Extreme Maths: Infinity - The Art of the Infinite

"I sent my soul through the invisible," wrote the eleventh century Persian mathematician and poet Omar Khayyam. Let's take only one excursion to illustrate this. That cube we just spoke of had 8 vertices, 12 edges, and 6 faces. What can we say about four-dimensional cubes? What can we say at all about four dimensions? Astonishingly enough, we can say a lot. We can't see a four-dimensional cube, but we can think it, and it has16 vertices, 32 edges, and 24 faces! Shall we go on? A seven-dimensional cube has 672 faces. A ten-dimensional cube has 5,120 edges. We could go on...

Like the structures they probe for, what is essential to mathematicians often lies concealed - for not only does nature hide itself, as Heraclitus said long ago, but it is art to hide art. And it is the infinite that lies hidden in the least grain of sand.

Text Copyright 2003 - Robert and Ellen Kaplan

These and other mysteries are unravelled in the Kaplan’s' new book, "The Art of the Infinite", published by Allen Lane/Penguin on August 28th, 2003. The authors plunge into these mysteries of maths with their students in The Maths Circle (begun nine years ago in America and soon to start up in the UK), where conversation takes the place of lectures and pleasure replaces fear.) Available to buy from Amazon.co.uk and Amazon.com