26 JAN
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THE BELIZE TIMES
2014
BELIZE TIMES WEEKLY
SCIENCE & TECH R
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Kazakh mathematician may have solved $1 million puzzle 22 January 2014 by Jacob Aron and Katia Moskvitch Mathematics is a universal language. Even so, a Kazakh mathematician’s claim to have solved a problem worth a million dollars is proving hard to evaluate – in part because it is not written in English. Mukhtarbay Otelbayev of the Eurasian National University in Astana, Kazakhstan, says he has proved the Navier-Stokes existence and smoothness problem, which concerns equations that are used to model fluids – from airflow over a plane’s wing to the crashing of a tsunami. The equations work, but there is no proof that solutions exist for all possible situations, and won’t sometimes “blow up”, producing unrealistic answers. In 2000, the Clay Mathematics Institute, now in Providence, Rhode Island, named this one of seven Millennium Prize problems offering $1 million to anyone who could devise a proof. Otelbayev claims to have done just that in a paper published in the Mathematical Journal, also based in Kazakhstan. “I worked on the problem on and off, for 30 years,” he told New Scientist, in Russian – he does not speak
English. Mathematical Babel fish However, the combination of the Russian text and the specialist knowledge needed to understand the Navier-Stokes equations means the international mathematical community, which usually communicates in English is having difficulty evaluating it. Although mathematics is expressed through universal symbols, mathematics papers also contain large amounts of explanatory text. “Over the years there have been several alleged solutions to the Navier-Stokes problem that turned out to be wrong,” says Charles Fefferman of Princeton University, who wrote the official formulation of the problem for Clay. “Since I don’t speak Russian and the paper is not yet translated, I’m afraid I can’t say more right now.” Otelbayev is a professional, so mathematicians are paying more attention to his proof than is typical for amateur efforts to solve Millennium Prize problems, which are regularly posted online. The Russian-speaking Misha Wolfson, a computer scientist and chemist at the Massachu-
Becoming a millionaire mathematician
setts Institute of Technology is attempting to spark an online, group effort to translate the paper. “While my grasp on the math is good enough to enable translation up to this point, I am not qualified to say anything about whether or not the solution is any good,” he says. Stephen Montgomery-Smith of the University of Missouri in Columbia, who is working with Russian colleagues to study the paper, is hopeful.”What I have read so far does seem valid,” he says “but I don’t feel that I have yet got to the heart of the proof.” Otelbayev says that three colleagues in Kazakhstan and another
in Russia agree that the proof is correct. Burden of proof Understandably, a high burden of proof is required to claim the $1 million prize. Clay’s rules say the solution must be published in a journal of “worldwide repute” and remain unchallenged for two years before it can even be considered. Nick Woodhouse, president of the Clay Mathematics Institute, declined to comment on Otelbayev’s proof. “It is currently being translated by my students, and will be available soon,” says Otelbayev. He says that he will publish it again once it is translated into English – initially in a second Kazakh journal, and then perhaps abroad. To date, only one Millennium Prize problem has been officially solved. In 2002, Grigori Perelman proved the Poincaré conjecture, but later withdrew from the mathematical community and refused the $1 million prize. A possible solution for another problem, known as P vs NP, caught mathematicians’ attentions in 2010, but later proved to be flawed. Whether Otelbayev’s proof will share the same fate remains to be seen.
New species of river dolphin born of Amazon rapids 22 January 2014 by Adrian Barnett A new species of river dolphin has been found, the first of its kind for a century. Tomas Hrbek of the Federal University of Amazonas in Manaus, Brazil, and colleagues took DNA from river dolphins in the Araguaia and Tocantins rivers. He found they differed from all other species in Brazil. They also only have 24 teeth per jaw, rather than the 25 to 29 found in the Amazon’s other river dolphins. He calls the species Inia araguaiaensis.
Already a rare sight (Image: Nicole Dutra)
The team’s analysis of I. araguaiaensis’s genes suggest that the species formed 2.08 million years ago, when the Ara-
guaia-Tocantins basin was cut off from the rest of the Amazon river system by huge rapids and waterfalls. River dolphins are slow swimmers that rarely leap, so the shifting landscape isolated the dolphins from their fellows. Hrbek thinks the formation of rapids has been crucial to river dolphin evolution. The Madeira river’s Inia boliviensis arose 2.87 million years ago when the Teotônio rapids formed, while the Casiquiare rapids in the Orinoco river gave rise to the subspecies Inia geoffrensis humboldtiana. Dammed However, a different obstacle poses a threat to I. araguaiaensis. Hrbek
says dam construction on the Araguaia and Tocantins rivers may wipe it out. “Its future is pretty bleak,” he says. “The Araguaia-Tocantins basin suffers huge human disturbance and there are probably less than 1000 I. araguaiaensis in existence.” That means it could soon follow in the footsteps of China’s iconic baiji, which was declared extinct in 2007. “It’s exciting evidence for a previously unrecognised species within the ancient lineage of Amazon river dolphins,” says Scott Baker of Oregon State University in Newport. “Yet it’s already rare, and its habitat is now fragmented by dams.”