Riemann Hypothesis dilemma

My question is quite simple. I understand the basis of Riemann Hypothesis and general idea, what I don't understand is why it hasn't been proven yet. What part of the hypothesis that causes such a problem, that apparently makes it impossible to prove. When Hilbert gave his speech in 1900 he thought the "Prime Number problem" would be squared out and proved in a few years after his famous presentation of 23 ongoing dilemmas, so what is it, that prevents mathmaticians from prooving it.
I'd like to  know where exactly or what causes the proove of the hypothesis to be so difficult. And also if anyone know how Riemann derived his zeta function. I know he took the basic concept from Euler', but how he figure out what it suppose to be that I don't know.
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grg99Connect With a Mentor Commented:
Dunno, just seems likely to be a difficult question as it's over 100yrs old and though there's lots of hints that it's true for around 40% of the tine, the remaining parts are being quite stubborn.

A whole bunch of RH links at:


nicholassolutionsConnect With a Mentor Commented:
Yo might find this page interesting:
This paper also provides some very good information:

And this page offers multiple derivations of the zeta function:

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lombardpConnect With a Mentor Commented:
Here is the recent (June 2004) "Apology for the proof of the Riemann hypothesis (in pdf format)."


The Riemann Hypothesis?  Oh, that's easy. You just have to
mal4macConnect With a Mentor Commented:
Looks like you need to do some reading. Roger Penrose does a swift canter past the Riemann hypothesis(and just about everything else in Maths & Physics) in his incredible new book:


His discussion is on p.133 and he gives lots of references on p.134 note 7.8. He calls it "perhaps the  most important unsolved mathematical problem today".
klepaAuthor Commented:

let me spend some time reading everything. Thanks for reply'. I'll give everyone points once I'll get a clear picture. Unless I'll just confuse myself to death and will have to dedicate my life searching for the great proof of Riemann Hypothesis.
You'll probably have to dedicate your life so no points for us :-(
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