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.

When ancient Greece fell into decline, mathematical progress stagnated as Europe entered the Dark Ages, but in the East mathematics reached new heights. In the second episode, Du Sautoy explores how maths helped build imperial China and discovers how the symbol for the number zero was invented in India. He also looks at the Middle Eastern invention of algebra and how mathematicians such as Fibonacci spread Eastern knowledge to the West.

This four-part British television series outlines aspects of the history of mathematics. Written and presented by University of Oxford professor Marcus du Sautoy, it is a co-production between the Open University and the BBC. In the first episode, Marcus du Sautoy in Egypt uncovers use of a decimal system based on ten fingers of the hand and discovers that the way we tell the time is based on the Babylonian Base 60 number system. In Greece, he looks at the contributions of some of the giants of mathematics including Plato, Archimedes and Pythagoras, who is credited with beginning the transformation of mathematics from a counting tool into the analytical subject of today. A controversial figure, Pythagoras’ teachings were considered suspect and his followers seen as social outcasts and a little be strange and not in the norm. There is a legend going around that one of his followers, Hippasus, was drowned when he announced his discovery of irrational numbers. As well as his work on the properties of right angled triangles, Pythagoras developed another important theory after observing musical instruments. He discovered that the intervals between harmonious musical notes are always in whole number intervals.

In the fourth episode, Professor Marcus du Sautoy concludes his investigation into the history of mathematics with a look at some of the great unsolved problems that confronted mathematicians in the 20th century. After exploring Georg Cantor's work on infinity and Henri Poincare's work on chaos theory, he sees how mathematics was itself thrown into chaos by the discoveries of Kurt Godel and Paul Cohen, before completing his journey by considering some unsolved problems of maths today, including the Riemann Hypothesis.

Everywhere you go, you generate a cloud of data. You're trailing data, everything that you do is producing data. And then there are computers looking at that data that are learning, and these computers are essentially trying to serve you better. They're trying to personalize things to you. They're trying to adapt the world to you. So on the one hand, this is great, because the world will get adapted to you without you even having to explicitly adapt it. There's also a danger, because the entities in the companies that are in control of those algorithms don't necessarily have the same goals as you, and this is where I think people need to be aware that, what's going on, so they can have more control over it.
We came into this new world thinking that we were users of social media and search engines. It didn't occur to us that social media and search engines were actually using us.

Frequent security expos feature companies like Megvii and its facial- recognition technology. They show off cameras with A.I. that can track cars, and identify individuals by face, or just by the way they walk. In China it's been projected that over 600 million cameras will be deployed by 2020. Here, they may be used to discourage jaywalking, but they also serve to remind people that the state is watching. Matching with the most advanced artificial intelligence algorithm, they can actually use this data, real-time data, to pick up a face or pick up a action.
A.I. is a technology that can be used for good and for evil. So, how do governments limit themselves in, on the one hand, using this A.I. technology and the database to maintain a safe environment for its citizens, but not to encroach on a individual's rights and privacies?