In the second episode, Andrew Carnegie builds an empire around steel, but finds himself struggling to save face after the ruthless tactics of his business partner, Henry Frick, result in both the Johnstown Flood as well as the bloody 1892 strike at the Homestead Steel Works.

J.P. Morgan proceeds to banish the dark with the direct current electric light of Thomas Edison, but the two soon face serious competition from the alternating current of George Westinghouse and Nikola Tesla. As the 19th century comes to a close, the titans of industry must try to work together to stop a new threat in budding politician William Jennings Bryan, who threatens to dissolve monopolies in America.

Rockefeller, Carnegie and Morgan team up to help elect William McKinley to the U.S. presidency by paying for his 1896 campaign, to avoid a possible attack on monopolies. However, fate intervenes when McKinley is suddenly assassinated, and vice president Theodore Roosevelt assumes the presidency and promptly begins dissolving monopolies and trusts in America. Meanwhile, Morgan buys out Carnegie Steel to make Carnegie the richest man in the world, and Henry Ford designs an affordable automobile with his Model T and starts his own business, Ford Motor Company, which sets a new business model for companies to follow.

In the second episode, the directors learn their vision for the films is not always permissible by the U.S. government. Wyler is shocked by the racism he encounters against African American soldiers and refused to make a film recruiting black soldiers. Meanwhile, the films' racist depiction of the Japanese versus human depiction of the Germans causes worry for the War Department, which at that time planned to redistribute the Japanese-American population from internment camps into towns across the United States.

The years 1825-1918 were bloody and traumatic, a period when four tsars tried - and failed - to deal with the growing pressure for constitutional reform and revolution. In 1861, millions of enslaved serfs were freed by the Tsar-Liberator, Alexander II. But Alexander paid the ultimate penalty for opening the Pandora's box of reform when he was later blown up by terrorists on the streets of St Petersburg. Elsewhere, there was repression, denial, war and - in the case of the last tsar, Nicholas II - a fatalistic belief in the power of God, with Nicholas's faith in the notorious holy man Rasputin being a major part in his undoing. Lucy Worsley also details the chilling murder of Nicholas and his family in 1918, and asks whether all of this horror have been avoided.

Dr Hannah Fry travels down the fastest zip wire in the world to learn more about Newton's ideas on gravity. His discoveries revealed the movement of the planets was regular and predictable. James Clerk Maxwell unified the ideas of electricity and magnetism, and explained what light was. As if that wasn't enough, he also predicted the existence of radio waves. His tools of the trade were nothing more than pure mathematics. All strong evidence for maths being discovered.
But in the 19th century, maths is turned on its head when new types of geometry are invented. No longer is the kind of geometry we learned in school the final say on the subject. If maths is more like a game, albeit a complicated one, where we can change the rules, surely this points to maths being something we invent - a product of the human mind. To try and answer this question, Hannah travels to Halle in Germany on the trail of perhaps one of the greatest mathematicians of the 20th century, Georg Cantor. He showed that infinity, far from being infinitely big, actually comes in different sizes, some bigger than others. This increasingly weird world is feeling more and more like something we've invented. But if that's the case, why is maths so uncannily good at predicting the world around us? Invented or discovered, this question just got a lot harder to answer.