Fields medals: Mathematicians win awards for geometry, physics, and probability

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more important for younger men than forolder men,” Reich says.

That finding is the study’s most impor-tant new observation, says geneticist B. JillWilliams of Louisiana State UniversityHealth Sciences Center in Shreveport.

Its other findings merely confirm datareported in the June Nature Genetics, con-tends Kári Stefánsson of deCODE Genet-ics in Reykjavik, Iceland. In that study, heand his colleagues linked an elevated riskof prostate cancer to a gene variant in thechromosome-8 segment examined byReich’s team. That variant is carried bynearly one-third of African Americans butappears at lower frequencies in Europeansand white Americans, Stefánsson says.

However, the variant identified by Ste-fánsson’s group explains only a fraction ofthe newly reported association betweenprostate cancer and African ancestry in thecritical stretch of chromosome 8. “Theremust be important and unidentified riskfactors for prostate cancer in this section ofgenetic material,” Reich concludes.

“It’s also possible and, I think, more likelythat there are other variants of the samegene,” counters Stefánsson. —B. HARDER

Fields MedalsMathematicians winawards for geometry,physics, and probability

Grigori Perelman electrified the mathe-matical world 3 years ago with his claim tohave solved one of the most famous prob-lems in mathematics (SN: 6/14/03, p. 378).The Russian mathematician has now beenawarded a Fields Medal, the highest honorin mathematics, given every 4 years to upto four recipients age 40 or under.

Fields Medals, presented this week at theInternational Congress of Mathematiciansin Madrid, also went to Wendelin Wernerof the University of Paris-Sud in Orsay,Andrei Okounkov of Princeton University,and Terence Tao of the University of Cali-fornia, Los Angeles.

Perelman’s work provides proofs of twomajor questions in topology, the mathe-matical theory of shapes. The century-oldPoincaré conjecture states that if every loopembedded in a compact three-dimensionalshape can be pulled down to a single point,then the shape is a three-dimensionalsphere, albeit possibly a deformed one. The

more recent but even more far-reachingThurston geometrization conjecture statesthat every three-dimensional shape can bebroken down into chunks and that eachchunk possesses one of eight simplegeometric structures.

In 3 years of scrutiny,mathematicians haveuncovered no majorflaws in Perelman’sproofs of the two con-jectures. Researchershave now written morethan 1,000 pages elu-cidating his ideas. Ifhis Poincaré proof goesunrefuted for another2 years, Perelman maybe eligible for a $1 mil-lion prize offered bythe Clay MathematicsInstitute in Cam-bridge, Mass., for aproof of the conjec-ture. However, Perel-man has dropped outof the mathematicalscene, and whentracked down in St. Petersburg, Russia, herefused to accept the award.

Werner, another of this year’s FieldsMedal winners, has made seminaladvances in areas including percolationtheory, an abstract model of how a fluid orgas filters through a semiporous materialsuch as a sponge. At a critical degree of amaterial’s porosity, the fluid inside formsa pattern of clusters that looks roughly thesame at any scale larger than very smallones. Werner and his collaborators calcu-lated such a pattern’s fractal dimension, ameasurement of the jaggedness of the clus-ters’ boundary. The researchers alsorelated these patterns to the trajectory ofa Brownian path—the random route takenby, say, a pollen grain in a glass of water—to prove a decades-old conjecture.

Werner’s work is “a watershed in theinteraction between mathematics andphysics,” says Charles Newman, director ofNew York University’s Courant Institute ofMathematical Sciences.

The other two winners’ work also forgednew links between physics and mathe-matics. For instance, Okounkov has usedideas from geometry and probability tocharacterize random shapes, such as theones that form as tiny blocks melt off thecorners of a cubical crystal. Okounkovlinked the distribution of blocks of differ-ent sizes to the ways in which a whole num-ber can be partitioned into a sum of smallernumbers. Using this connection, he andRichard Kenyon of the University of BritishColumbia in Vancouver showed that thetwo-dimensional shadow of such a crystalalways has a distinctive shape and liesinside a simple curve. Okounkov possesses

“an unusual intuition that makes him ableto find unexpected bridges between seem-ingly distant theories,” says Enrico

Arbarello, a mathematician at the Uni-versity of Rome.

Tao’s interests include primenumbers and quantum physics.In 2004, he and Ben Green ofthe University of Bristol inEngland proved that even

though primes are fewand far between, theirsequence containsarithmetic progres-sions—sequences ofnumbers that differby a fixed amount—

of every possiblelength (SN: 4/24/04, p.

260). Tao has also made con-tributions to the study of wave maps,

which are related to Einstein’s equationsof general relativity, and nonlinearSchrödinger equations, which describethe behavior of light in a fiberoptic cableand other quantum phenomena.

“Some of his work gives one a feel-ing of awe that a human mind can mas-

ter such complexity,” says Princetonmathematician Charles Fefferman. “Andsome makes one wonder how so manyresearchers could have missed somethingso seemingly obvious.” —E. KLARREICH

Sweet FindingResearchers proposecandidate sour sensor

Two teams of scientists have identified aprotein on the surfaces of select tonguecells that may be the long-sought detectorof sour taste.

People and some other animals, includ-ing mice, distinguish five recognizedtastes: sweet, bitter, sour, salty, andumami, the flavor of monosodium gluta-mate. Over the past 6 years, researchersincluding Charles S. Zuker of the Univer-sity of California, San Diego have ferretedout proteins on tongue-cell surfacesresponsible for receiving sweet, bitter, andumami sensations.

To locate the sour-taste receptor, Zuker’steam started with a few assumptions basedon previous findings. For example, a sour-detecting protein would weave in and outof the membranes of tongue cells, as thetaste receptors already identified do. Pre-vious studies also suggested that eachtongue cell produces no more than onetype of taste receptor.

Zuker’s team scanned the mousegenome, looking first for genes that encodemembrane-spanning proteins that resem-ble the known taste receptors. To narrow

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SCIENCENEWSThis Week

PRIZENUMBERS Inwork recognized witha Fields Medal, a heart-shaped curve encirclesthe melting region in acrystal representation of a random surface.

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