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.

To Infinity and Beyond

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.

The Frontiers of Space

By the 17th century, Europe had taken 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.

The Genius of the East

When ancient Greece fell into decline, mathematical progress stagnated as Europe entered the Dark Ages, but in the East mathematics reached new heights. 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.

When ancient Greece fell into decline, mathematical progress stagnated as Europe entered the Dark Ages, but in the East mathematics reached new heights. 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.

The famously difficult green-eyed logic puzzle

One hundred green-eyed logicians have been imprisoned on an island by a mad dictator. Their only hope for freedom lies in the answer to one famously difficult logic puzzle. Can you solve it? Alex Gendler walks us through this green-eyed riddle.

What is Zeno's Dichotomy Paradox?

Can you ever travel from one place to another? Ancient Greek philosopher Zeno of Elea gave a convincing argument that all motion is impossible - but where's the flaw in his logic? Colm Kelleher illustrates how to resolve Zeno's Dichotomy Paradox.

Brady Numbers

The new "Brady Sequence" demonstrates why Fibonacci Numbers are not so special.

Why are manhole covers round?

Why are most manhole covers round? Sure it makes them easy to roll, and slide into place in any alignment. But there’s another, more compelling reason, involving a peculiar geometric property of circles and other shapes. Marc Chamberland explains curves of constant width and Barbier’s theorem.

The Joy of Data

A witty and mind-expanding exploration of data, with mathematician Dr Hannah Fry. This high-tech romp reveals what data is and how it is captured, stored, shared and made sense of. Fry tells the story of the engineers of the data age, people most of us have never heard of despite the fact they brought about a technological and philosophical revolution. For Hannah, the joy of data is all about spotting patterns. Hannah sees data as the essential bridge between two universes - the tangible, messy world that we see and the clean, ordered world of maths, where everything can be captured beautifully with equations. The film reveals the connection between Scrabble scores and online movie streaming, explains why a herd of dairy cows are wearing pedometers, and uncovers the network map of Wikipedia. What's the mystery link between marmalade and One Direction? The film hails the contribution of Claude Shannon, the mathematician and electrical engineer who, in an attempt to solve the problem of noisy telephone lines, devised a way to digitise all information. Shannon singlehandedly launched the 'information age'. Meanwhile, Britain's National Physical Laboratory hosts a race between its young apprentices in order to demonstrate how and why data moves quickly around modern data networks. It's all thanks to the brilliant technique first invented there in the 1960s by Welshman Donald Davies - packet switching. But what of the future? Should we be worried by the pace of change and what our own data could be used for? Ultimately, Fry concludes, data has empowered all of us. We must have machines at our side if we're to find patterns in the modern-day data deluge. But, Fry believes, regardless of AI and machine learning, it will always take us to find the meaning in them.

2016 • Math