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.

They are the most powerful objects in the universe. Nothing, not even light, can escape the gravitational pull of a black hole. Astronomers now think there are billions of them out in the cosmos, swallowing up planets, even entire stars in violent feeding frenzies. New theoretical research into the twisted reality of black holes suggests that three-dimensional space could be an illusion. That reality actually takes place on a two-dimensional hologram at the edge of the universe.

Beginning with the origins of the universe in the Big Bang, Sagan describes the formation of different types of galaxies and anomalies such as galactic collisions and quasars. The episodes moves further into ideas about the structure of the Universe, such as different dimensions (in the imaginary Flatland and four-dimensional hypercubes), an infinite vs. a finite universe, and the idea of an oscillating Universe (similar to that in Hindu cosmology). The search into other ideas such as dark matter and the multiverse is shown, using tools such as the Very Large Array in New Mexico. Cosmos Update shows new information about the odd, irregular surfaces of galaxies and the Milky Way perhaps being a barred spiral galaxy

Time is woven into the fabric of the universe as one of the dimensions in which we live our daily lives. But maybe it is only a brain state that we use to piece together events. Could it exist only in our minds? Your sense of time can be totally different than the person next to you. This and other theories illustrate that time is an illusion and does not really exist. The world's top physicists tackle this fundamental question, does time exist, and offer new ways to perceive the physical world.

The biggest rabbit-hole in history: the search of the smallest thing in the Universe. It is a journey where things don't just become smaller but also a whole lot weirder. Scientists hope to catch a glimpse of miniature black holes, multiple dimensions and even parallel Universes. As they start to explore this wonderland, where nothing is quite what it seems, they may have to rewrite the fundamental laws of time and space.

Zachary Quinto charts a journey to determine whether time travel is possible. He meets a man who claims to have traveled back in time due to a secret government program and a group of people living in Liverpool known as 'time slippers'.
Zachary makes a visit to the CERN headquarters in Geneva, where he attempts to understand the origins of the universe and the dimension of time. Equipped with this new knowledge, Zachary tests his own perception of time with an elaborate skydiving experiment to see if he can slow down time itself.