Set in the inner-city of Memphis, Undefeated chronicles the Manassas Tigers' 2009 football season, on and off-the-field, as they strive to win the first playoff game in the high school's 110-year history. A perennial whipping boy, in recent decades Manassas had gone so far as to sell their home games to the highest bidder, but that all changed in the spring of 2004 when Bill Courtney, a former high school football coach turned lumber salesman, volunteered to lend a hand.

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.

Predictions underlie nearly every aspect of our lives, from sports, politics, and medical decisions to the morning commute. With the explosion of digital technology, the internet, and 'big data,' the science of forecasting is flourishing. But why do some predictions succeed spectacularly while others fail abysmally? And how can we find meaningful patterns amidst chaos and uncertainty? From the glitz of casinos and TV game shows to the life-and-death stakes of storm forecasts and the flaws of opinion polls that can swing an election, 'Prediction by the Numbers' explores stories of statistics in action. Yet advances in machine learning and big data models that increasingly rule our lives are also posing big, disturbing questions. How much should we trust predictions made by algorithms when we don't understand how they arrive at them? And how far ahead can we really forecast?

The power of visual storytelling is not a modern phenomenon, feature films today are using techniques developed way back in the distant past. For thousands of years, artists grappled with ways to bring their stories alive, to engage their audience. This is the story of how our ancient ancestors made the discoveries that have given films such a hold over our imaginations.

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.

In the last episode of the series, lavish imperial games at the Colosseum are highlighted by the emperor's bloody victories, but his paranoid abuses of power lead to a final betrayal.