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8 Nov 2009

Extreme Maths: Infinity - The Art of the Infinite

- 6 Jan 2001
By Robert and Ellen Kaplan   
Page 3 of 3

"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...

We could go on, because the true home of mathematics is at the limit of all our thinking. Calculus, that wonderful invention of Newton (and independently, of the German diplomat, philosopher, and mathematician, Gottfried Leibniz), comes to grips with change as Seurat and the Impressionists did, by reducing reality to flickering points, and then rebuilding the world more profoundly. Artist’s live flamboyant lives, mathematicians tend to be thought of as reclusive and dry. How could they possibly be of the same breed? Mathematicians come in all the usual flavours: some are playful, some arrogant, some devious, and others direct. John Maynard Keynes pictured Newton as the last of the Magi, trying to wrest its secrets from the universe alone in his tower at night. Da Vinci - half artist, half mathematician - comes down to us as ambiguous as his Mona Lisa's smile.

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Stare into the maelstrom...

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

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Have your say
 
How do you prove that 1 = 0 with infinity maths?
Posted by: guest - 2009-04-27 - 13:08 GMT

This article has been very helpful
Posted by: jessi34811 - 2008-12-21 - 15:23 GMT

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