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To our medieval forebears the world could appear mysterious, even enchanted. Sightings of green men, dog heads and alien beings were commonplace. The world itself was a book written by God. But as the Middle Ages grew to a close, it became a place to be mastered, even exploited.

Dr Janina Ramirez shows how medieval manuscripts gave power to the king and united the kingdom in an age of plague, warfare and rebellion, discovers that Edward III used the manuscripts he read as a boy to prepare him for his great victory at the battle of Crecy and reveals how a vigorous new national identity bloomed during the 100 Years War with France. In the British Library's Royal Manuscripts collection Dr Ramirez finds out that magnificent manuscripts like the Bedford Hours, taken as war booty from the French royal family, were adapted for the education of English princes. She also explores how knowledge spread through a new form of book - the encyclopaedia.

The story of the British Library's Royal Manuscripts collection reaches its end with the last great flowering of illumination, in the magnificent courts of the Tudors. Dr Janina Ramirez investigates astrological texts created for Henry VII, and unwraps his will - still in its original, extravagantly-decorated velvet and gold cover. She hears music written for Henry VIII, which went unperformed for centuries; and reads love notes between the king and Anne Boleyn, written in the margins of a prayer book. Nina also visits Bruges, the source of many of the greatest manuscripts, where this medieval art form collided with the artistic innovations of the Renaissance.

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.

American troops launch widespread 'search and destroy' operations; body count, not territory, becomes the measure of success in Vietnam. Charles Brown fights for survival on the bloody slopes of Hill 875 and at home, the American public begins to question U.S. military strategy.

The enemy gains ground when the massive Tet Offensive catches the Americans by surprise. At Khe Sanh and Pleiku, U.S. troops are under siege. Americans mount a counteroffensive but the shock of the assault ignites anti-war fervour at home.