When ancient Greece fell into decline, mathematical progress stagnated as Europe entered the Dark Ages, but in the East mathematics reached new heights. In the second episode, Du Sautoy explores how maths helped build imperial China and discovers how the symbol for the number zero was invented in India. He also looks at the Middle Eastern invention of algebra and how mathematicians such as Fibonacci spread Eastern knowledge to the West.

The defeated Cato and Scipio fall back on the African city of Utica after the Battle of Thapsus where they decide to end it all. Caesar, after two years of fighting in Greece and Egypt, returns to Rome and receives a hero's welcome.
Meanwhile, Servilia's cold rage against the Julii clan makes Brutus's submission to Caesar even more painful. Octavian returns home from military school and Caesar, impressed with his nephew's incisive political acumen, appoints him a pontiff despite his youth.