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Sunday, Jul 12, 2009
Explaining what the winners of the world's top awards in mathematics actually do isn't as easy as adding 2+2. But we'll give it a try.
Sep 5, 2002 | There is no Nobel Prize for mathematicians, the story goes, because of a love affair.
Alfred Nobel, the inventor of dynamite who established the prizes to spruce up his image, refused to endow a prize in mathematics because his wife was having an affair with the Swedish mathematician Gosta Magnus Mittag-Leffler. Nobel was afraid a math prize would be awarded to the mathematician-cum-Romeo, and so the mathematics community has forever been excluded from the most recognized award in all of science.
Alas, the story is not true. Nobel never married and by all accounts was quite a lonely man. But his oversight may perhaps be why mathematicians get so little press. That, and the fact that non-mathematicians have no clue what they're up to.
"Most people are so frightened of the name of mathematics that they are quite ready, quite unaffectedly, to exaggerate their own mathematical stupidity," said the English number theorist G.H. Hardy. But admit it: Whether you left math after a humiliating D in high school trigonometry or crawled away, exhausted and defeated, from a year of college calculus, you've always suspected that, deep down, mathematics rules the world.
As you read this, ex-physicists are probably devising ever more sophisticated ways to wager your pension fund on Wall Street, and no doubt five geniuses in a government agency that does not officially exist are developing data-mining algorithms that will calculate the likelihood your baby sister is a terrorist.
But there was little to no popular media coverage of the Aug. 20 announcement of the Fields Medals, the highest honor in mathematics. Given every four years to the best mathematicians under the age of 40, this year's prizes were awarded at the International Congress of Mathematicians in Beijing. No doubt you didn't even know they were getting together.
The medals went to Laurent Lafforgue of the Institut des Hautes Etudes Scientifiques, in Bures-sur-Yvette, France, and to Vladimir Voevodsky of the Institute for Advanced Study at Princeton. The 2002 Nevanlinna Prize, one of the highest honors in computer science, went to Madhu Sudan of the Massachusetts Institute of Technology.
Speaking by e-mail, Lafforgue said: "When non-mathematicians ask me what I work on, I don't try to explain it to them because I believe that this is nearly impossible. The same with mathematicians who work in other fields." Voevodsky is traveling and could not be reached. But Sudan has been successful, he said, in explaining his work to his 3-year old daughter. If she can get it, so can we.
Let us recognize that mathematicians are not like you or me. We the many can detect some beauty in the paintings of Titian, feel a certain sad hope in a Chopin sonata, recognize the grace in Frank Lloyd Wright's Fallingwater. But, most likely, the isomorphism between a modified motivic cohomology of an algebraic variety and the modified singular cohomology of its natural topological space does little for us.
Which is, really, a shame. For there is a beauty in mathematics, which you may have glimpsed that day in first grade when it struck you how peculiar zero was: that you could add it to any other number -- any number at all! -- and the number would stay the same. Or maybe you've encountered a slick little thing called the square root of -1. There are men who have this number engraved on their tombstones.
This wonder, of course, gets beaten out of us by dull teachers, media stereotypes, the massacre of our attention span, and the manufacturers of standardized college entrance exams. But it hasn't been beaten out of these guys. "There exist in mathematics things extremely beautiful," said Lafforgue. "One thing that's always astonishing is that, occasionally, one realizes that in mathematics the truth is beautiful."
