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posted by takyon on Saturday September 22 2018, @06:35AM   Printer-friendly
from the non-trivial dept.

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.

New Scientist

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Sir Atiyah's conference on the Riemann Hypothesis

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  • (Score: 3, Interesting) by FatPhil on Sunday September 23 2018, @01:28AM (1 child)

    by FatPhil (863) <pc-soylentNO@SPAMasdf.fi> on Sunday September 23 2018, @01:28AM (#738721) Homepage
    Cracking PK does not involve any "searching".

    Truthiness of *RH does not affect crypto in any way, shape, or form. Some computational bounds when it comes to *proof* of primality are defined contingent on *RH, but the reality is that you don't need *proof* of primality, you just need a number that seems to behave like a prime, and these bounds are irrelevant once P(you're wrong about a number's primality) < P(attacker can guess your factors). That, and you can use Maurer's method to generate easily-provable primes, if you really care about proof, which you shouldn't. Or just not use a M-R test for the proof stage - maybe ECPP or APRCL instead, depending on the sizes involved.

    The amount of wrongthink in this subthread is quite painful to read. I'm not picking on you, the people you're responding too are just as wrong in other ways. For more info, just read C&P PN:ACP.
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  • (Score: 2) by theluggage on Sunday September 23 2018, @02:28PM

    by theluggage (1797) on Sunday September 23 2018, @02:28PM (#738847)

    The amount of wrongthink in this subthread is quite painful to read. I'm not picking on you, the people you're responding too are just as wrong in other ways. For more info, just read C&P PN:ACP.

    My comments were based on assertions made by other posters (I did try to make liberal use of conditional phrases like "If Riemann predicts such-and-such then...").

    What I was really challenging was the proposition that (Hypothesis X) could be used to greatly optimise a real-world application but only after it had been mathematically proven... despite (X) having survived so much scrutiny that the risk of it being false was tiny c.f. the benefits of assuming its truth. That's not really a mathematical issue and doesn't depend on the details of (X).

    Of course, if, as you're claiming, RH has no significant application to crypto then, well, garbage in - garbage out :-) - but whether or not other posters' assertions about the mathematics of RH were true, their application those assertions it to the real world was flawed. Proof of RH would be of huge mathematical significance, but even if RH were useful for crypto, it would already have been useful for crypto for years.

    There's a sort of argument that occurs when A is challenging the assumptions made by B in applying a mathematical principle to a practical problem, but B responds as if A were attacking the mathematics itself...