Mathematician's Nobel

Print edition : September 08, 2006

THE FIELDS MEDAL. -

EVERY year, the coveted Nobel Prize is awarded in each of the following six fields: Physics, Chemistry, Physiology and Medicine, Economics, Literature and Peace. Conspicuously absent from the categories is Mathematics. The reason for this omission, though not entirely clear, has been extensively speculated upon and written about based on a mix of rumours and facts.

The Fields Medal, a maximum of four of which are awarded every four years at the International Congress of Mathematicians (ICM), is the most prestigious award in mathematics and is commonly regarded as the "Mathematicians' Nobel". The comparison, however, is not quite accurate.

The Fields Medal is awarded to young mathematicians in recognition of outstanding mathematical achievement for existing work and for the promise of future achievement. That is Fields Medal is given for a body of work rather than a particular result, which is not always the case with the Nobel Prize. From this perspective, it has been decided that a candidate's 40th birthday must not occur before January 1 of the year of the Congress.

In the 70 years since the first award was given in Oslo in 1936, there have been 42 Fields Medallists. Three have gone to candidates making significant advances towards proving the Poincare Conjecture, the 102-year-old conjecture in mathematics posed by French mathematician Henri Poincare (1854-1912).

Perhaps more than ever before, this year's Fields Medal awards have generated a great deal of interest both in the mathematics community and the general public, particularly the media. It was generally expected that Grigori `Grisha' Perelman, the Russian mathematician from St. Petersburg, would most certainly be an awardee for having proved the Poincare Conjecture, one of the most burning mathematical problems of our times.

But greater interest in the award was because of the personality of Perelman, a reclusive and ascetic genius, who seemed not only the least interested in any kind of recognition to his work, the Fields Medal included. He was also not keen to publish his monumental achievement in any peer-reviewed journal that would make him eligible for the $1 million prize instituted by the U.S.-based Clay Mathematics Institute (CMI) for solving one of the seven Millennium Problems identified by CMI.

As was widely expected, the four 2006 Fields Medal winners announced at the inauguration of ICM-2006 on August 22 at Madrid included Perelman (who turned 40 on June 13) but, true to his form and reputation, he has rejected the award and also does not seem interested in attending the Congress, one of whose main themes is the Poincare Conjecture.

As the International Mathematics Union (IMU) newsletter said, the Congress would mark "the occasion of the conjecture becoming a theorem". But the deliberations on the Conjecture will miss its main protagonist, while others who have spent over three years trying to understand his proof since he posted it on the Internet will talk.

"I deeply regret that Dr. Perelman has declined to accept the medal," said IMU president Sir John M. Ball, at the presentation of the awards by the King of Spain, Juan Carlos I. Despite his refusal, the ICM has declared Perelman to be officially a Fields Medallist, setting perhaps a unique precedent. "He has a say whether he accepts it or not, but we have awarded it," Ball had stated.

There has, however, been a precedent of the winner not being able to travel to receive the award due to political reasons as in the case of Soviet mathematician Gregori Margulis in 1978.

The Fields Medals were first proposed at the 1924 ICM in Toronto, where, in the backdrop of exclusion of German mathematicians by the nascent IMU, it was resolved that at each subsequent Congress, two gold medals should be awarded for outstanding mathematical achievement.

The Canadian mathematician J.C. Fields, who was the Secretary of the 1924 Congress, later donated funds towards these awards. Fields considered two fundamental principles for the award: the solution of a difficult problem and the creation of a new theory enlarging the fields of application of mathematics. Despite his wishes in that regard, the awards were named after him. In 1966, in view of expanding mathematical research, it was decided that up to four medals could be given.

The Fields Medal is made of gold and the award includes Canadian $15,000 (about $9,500).

R. Ramachandran

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