The entire field of mathematics summarised in a single map! This shows how pure mathematics and applied mathematics relate to each other and all of the sub-topics they are made from.

To Infinity and Beyond

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.

The Secret Life of Chaos

Professor Jim Al-Khalili shows how chaos theory can answer a question that mankind has asked for millennia - how does a universe that starts off as dust end up with intelligent life? It's a mindbending, counterintuitive and for many people a troubling idea.

The Language of the Universe

In Egypt, professor Marcus du Sautoy 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.

Tails You Win: The Science of Chance

Professor David Spiegelhalter tries to pin down what chance is and how it works in the real world. A blend of wit and wisdom, animation, graphics and gleeful nerdery is applied to the joys of chance and the mysteries of probability, the vital branch of mathematics that gives us a handle on what might happen in the future. How can you maximise your chances of living till you're 100? Why do many of us experience so many spooky coincidences? Should I take an umbrella? These are just some of the everyday questions the film tackles as it moves between Cambridge, Las Vegas, San Francisco and Reading. Spiegelhalter discovers One Million Random Digits, a book full of hidden patterns and shapes, introduces us to the unit called the micromort (a one-in-a-million chance of dying), and uses the latest infographics to demonstrate how life expectancy has increased in his lifetime and how it is affected by our lifestyle choices - drinking, obesity, smoking and exercise.

2012 • Math

The mathematical secrets of Pascal’s triangle

Pascal’s triangle, which at first may just look like a neatly arranged stack of numbers, is actually a mathematical treasure trove. But what about it has so intrigued mathematicians the world over?

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.