In the third episode we will see Europe by the 17th century taking over from the Middle East as the powerhouse of mathematical ideas. Great strides had been made in understanding the geometry of objects fixed in time and space. The race was on to discover the mathematics to describe objects in motion. This programme explores the work of Rene Descartes, Pierre Fermat, Isaac Newton, Leonard Euler and Carl Friedrich Gauss. Du Sautoy proceeds to describes René Descartes realisation that it was possible to describe curved lines as equations and thus link algebra and geometry. He talks with Henk J. M. Bos about Descartes. He shows how one of Pierre de Fermat’s theorems is now the basis for the codes that protect credit card transactions on the internet. He describes Isaac Newton’s development of math and physics crucial to understanding the behaviour of moving objects in engineering. He covers the Leibniz and Newton calculus controversy and the Bernoulli family. He further covers Leonhard Euler, the father of topology, and Gauss' invention of a new way of handling equations, modular arithmetic. The further contribution of Gauss to our understanding of how prime numbers are distributed is covered thus providing the platform for Bernhard Riemann's theories on prime numbers. In addition Riemann worked on the properties of objects, which he saw as manifolds that could exist in multi-dimensional space.

In 1985, two adventurous young mountaineers, Joe Simpson and Simon Yates, set off to climb the treacherous west face of the Siula Grande in the Peruvian Andes. They were experienced climbers, and climbed "Alpine-style," climbing the mountain in "one great push," without setting up ropes or base camps ahead of time. After dealing with a snowstorm and some dangerous climbing over powder formations, they reached the summit (about 21,000 feet) on the third day. The climb down proved to be far more difficult. Simpson fell and broke his leg badly. Yates decided to try to lower Simpson down the mountain, one 300-foot section of rope at a time. The climbers had run out of gas to melt snow, so they couldn't risk stopping as night came, and a violent snowstorm began. Their plodding, painful journey hit a snag when Yates inadvertently lowered Simpson over the edge of a cliff. In the storm, the men couldn't hear each other's cries, and, Yates, uncertain as to Simpson's position, and gradually sliding down the slope himself, decided to cut the rope that connected them, sending Simpson plummeting to certain death. Miraculously, Simpson survived the fall, and was faced with the prospect of getting off the mountain alone with no food, no water, and a broken leg. In Touching the Void, filmmaker Kevin Macdonald (One Day in September) tells their story, based on Simpson's book, using contemporary interviews with the two men, and a reenactment of their climb and descent, featuring Brendan Mackey as Simpson and Nicholas Aaron as Yates

Friendship, love, peace and freedom-these ideals drew young hearts from around the globe to Nova's EDM music festival in the South of Israel. But as the sun rose on October 7th, the fantasy shattered. Rockets sliced through the sky, and the dancing stopped. Confusion morphed into fear as gunfire erupted amidst the chaos. Terror breached the border fence and unleashed violence on the unsuspecting people in its rawest form.
The film is a stark portrayal of the experiences of those who survived and those who didn't. The film meticulously reconstructs the events, capturing the raw emotions and heroism that emerged.