Maths 'Nobel' Rumoured for Russian Recluse
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3.8 News 490-491 MH NEW 1/8/06 9:59 AM Page 490 Vol 442|3 August 2006 NEWS Maths ‘Nobel’ rumoured for Russian recluse Some speculation always precedes the ann- The geometrization conjecture classifies all ouncement of the Fields medals, the most the possible forms that three-dimensional illustrious awards in mathematics. But this surfaces, called three-manifolds, can take. year rumours have an extra dimension: one of The Poincaré conjecture describes the prop- the prizes to be awarded at the International erties of a subset known as ‘simply connected’ Congress of Mathematicians in Madrid on manifolds — in particular, those for which 22 August may be given for the solution of a every loop drawn on the surface can be century-old problem. shrunk to a point. Favourite to win a medal is Russian mathe- To tackle the conjecture, Perelman used a matician Grigory ‘Grisha’ Perelman, for his mathematical tool known as Ricci flow, devel- work on the Poincaré conjecture. Three papers oped by Richard Hamilton of Columbia Uni- now suggest that his proof of the conjecture is versity. Perelman, formerly of the Steklov right. If it stands up to two years of scrutiny, Institute in Moscow, advanced Hamilton’s Perelman will also be eligible for at least a share work by finding a way to deal with certain of a million-dollar mathematics prize (see problems encountered in using Ricci flow to ‘Clay feats’). study the deformation of surfaces. “I am completely convinced “For people studying The advent of a possible that Perelman has proved the proof shook a small contingent Poincaré conjecture,” says John topology, the of mathematicians. “For people Morgan, a topologist at Col- whole landscape studying topology, the whole umbia University in New York has changed.” landscape has changed. It’s like and co-author of the most waking up one morning after recent paper analysing Perelman’s work. an earthquake,” says Bruce Kleiner of Yale The Poincaré conjecture is a seemingly University in New Haven, Connecticut. simple statement about the nature of three- Perelman followed his first article with two is that clever people, experts in the area, read it dimensional surfaces, but it had resisted proof further papers, and in the spring of 2003 he and come to an opinion.” since French mathematician Henri Poincaré toured the United States to lecture about his Three pairs of respected mathematicians put it forward in 1904. work2. He has since retreated from the public have produced written accounts filling in the In 2002, Perelman posted to an online eye, leaving other mathematicians to comb details of Perelman’s work. preprint server a paper1 that claimed to “give a through his papers line by line, filling in details Kleiner and John Lott of the University of sketch of an eclectic proof of this conjecture”. and searching for holes in his logic. Michigan, Ann Arbor, posted their most By this, Perelman meant not just the Poincaré “How do you decide whether anything is recent paper to the arXiv preprint server on PRINCETONIAN C. CHANG/DAILY conjecture, but the geometrization conjecture, correct?” asks John Ball, president of the Inter- 25 May3. “There was a moment when I really a much broader theorem of which Poincaré’s national Mathematical Union and chair of the thought there was a problem with the argu- statement is a special case. Fields medal committee. “All that can happen ment,” says Kleiner. “But that state of mind Bird flu not set for pandemic, says US team Researchers have tried to create a H5N1 virus will require a complex strain could evolve. For instance, and wild birds have died owing to pandemic H5N1 influenza strain — series of genetic changes to evolve strains other than those used in the the H5N1 strain of flu. It has infected and failed. into a pandemic strain. experiments could get together. at least 232 people and killed 134 of Simply mixing genes from an H5N1 “These data do not mean that “They need to look at other viruses, them. Scientists are worried that bird-flu strain with those from an H5N1 cannot convert to become because both human and avian flu H5N1 will learn to pass easily H3N2 human strain did not result in a transmissible from person to continue to evolve,” says Frederick between humans and kill millions strain that was readily transmissible, person,” says Julie Gerberding, Hayden, a flu specialist at the more. In 1957 and 1968, pandemic at least among ferrets. The scientists director of the CDC. “We are not out University of Virginia, strains of flu seem to have emerged who conducted the work, at the of the woods on pandemic Charlottesville, who is currently when bird and human flu viruses Centers for Disease Control and preparedness yet.” working with the World Health exchanged genes, allowing the bird- Prevention (CDC) in Atlanta, Others agree, pointing out that Organization. flu virus to be easily transmitted Georgia, say it suggests that the there are many ways a pandemic Since 1997, millions of domestic between people. 490 © 2006 Nature Publishing Group 3.8 News 490-491 MH NEW 1/8/06 9:59 AM Page 491 NATURE|Vol 442|3 August 2006 NEWS INDONESIAN FLU CASES GO UNSTUDIED No sequence data have been acquired from birds for nearly a year. www.nature.com/news Clay feats: the million-dollar questions In 2000, the privately funded serve to start the clock on the Clay Mathematics Institute in waiting period,” he says. Cambridge, Massachusetts, Some mathematicians announced a prize of $1 million suggest that the prize money for the solution of each of should be shared between seven mathematical Perelman and Richard conundrums — including the Hamilton, a mathematician at INST. MATHEMATICS CLAY Poincaré conjecture. Columbia University in New “I didn't think that I would York, who laid much of the live to see the Poincaré groundwork. Those who have Great foundations: the Clay conjecture solved,” says followed up the proof could Mathematics Institute. James Carlson, president of also theoretically lay claim to the institute. “But we're there, appear online but have not the money. or almost there.” been formally reviewed. Bruce Kleiner of Yale The rules require that Those who have tried to University says he will not the proof appear in a peer- persuade Perelman to seek a share. “I’m not saying reviewed outlet and then publish say that he shows no that it was easy to fill in the survive two years of scrutiny. interest. Other recent papers details,” he says. “But you Grigory Perelman’s papers on his work by different can’t compare it to the level of containing a possible proof mathematicians may count ingenuity required to sketch of the Poincaré conjecture instead, says Carlson. “These out the proof.” J.H. in Guangzhou, China, was published in June5. achievement in mathematics, it would be It claims to complete the proof of both conjec- funny if they didn’t,” says Morgan. There is also tures, rather than simply fleshing out Perelman’s a precedent. Two previous Fields medals have work. This is justified, argues Shing-Tung Yau, been awarded for proofs of an equivalent of the an editor-in-chief on the journal, because Cao Poincaré conjecture in higher dimensions — and Zhu follow a somewhat different argument to Stephen Smale in 1966 and Michael Freed- to Perelman. man in 1986. The appearance of these three papers has And in 2006? Morgan, along with 4,000 Board meeting: Grigory Perelman presents his fuelled rumours that Perelman will receive a guests, will find out in a few weeks — when proof of the intractable Poincaré conjecture. Fields prize. Up to four medals are awarded the medals are announced at the opening every four years to mathematicians no older ceremony of the congress in Madrid. ■ persisted for only a week or two before the than 40, making Perelman just eligible for this Jenny Hogan issue was resolved.” year’s crop. Not that he will attend the Madrid 4 1. Perelman, G. Preprint at http://arxiv.org/abs/math.DG/ A 473-page paper by Morgan and Gang meeting: the organizing committee received 0211159 (2002). Tian of the Massachusetts Institute of Technol- no reply when they invited him to give a 2. Singer, E. Nature 427, 388–389 (2004). ogy appeared on 25 July. plenary lecture. 3. Kleiner, B. & Lott, J. Preprint at http://arxiv.org/abs/ math.DG/0605667 (2006). The third paper, from Huai-Dong Cao of Even so, many mathematicians think Perel- 4. Morgan, J. W. & Tian, G. Preprint at http://arxiv.org/abs/ Lehigh University in Bethlehem, Pennsylvania, man will be honoured with a medal. “I hope math.DG/0607607 (2006). and Xi-Ping Zhu of Zhongshan University that they give him one. This is such a major 5. Cao, H.-D. & Zhu, X.-P. Asian J. Math. 10, 165–492 (2006). To test whether H5N1 might virus. In addition, the ferrets did other animals, the scientists human disease, say scientists not do this, the CDC scientists used a not pass the hybrid virus easily to say. They hope to repeat the involved in the experiments. Nor technique called reverse genetics others. And even if they did pass on experiments to test the pandemic does the study address whether to snip genes out of H3N2 and H5N1 the virus, the other ferrets did not potential of other viruses — H5N1 could evolve into a pandemic viruses and recombine them into become fatally ill. including those taken from patients strain by accumulating mutations if hybrid bird–human viruses. They “They need to look at after 1997, the year that the H5N1 it passed through many people.