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Science
THE MATERIAL WORLD
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Thursday 16:30-17:00
Quentin Cooper reports on developments across the sciences. Each week scientists describe their work, conveying the excitement they feel for their research projects.
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ThursdayÌý24ÌýAugustÌý2006
Grigori Perelman, mathematician
Mathematician Grigori Perelman

THE FIELDS MEDAL

Top mathematicians from all over the world are meeting in Madrid this week at the International Mathematical Union. The high point of their celebrations is the awarding of the Fields Medal - in effect the Nobel Prize of Maths. Only awarded everyÌýfour years, and only to younger mathematicians, the medal is their highest accolade.

The most controversial of this year'sÌýfour winners is the Russian, Grigori Perelman. And it seems that he has refused the medal! His work investigates the possible geometries of 3-dimensional shapes in 4-dimensional space. In particular, he seems to have proved what's called the Poincaré Conjecture, identified as one of the major remaining goals in pure mathematics. His proof is so complex that other mathematicians have so far taken 3 years checking it. As yet they have found no significant mistakes!

But does all this make a difference? "Pure maths" often has unexpected applications. When Albert Einstein was developing Relativity he found that he needed a theory of curved space. On investigation, Einstein found that a mathematician had devised this exact theory more than 30 years earlier. Perelman's work could tell us about the possible shape of the universe. But he remains a comparative recluse. He has so far refrained from applying for another prize, worth a million dollars, saying it might distract him from maths! Now he has refused the top honour of a Fields Medal as well.

On the line from Madrid, Professor Sir John Ball, President of the International Mathematical Union, and Oxford Mathematician Marcus Du Sautoy discuss the prize and why pure maths matters.

QUANTUM TOOLKITS FOR ARCHAEOLOGY

Archaeologists spend all their time digging holes in the ground and scratching about in the mud, right? Wrong. There's a lot more science and technology involved these days. If you've visited a site or watched a dig on TV, you may have noticed that it usually begins with geophysics or 'geophys'. People walk up and down carrying strange pieces of equipment which eventually produce plans covered in coloured blotches!

As Quentin hears from geophysicist Chris Leach and archaeologist Henry Chapman, there's more too it than that. The latest instruments use techniques from quantum physics to detect the slightest magnetic anomalies in the soil and new radars can literally see into the ground without you ever picking up a spade. What's more, several instruments now come on a single sledge to tow behind a vehicle. And it can move randomly across a field as all the measurements are put in place using GPS technology.
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