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<i>Mathematicians could be on the verge of solving two separate million dollar problems. If they are right - still a big if - and somebody really has cracked the so-called Riemann hypothesis, financial disaster might follow. Suddenly all cryptic codes could be breakable. No internet transaction would be safe...
The Riemann hypothesis would explain the apparently random pattern of prime numbers - numbers such as 3, 17 and 31, for instance, are all prime numbers: they are divisible only by themselves and one. Prime numbers are the atoms of arithmetic. They are also the key to internet cryptography: in effect they keep banks safe and credit cards secure.
This year Louis de Branges, a French-born mathematician now at Purdue University in the US, claimed a proof of the Riemann hypothesis. So far, his colleagues are not convinced. They were not convinced, years ago, when de Branges produced an answer to another famous mathematical challenge, but in time they accepted his reasoning. This time, the mathematical community remains even more sceptical.
"The proof he has announced is rather incomprehensible. Now mathematicians are less sure that the million has been won," Prof du Sautoy said.
"The whole of e-commerce depends on prime numbers. I have described the primes as atoms: what mathematicians are missing is a kind of mathematical prime spectrometer. Chemists have a machine that, if you give it a molecule, will tell you the atoms that it is built from. Mathematicians haven't invented a mathematical version of this. That is what we are after. If the Riemann hypothesis is true, it won't produce a prime number spectrometer. But the proof should give us more understanding of how the primes work, and therefore the proof might be translated into something that might produce this prime spectrometer. If it does, it will bring the whole of e-commerce to its knees, overnight. So there are very big implications..." </i> [read more at <A HREF="http://www.guardian.co.uk/uk_news/story/0,3604,1298728,00.html">Guardian.co.uk</A>]
The Riemann hypothesis would explain the apparently random pattern of prime numbers - numbers such as 3, 17 and 31, for instance, are all prime numbers: they are divisible only by themselves and one. Prime numbers are the atoms of arithmetic. They are also the key to internet cryptography: in effect they keep banks safe and credit cards secure.
This year Louis de Branges, a French-born mathematician now at Purdue University in the US, claimed a proof of the Riemann hypothesis. So far, his colleagues are not convinced. They were not convinced, years ago, when de Branges produced an answer to another famous mathematical challenge, but in time they accepted his reasoning. This time, the mathematical community remains even more sceptical.
"The proof he has announced is rather incomprehensible. Now mathematicians are less sure that the million has been won," Prof du Sautoy said.
"The whole of e-commerce depends on prime numbers. I have described the primes as atoms: what mathematicians are missing is a kind of mathematical prime spectrometer. Chemists have a machine that, if you give it a molecule, will tell you the atoms that it is built from. Mathematicians haven't invented a mathematical version of this. That is what we are after. If the Riemann hypothesis is true, it won't produce a prime number spectrometer. But the proof should give us more understanding of how the primes work, and therefore the proof might be translated into something that might produce this prime spectrometer. If it does, it will bring the whole of e-commerce to its knees, overnight. So there are very big implications..." </i> [read more at <A HREF="http://www.guardian.co.uk/uk_news/story/0,3604,1298728,00.html">Guardian.co.uk</A>]