Editorial–

IT WAS inevitable that this week’s award of the Fields medals, mathematics’ highest honour, would be dominated by Grigori Perelman’s refusal to accept his. Perelman’s work on the Poincaré conjecture is of such stature that he would have dominated the headlines whether he had turned up or not. Even so, Perelman’s no-show is small beer compared with other upheavals taking place in mathematics today.

For one thing, mathematicians are struggling to stomach the implications of computer-assisted proofs. For millennia, mathematics has held a unique position: once the truth of a proposition is established, it exists unassailable forever. No other science can boast such certainty. Now computer-assisted proofs, which use software to analyse details too numerous to check by hand, are introducing uncertainty. How do you prove there isn’t a programming error? Suddenly mathematicians are finding it hard to decide what even constitutes a proof (see page 41).

One way maths can best take on future problems is to have a clearer picture of those it has already slain. A global effort is under way to digitise paper-based archives so that the entire history of the subject is available electronically. Sadly, the project is bogged down by petty disputes over formatting, but with the right leadership, this so-called

retrodigitisation could inject new life into many areas of mathematics.

There is also a sense that mathematicians should increase their cross-pollination with other fields, not restricting themselves to physics but ranging further afield. This week saw the first award of the Gauss prize, which celebrates the influence of mathematics in other disciplines. The winner was Japan’s Kiyoshi Ito, whose work on modelling random events has been hugely influential in physics, economics and biology.

In the past, collaboration was thought to reduce an individual’s chance of bagging the biggest prizes. The International Mathematical Union, which awards the Fields medals, has sent a powerful message with its choice of winners this year by recognising Terence Tao and Wendelin Werner, who have built impressive reputations as serial collaborators.

So far so good, but there is more to do. Mathematics must increase its nurturing of talent from developing nations, for example. And it ought to be a matter of embarrassment that many maths meetings do not have a single woman present. Only by evolving can mathematics hope to face down its demons and reveal new truths. Only by including everyone will it continue to be a powerful cultural force. ●

SOCIETY has always struggled to deal fairly with the psychiatric casualties of conflict. In the first world war, the British army shot men who refused to fight, some of whom were known to have suffered from shell shock. The horrific conditions in the trenches left them so mentally damaged they could barely walk, let alone fight. It took until last week for the UK government to decide that an injustice had been done, and that those shot for desertion and cowardice should receive a pardon.

Since 1918, systematic study has given us a better idea of how people can be affected by the trauma of war. Notions of shell shock and battle fatigue have given way to post-traumatic stress disorder (PTSD). Science is also giving new hope for treatments (New Scientist, 3 December 2005, p 32).

Controversy, however, is never far away.

This week it resurfaced in the US following a study that estimates the rate of PTSD in Vietnam veterans at 18.7 per cent, considerably lower than the previous estimate of 30.9 per cent (Science, vol 313, p 979). Politicians have already clashed over spending on mental health at the US Department of Veterans Affairs, and fears are growing that this latest study will provide ammunition for those who want to see such spending cut.

That would, indeed, be a mistake at a time of large-scale conflicts in Iraq and Afghanistan. Military personnel hurt while implementing the policies of democratic governments deserve the best of care. Cutting spending on mental health services and research cannot, of course, be equated with executing men suffering from shell shock, but history may judge such a move just as harshly. ●

Caring for war’s hidden casualties

www.newscientist.com 26 August 2006 | NewScientist | 5

Open problemsIn the quest for universal truths, maths must first face a few closer to home

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