Riemann Hypothesis Re: Friendly AI

[Jeff Bone]

rbfar@ebuilt.com wrote:

> What's the Reimann Hypothesis

BTW, my bad for mispelling "Riemann" in the original subject line.

Hard to discuss with any specificity in ASCII.  ;-)  At heart it's a conjecture
about the frequency distribution of the primes.  [1] below is the Clay Math
Institute page describing the problem in sketchy terms, and a much better formal
description in PDF form can be had off that page at [2].  The interesting thing
about RH is what it tells us about the primes, if true.  The implications are
broad, with applications in information theory, cryptology, quantum mechanics,
and chaos theory.  In this sense, it's much more interesting (IMO) than Fermat's
Last Theorem.

For whatever reason, "proving the Riemann Hypothesis by brute force" is
sometimes used --- as by Eli, but certainly not only by him --- as an example of
an intractable problem, because it would require unbounded resources and time.
As such, it's not particularly more illustrative of intractability than simply
saying "compute all the primes."  Obviously, an open-ended problem.  However,
clearly we can speak *about*, analyze, manipulate, possibly even prove RH
without literally producing all solutions to Zeta(s) = 0.  Indeed, we *always*
do.

jb

[1] http://www.claymath.org/prizeproblems/riemann.htm
[2] http://www.claymath.org/prizeproblems/riemann.pdf