The turmoil of 1968 helps Nixon win the presidency. Troop strength in Vietnam peaks and the draft accelerates. Karl Marlantes endures bitter jungle fighting on Hill 484, and draftee Arthur Wiknik gets a grim introduction to combat on 'Hamburger Hill'. But shortly after winning both hills, US troops abandon them.

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.

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.

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.

This award-winning series, Private Life of a Masterpiece, reveals the full and fascinating stories behind famous works of art, not just how they came to be created, but also how they influenced others and came to have a life of their own in the modern world. The works of art featured here are both instantly familiar and profoundly mysterious. Revolutionary in their conception, and iconic years after their execution, they each have their own compelling stories. For behind the beautiful canvases and sculptures are tales of political revolution, wartime escapes, massive ego clashes, social scandal, financial wrangling and shocking violence. In this fascinating series key works of art are investigated and the intricate details of their lives revealed - the history, contemporary reactions, and legacies of each are illustrated.
A Sunday Afternoon on the Island of La Grande Jatte is a popular masterpiece and yet an enduring enigma. It seems to show a quiet scene in a Paris park but there are hints at the demi-monde, if you know where to look. The most remarkable aspect of this vast canvas however remains Seurat's technique his revolutionary pointillism.

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.