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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 breakthrough with far-reaching repercussions in the field.
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(Score: 3, Interesting) by khallow on Saturday September 22 2018, @11:54AM
I guess Atiyah is referring to factorization of von Neumann algebras [wikipedia.org], the Hirzebruch-Riemann-Roch [wikipedia.org] theorem (which Atiyah himself, along with Isadore Singer, provided [wikipedia.org] a big generalization of about nine years later), and maybe Dirac's theory of the electron, which would be the first quantum field theory.
I don't know what would be the "radically new approach" using those particular tools (the newest is after all over 60 years old). Perhaps there are operators over some sort of fields (perhaps in both senses of the word, both the quantum field theory and algebraic fields which are very different objects with a name conflict) that happen to have characteristics that prove Riemann's hypothesis. At the least, the study of carefully contrived operators has been one of the approaches for trying to solve the hypothesis.
As usual with this sort of thing, the even bigger news may be what else can be done with what has been discovered and it may still not prove the hypothesis. We'll see.