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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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Sir Atiyah's conference on the Riemann Hypothesis
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(Score: 2) by theluggage on Saturday September 22 2018, @11:53PM (1 child)
That actually was my point, in response to the G.P. arguing that you couldn't find a counter-example: if Riemann makes a falsifiable prediction (like there are "10 primes in this range") then potentially it could be disproved by counter-example (e.g. finding 11 primes in the range). If it couldn't make a falsifiable prediction (i.e. it only said where a prime is likely to be) then it would be no more then a rule of thumb that couldn't guarantee success - which would have made the rest of the discussion moot.
You can already exclude those areas from your search by simply assuming that Riemann is true on the basis that its been around since the 19th century and nobody has managed to disprove it. An algorithm that will almost certainly crack a key in a week is better than an algorithm that is guaranteed to crack it in a year (or whatever the relative time spans are).
No, if you want to be deep down practical you realise that it could be years before everybody adopts the current recommendation and you usually don't have any control over what encryption other people use. (God, if only other people even knew how to generate a key and paste the public part into an email or web form...)
(Score: 2) by DrkShadow on Sunday September 23 2018, @01:47AM
Unsure if it's been said, but per the original comment's question.. the reason that having a proof of Reimann's hypothesis is that now you can be sure you fully covered a given area. If you _assumed_ it, but it was taking an awful long time to search for the solution while skipping chunks per Reimann, you can't be sure that you covered all the possible primes in an area -- whereas with a proof, you can be sure, even without checking every last number.