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# A ‘simple’ solution to a 160-year-old problem could net Cambridge mathematician a \$1 million prize A simple solution to a 160-year-old problem could net one retired University of Cambridge mathematician a \$1 million (£760,000) prize.

Professor Michael Atiyah claims he has proof of the Riemann hypothesis – a way to map prime numbers, which can only be divided by one and themselves.

The 90-year-old suggested his ‘simple proof’ would likely ruffle feathers among his fellow mathematicians.

Some academics have expressed doubts, with one highlighting that many great minds have seemingly solved the problem before, only for other researchers to pick holes in their proof later down the line.

A simple solution to a 160-year-old problem could net one retired University of Cambridge mathematician a \$1 million (£760,000) prize. Professor Michael Atiyah (file photo) claims he has proof of the Riemann hypothesis – a way to map prime numbers

The Riemann hypothesis was first poised in 1859 by German mathematician G.F.B Riemann.

He proposed that the distribution of these numbers is very similar to a function called the Riemann Zeta Function: ζ(s) = 1/1s + 1/2s + 1/3s + 1/4s + …. up to infinity.

If this hypothesis is proved correct it could provide a neat way for mathematicians to find new prime numbers, which are useful for everything from computer encryption to the programming of super computers.

Scientists have spent 160 years attempting to prove Riemann’s formula is correct, but all attempts have failed so far.

Professor Atiyah, who spent who spent most of his academic career at Cambridge, unveiled his attempt at the Heidelberg Laureate Forum in Germany this week.

He said: ‘Solve the Riemann hypothesis and you become famous. If you are famous already, you become infamous. The Riemann hypothesis was first poised in 1859 by German mathematician G.F.B Riemann. He proposed that the distribution of these numbers is very similar to a function called the Riemann Zeta Function: ζ(s) = 1/1s + 1/2s + 1/3s + 1/4s + …. up to infinity (stock image)

### WHAT IS THE RIEMANN HYPOTHESIS?

The Riemann hypothesis was first poised in 1859 by German mathematician G.F.B Riemann.

It is based around prime numbers – those that can only be divided by themselves and one.

Riemann proposed that the distribution of these numbers is very similar to a function called the Riemann Zeta Function:

ζ(s) = 1/1s + 1/2s + 1/3s + 1/4s + …. up to infinity.

If this hypothesis is proved correct it could provide a neat way for mathematicians to find new prime numbers.

Primes are useful for everything from computer encryption to the programming of super computers.

‘Nobody believes any proof of the Riemann hypothesis because it is so difficult.

‘Nobody has proved it, so why should anybody prove it now? Unless, of course, you have a totally new idea.’

The academic says he combined the work of two mathematicians for his proof – 2oth century visionaries John von Neumann and Friedrich Hirzebruch.

By combining their insights on prime numbers, Professor Atiyah claims to have reached a logical contradiction, suggesting the hypothesis is correct.

‘It looks miraculous, ‘but I claim that all the hard work was done 70 years ago,’ he said.

The hypothesis is ranked among the Clay Mathematics Institute’s the six unsolved Clay Millennium Problems.

A correct solution would earn its author a \$1 million (£760,000) prize.

But doubts have been raised over the legitimacy of Professor Atiyah’s solution.

His presentation was made up of just a few slides, in which the academic claimed to have found a connection with the fine structure constant.

The physical parameter describes the interaction between light and matter, and many academics have called its existence into question.

‘The Riemann hypothesis is a notoriously difficult problem,’ Dr Nicholas Jackson at Warwick University told New Scientist.

‘Lots of other top-rate mathematicians have nearly but not quite managed to prove it over the years, only for a subtle flaw in the proof to become apparent.’