Rebooting Britain: Teach kids to see in four dimensions


Governments across the world recognise that a mathematically literate work-force is more likely to capitalise on the technological changes that are sweeping through society. The power of Google to hunt out the page you want, the ability of cameras to cram more detailed pictures into tinier memories, the sophisticated games and animations we watch, all depend on clever mathematics. To innovate further you need to understand the mathematical language that underpins these technologies.

However, in the UK our kids are slipping lower and lower in the mathematical league tables. They are losing interest and are bored by the subject. If we are going to be in a position to upgrade the UK we need kids who are fired up and fluent in this mathematical code. My solution: teach them to see in 4D.

Isn't teaching a kid to see in 4D a pipe dream? How can you teach such difficult maths? It doesn't actually take much to get someone exploring the contours of a 4D cube. The key is to use Descartes' method for translating geometry into numbers. Every location on the surface of the earth can be translated into a pair of numbers, one denoting its longitude, the other its latitude. For example, the GPS location of my college in Oxford is (-1.251288, 51.754277). Using these coordinates we can translate shapes into numbers: a square can be described by the coordinates of its corners: (0,0), (1,0), (0,1) and (1,1) - mark these locations on a map and you've got the corners of a square. The corners of a cube are got by adding an extra dimension and hence an extra number. So the eight corners of the cube can be described by the eight coordinates of numbers starting at (0,0,0), (1,0,0), (0,1,0) ... continuing to the far point at (1,1,1).

With a four-dimensional cube, although the pictures run out, the numbers don't. So a mathematician will describe a four-dimensional cube as the object whose corners are given by the coordinates with four numbers starting at (0,0,0,0), (1,0,0,0) and stretching out to the furthest point at (1,1,1,1). Using the numbers I can explore the geometry of this shape. A four-dimensional cube, what is known as a tesseract, has 16 corners, 32 edges and 24 square faces, and is constructed out of eight cubes.

Seeing the world through four-dimensional geometry is just one of the big stories of maths that has the potential to excite kids about the subject. Other great tales include the story of prime numbers, topology and symmetry. It is this exciting maths that underpins the digital age. Primes are the keys to protecting the internet's secrets. Navigating the complexity of the web relies on the maths of networks. The errors that creep into the digital signals as they bounce between satellites are corrected on arrival by the theory of symmetry. And all those 0s and 1s flying down the wires are mapping out corners on high-dimensional cubes.

If kids can be taught Macbeth, why can't they be exposed to the Shakespearean enchantments of maths?

Marcus du Sautoy is the Charles Simonyi Professor for the Public Understanding of Science at the University of Oxford. He recently opened an internet maths school,, with Toby Rowland, founder of the gaming website - school motto: "Where maths is just a game".

