egypt's treasure.
Antony, in an unusual show of prudence, advises against this with only half a legion in Alexandria and Cato and Scipio still at large in Africa. In Rome, Brutus gets a chilly reception from Servilia when he returns home from Greece.

Even though his wife and children are avenged by the Erastes killing, Lucius Vorenus keeps mourning for over a month till Pullo gets Marc Antony who scolds him for Caesar's death and the continuing bloody Aventine gang riots that have resulted in the gangs wanting to fill the void left by Erastes sudden demise.
Octavian is loosing patience with Mark Antony for payment of Caesar's inheritance. Meanwhile, Queen Cleopatra of Egypt arrives in Rome to pay her respects to Caesar and she also negotiates with Antony's military protection for her Pharaonic throne.