Proof of the Riemann Hypothesis

In summary, there are multiple attempts at proving the Riemann Hypothesis, including one recent paper that was withdrawn due to an error. Some experts in the field have doubts about the approaches being taken, while others believe there may be something to be gained from them.
  • #1
Count Iblis
1,863
8
http://arxiv.org/abs/0806.0892"
 
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  • #2
Count Iblis said:
http://arxiv.org/abs/0806.0892"
... we may have proved the Riemann Hypothesis...​
I confess if they aren't even convinced, I find it hard to be optimistic.
 
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  • #3
Crackpots don't doubt themselves, so this guy passes the crackpot test.
 
  • #4
I wish I could understand it better even with many years of college math and wikipedia
 
  • #5
perhaps he tries to be humble... the positivity 'test' of the double integral given by Polya seems correct , perhaps an expert of number theory should take a look at this paper
 
  • #6
Dragonfall said:
Crackpots don't doubt themselves, so this guy passes the crackpot test.

Did Wiles also pass the Crackpot test when he announced he found the proof of Fermat's theorem, only to discover later that there was a fatal flaw in it [which he was able to fix later at the very moment when he was taking a final look to understand better why he had faled and why he would not be able to succeed (making it easier to put the matter to rest in his mind)].

Or does the Crackpot test itself pass the Crackpot test :rofl:
 
  • #7
Count Iblis said:
Did Wiles also pass the Crackpot test when he announced he found the proof of Fermat's theorem, only to discover later that there was a fatal flaw in it [which he was able to fix later at the very moment when he was taking a final look to understand better why he had faled and why he would not be able to succeed (making it easier to put the matter to rest in his mind)].

Or does the Crackpot test itself pass the Crackpot test :rofl:

you pass the crackpot test but fail the reading comprehension test. to pass the crackpot test is to not be a crackpot. you passed since you have doubts.
 
  • #8
Hurkyl said:
I confess if they aren't even convinced, I find it hard to be optimistic.
I suppose this is a catch-22, for if they were convinced, I'd generally be even less optimistic. :smile:
 
  • #9
When asked "what if" his general theory of relativity had been disproven by experiment, Albert Einstein replied: "Then I would feel sorry for the good Lord. The theory is correct."

Sounds pretty self-assured to me, but he was no crackpot.
 
  • #11
Good lord, that's a hell'a'va proof he has there. I wish I understood the half of it (I barely understand the zeta function by itself...) What do you fella's make of it?
 
  • #12
Just a gut feeling that none of them are even close. Of course I know nothing either.
 
  • #14
Well, far be it for us to question a Fields medalist.

EDIT: Ok I applaud the effort of this auto-keyword-link thing, but this has gone too far!
 
  • #15
Dragonfall said:
Well, far be it for us to question a Fields medalist.

EDIT: Ok I applaud the effort of this auto-keyword-link thing, but this has gone too far!

Heh, yeah. Maybe we can have a list of stop-phrases?
 
  • #16

1. What is the Riemann Hypothesis?

The Riemann Hypothesis is one of the most famous unsolved problems in mathematics. It was proposed by the German mathematician Bernhard Riemann in 1859 and states that all non-trivial zeros of the Riemann zeta function lie on the critical line with real part equal to 1/2.

2. Why is proving the Riemann Hypothesis important?

Proving the Riemann Hypothesis would have significant implications in number theory and other areas of mathematics. It would also lead to a better understanding of the distribution of prime numbers and potentially reveal connections between different branches of mathematics.

3. What progress has been made towards proving the Riemann Hypothesis?

Many mathematicians have tried to prove the Riemann Hypothesis over the years, but it remains unsolved. However, there have been some notable progress and partial results, such as the work of Russian mathematician Aleksandr Gelfond in the 1930s and the proof of the Prime Number Theorem by Jacques Hadamard and Charles Jean de la Vallée Poussin in 1896.

4. What challenges are faced in proving the Riemann Hypothesis?

The main challenge in proving the Riemann Hypothesis is that it requires a deep understanding of complex analysis and number theory. It also requires creative and innovative thinking, as well as perseverance, as it has withstood many attempts at proof over the years.

5. Is there a reward for proving the Riemann Hypothesis?

As with most unsolved problems in mathematics, there is no monetary reward for proving the Riemann Hypothesis. However, the prestige and recognition from solving one of the most famous and challenging problems in mathematics would be a significant reward for any mathematician.

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