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, Informative) by ants_in_pants on Sunday September 23 2018, @12:57AM (1 child)
the fastest known probabalistic primality test(which is what's relevant here) is very likely correct independent of RH. I think it becomes always correct if RH, but I don't know the details.
Faster primality testing wouldn't make it easier to factor 2-large-prime-factor numbers. Primality testing takes the same asymptotic time even if you know every single prime number.
-Love, ants_in_pants
(Score: 2) by ants_in_pants on Sunday September 23 2018, @01:00AM
Factorization, not primes, in that last sentence there. Sorry.
-Love, ants_in_pants