Wednesday, October 10, 2018

Famed mathematician claims proof of 160-year-old Riemann hypothesis

Michael Atiyah

This is great news and i have scant doubt that he has the right of it. It will take a lot of work by several others to properly confirm this work so we have to wait a while.
I am familiar with the hypothesis itself having met a fellow who had obsessed over it.  It is an interesting problem and its solution is likely interesting as well.
I try to avoid problems beyond the scope of thousands, but i did do a drive on Fermat's Theorem, not to solve it but to understand why he was excited.   Turns out it produces a marvelous ordering of Pythagorean triples which also sets the stage for advances in two variable problems order n.  This is important in tackling the ultimate theorem of algebra for order n or at least i hope so.  The human efforts would take months if not years. I am twenty pages in on that particular task.

all good.

Famed mathematician claims proof of 160-year-old Riemann hypothesis

21 September 2018

Michael Atiyah claims to have found a proof of the Riemann hypothesis

James Glossop/The Times/News Syndication

By Gilead Amit​

One of the most important unsolved problems in mathematics may have been solved, retired mathematician Michael Atiyah is set to claim on Monday. In a talk at the Heidelberg Laureate Forum in Germany, Atiyah will present what he refers to as a “simple proof” of the Riemann hypothesis, a problem which has eluded mathematicians for almost 160 years.

Born in 1929, Atiyah is one of the UK’s most eminent mathematical figures, having received the two awards often referred to as the Nobel prizes of mathematics, the Fields medal and the Abel Prize. He also, at various times, served as president of the London Mathematical Society, the Royal Society and the Royal Society of Edinburgh.

If a solution to the Riemann hypothesis is confirmed, it would be big news. Among other things, the hypothesis is intimately connected to the distribution of prime numbers, those indivisible by any whole number other than themselves and one. If the hypothesis is proven to be correct, mathematicians would be armed with a map to the location of all such prime numbers, a As one of the six unsolved Clay Millennium Problems, any solution would also be eligible for a $1 million prize. The prestige has tempted many mathematicians over the years, none of which has yet been awarded the prize.

Atiyah is well aware of this history of failure. “Nobody believes any proof of the Riemann hypothesis, let alone a proof by someone who’s 90,” he says, but he hopes his presentation will convince his critics.

In it, he pays tribute to the work of two great 20th century mathematicians, John von Neumann and Friedrich Hirzebruch, whose developments he claims laid the foundations for his own proposed proof. “It fell into my lap, I had to pick it up,” he says.

New Scientist contacted a number of mathematicians to comment on the claimed proof, but all of them declined. Atiyah has produced a number of papers in recent years making remarkable claims which have so far failed to convince his peers.

“People say ‘we know mathematicians do all their best work before they’re 40’”, says Atiyah. “I’m trying to show them that they’re wrong. That I can do something when I’m 90.”

No comments: