Why is RH so difficult to prove?

[R.D. Silverman]

Originally Posted by m_f_h

2 useless comments regarding (1):
(a) This is not true for x=0.
(b) IMHO, this statement is roughly equivalent to the statement that \pi is irrational, so the proof of the latter is just hidden in the proof of the former.

:-D ! (ROTFL etc.)
I love it!

I wasn't flaming. I was simply pointing out that an opinion inserted into
a *technical* discussion is worthless unless one has knowledge of the
subject.

[devarajkandadai]

It is probable that RH will be proved only when an OR approach is made ;
a team consisting of analytical number theorists,algebraists, topologists,
programmers and perhaps a physicist jointly attack the problem.

A.K.Devaraj

[cheesehead]

Originally Posted by devarajkandadai

an OR approach

?

[Orgasmic Troll]

Originally Posted by cheesehead

?

Operations Research?
Operating Room?
Orgasmic Roll?
Optional Requirement?
Obstetrician Rhythm?
Obsequious Rigmarole?
Obstinate Restructuring?
Ovaltine Recipe?

ah HA!

Occult Rituals!!

[ewmayer]

I think the key to "understanding" that post is the word "jointly".

It's always amusing to see people who know just enough to be dangerous get fixated on the name of some way-k00l-sounding academic research field [e.g. "operations research" in this instance] and start invoking it like some mystical mantra ... "X will solve all these problems, perhaps by way of a paradigm-shifting interdisciplinary fubaristics mashup with eggsperts from Y and Z, plus a few out-of-work string theorists."

A fellow I know [in the just-wave-then-duck-your-head-look-really-busy-and-hope-he-doesn't-bend-your-ear-this-time-around category of social interactions] from the local coffee shop scene, when I once made the awful mistake of mentioning my interest in computation and number theory, got all excited and insisted on telling me how he was convinced that "linear programming" was gonna be the key to polynomial-time factorization. I tried to gently point out that he seemed to be talking about the P-time aspects of general LP, whereas factorization was an *integer* LP problem, believed to be NP-complete, to no avail - he just gave me one of those "sad old dinosaur, doesn't realize he's missing out on the new paradigm" looks and kept rattling away. Alas, not "jointly", either - I had to listen to the whole babelfest stone-cold sober.

[CRGreathouse]

Originally Posted by victor

"If I were to awaken after having slept for a thousand years, my first question would be: Has the Riemann hypothesis been proven?" - Hilbert

I've often seen this quoted, but I've never known the source. When did he say this?

[tha]

An article on current work on the Riemann Hypothesis on the website of slashdot.

[Damian]

Originally Posted by R.D. Silverman

The question itself is ridiculous. The same question may be asked of
any conjecture that has remain unproved for any moderate amount of
time. Noone knows why a theorem is hard until it is proved. Take,
for example, the Bieberbach conjecture. For a half century it was
thought to be out-of-reach until DeBrange proved it. Now it is
understandable by undergrads.

The mathematician Harold M. Edwards wrote: “One of the things which makes the Riemann Hypothesis so difficult is the fact that there is no plausibility argument, no hint of a reason, however, un-rigorous, why it should be true.”

Has anybody reviewed this proof?

[cheesehead]

Originally Posted by Damian

Has anybody reviewed this proof?

... (submitted two days ago)

http://arxiv.org/abs/0809.5120

Make an exponential transformation in the integral formulation of Riemann's zeta-function zeta(s) for Re(s) > 0. Separately, in addition make the substitution s -> 1 - s and then transform back to s again using the functional equation. Using residue calculus, we can in this way get two alternative, equivalent series expansions for zeta(s) of order N, both valid inside the "critical strip", i e for 0 < Re(s) < 1. Together, these two expansions embody important characteristics of the zeta-function in this range, and their detailed behavior as N tends to infinity can be used to prove Riemann's zeta-hypothesis that the nontrivial zeros of the zeta-function must all have real part 1/2.

[Kevin]

Originally Posted by cheesehead

... (submitted two days ago)

http://arxiv.org/abs/0809.5120

http://primes.utm.edu/notes/crackpot.html