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.

On the other hand, if somebody has already sorted out the so-called Poincaré conjecture, then scientists will understand something profound about the nature of spacetime, experts told the British Association science festival in Exeter yesterday.

Both problems have stood for a century or more. Each is almost dizzyingly arcane: the problems themselves are 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.

They are two of the seven “millennium problems” and four years ago the Clay Mathematics Institute in the US offered $1m (£563,000) to anyone who could solve even one of these seven. The hypothesis formulated by Georg Friedrich Bernhard Riemann in 1859, according to Marcus du Sautoy of Oxford University, is the holy grail of mathematics. “Most mathematicians would trade their soul with Mephistopheles for a proof,” he said.

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.

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