HT Correspondent
Bhopal, September 7
It's a million dollar mathematical problem, but if (and it's still a big if) a French-born Purdue University mathematician called Louis de Branges has actually 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.
The hypothesis is one of seven "millennium problems" (see boxes for other the other six) and four years ago the Clay Mathematics Institute in the US offered $1m to anyone who could solve even one of these seven. Formulated by Georg Friedrich Bernhard Riemann in 1859 it is, according to Marcus du Sautoy of Oxford University, the holy grail of mathematics.
"Most mathematicians would trade their soul with Mephistopheles for a proof," he said.
There's a reason why the problem has stood for over a century. It is almost dizzyingly arcane: quite beyond simple explanation, and the candidate answers published on the internet are so intractable that they could baffle the biggest brains in the business for many months.
This year Louis de Branges 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," Professor 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", Professor du Sautoy said.
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