Super quick computers and advanced mathematical formulas have taken over trading on the financial markets from human beings -algorithms- which seem to have a life of their own. The only ones who understand the system in any way are its architects, the algorithm developers. Haim Bodek is one such algo-developer. After finding some strange wrongdoings he set out on a personal crusade against this elusive system". The machinery behind our financial markets, consisting of mathematical models, data centers and miles and miles of fiber optic cables, is disguised by technological complexity and secrecy. The builders of this financial system are a new breed of Wall Street employees -quants- mathematicians and physicists who are responsible for a technological revolution. Haim Bodek is a quant; he specialized in artificial intelligence and worked for Goldman Sachs. He knows the system from the inside, he helped build it. Haim Bodek was invited to tell his story at the "Battle of the Quants" - a recurring event where quants discuss high-frequency trading, amongst other things. Bodek wrote an algorithm for trading machines that would generate guaranteed income - a money machine that weathered the financial meltdown of 2008. But then from one day to the next the algorithm stopped working.

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.

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.

By our third year, most of us will have learned to count. Once we know how, it seems as if there would be nothing to stop us counting forever. But, while infinity might seem like an perfectly innocent idea, keep counting and you enter a paradoxical world where nothing is as it seems. Mathematicians have discovered there are infinitely many infinities, each one infinitely bigger than the last. And if the universe goes on forever, the consequences are even more bizarre. In an infinite universe, there are infinitely many copies of the Earth and infinitely many copies of you. Older than time, bigger than the universe and stranger than fiction. This is the story of infinity.

It is a nightmare that has stalked us for centuries: hordes of human beings transformed into mindless, cannibalistic monsters. Could this civilization-ending nightmare become reality? Scientists have discovered pathogens that turn insects into the walking dead. New strains of viruses are attacking humans every day. Mathematicians have calculated the likelihood of surviving a zombie virus outbreak: they’re not hopeful. Now neuroscientists are discovering how easy it is for us to lose conscious control of our bodies. Are we at risk of becoming puppets? If we were in the middle of a zombie apocalypse, would we even know it?

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.