If you’ve been trying to solve the Riemann hypothesis — and, really, who hasn’t? — you can stop now. A Scottish mathematician claims to have done it.
It’s a 160-year-old math problem.
Prime numbers don’t follow a regular pattern.
German mathematician Bernhard Riemann, however, found that the frequency of the prime numbers followed this equation, according to the Clay Mathematics Institute:
ζ(s) = 1 + 1/2s + 1/3s + 1/4s + …
called the Riemann Zeta function. The Riemann hypothesis asserts that all interesting solutions of the equation
ζ(s) = 0
lie on a certain vertical straight line.
This has been checked for the first 10,000,000,000,000 solutions. A proof that it is true for every interesting solution would shed light on many of the mysteries surrounding the distribution of prime numbers.
We’re told this is one of math’s great unsolved problems. We’ll take the math world’s word for it. The institute has offered $1 million to whomever can solve it.
So yesterday, Michael Atiyah, mathematician emeritus at the University of Edinburgh, stepped forward to say he’s solved it, the magazine “Science” says.
This is the sort of thing that makes mathematicians feel stupid. Observe:
But the math world is rough and tumble and Atiyah is taking a tremendous beating for an 89-year-old man. The magazine writes:
For his part, Atiyah seems unfazed. “The audience there has fearlessly bright youngsters and well-informed golden oldies,” Atiyah wrote in an email before his presentation.
“I am throwing myself to the lions. I hope to emerge unscathed.” According to Atiyah, word of his proof and copies of his papers circulated online, prompting him to agree to the presentation.
He says in an interview that despite criticism, his work lays down a concrete basis for proving not only the Riemann hypothesis, but other unproven problems in mathematics. “People will complain and grumble,” Atiyah says, “but that’s because they’re resistant to the idea that an old man might have come up with an entirely new method.”
In his presentation, Atiyah devoted only a handful of slides to his proof, spending the majority of his time discussing the contributions of two 20th century mathematicians, John von Neumann and Friedrich Hirzebruch, on which he said his proof was based.
The crux of Atiyah’s proof depends on a quantity in physics called the fine structure constant, which describes the strength and nature of electromagnetic interaction between charged particles. By describing this constant using a relatively obscure relationship known as the Todd function, Atiyah claimed to be able to prove the Riemann hypothesis by contradiction.
It’s not the first time someone has claimed to solve the problem, but previous declarations have proven untrue.