For completeness sake, I would like to quote GuyP of Mind Candy-fame (from the PerplexCity.com forums, 29.09.06, emphasis by me):
Riemann has always been controversial because it's so hard to solve (yes, it does require proving the Riemann hypothesis, there is no other puzzle on the card)
If anybody still has some excessive brainpower left to spend on this (besides working on the other META-puzzles), please don't let that disencourage you.
Posted: Wed Nov 29, 2006 7:06 pm
Surely if it was unprovably false then it cannot be false either...oooh my head hurts!
Posted: Wed Nov 29, 2006 2:29 pm
Fermat's was not just for cubes, but for any power greater than 2.
x^n + y^n = z^n has no real answers for any n > 2
Andrew J. Wiles proved it in the nineties, formally; he's head of the Princeton University Mathematics Department as we speak.
But, going back to the point; yes. There are four possibilities of the proavbility of the Riemann hypothesis: true, false, unprovably true, unprovably false. BUT, since being false would indicate a zero off the critical line, one must be able to find that zero, or else it's not there. Thus, it cannot be unprovably false.
True, false, or unprovably true: that is the question.
Posted: Wed Nov 29, 2006 10:45 am
Okay. I just read a book on Fermat's Last Theorem, which stated more or less the same thing, (The Theorem was that x^3+y^3=z^3 had no solutions, by the way.) that should the theorem be unprovable, it would be true, as finding a counterexample would be impossible. That should apply to the Riemann Hypothesis as well, I'd imagine. So... knock yourself out solving it. ^^ As you might know, it's soon been 150 years since the hypothesis was created.
I think you could be right Boomanda...lol. I do beleive that there must be something to this puzzle that can be input into the solve page...I have previously tried unsolvable and Five Cows LOL
Posted: Fri Nov 24, 2006 12:49 pm
Gödel's Incompleteness Theorem
As the card states, the Riemann Hypothesis is that “ The real part of any non-trivial zero of the Riemann Zeta Function is ˝.”. If that's the case, doesn't that mean that the hypothesis has to have a solution? Suppose it can't be proven or disproven. If if was possible to find "a real part of a non-trivial zero of the Riemann Zeta Function" that was NOT ˝, it would be possible to disprove it. So, if you prove that it's not possible to prove or disprove it, you effectively prove that there is no such thing as a counterexample. Hence, every "real part of a non-trivial zero of the Riemann-Zeta Function" must be ˝, as if it weren't, it would be disprovable. If every "real part of a non-trivial zero of the Riemann-Zeta Function" is ˝, the Riemann Hypothesis is correct.
If I'm not extremely mistaken, wouldn't this mean that proving the Riemann Hypothesis would be as 'simple' as proving it has no proof.
Posted: Fri Nov 24, 2006 7:45 am
has anyone tried FIVECOWS??
Spoiler (Rollover to View):
my guess would be trying something to do with secure credit card details on the internet and prime numbers...
Posted: Tue Nov 21, 2006 10:17 pm
I just had an idea but i have no idea how to test it out.
Look at the text on the card, and look at the color change near the top of the card. dark... then changes to white, right on the line where CRYPTOGRAPHY
is the first word in the white area. ... how bout we try and decrypt this like its a block of text. and see if anything pops up?
the one thing about this card. MC wrote every word. maybe they snuck something into the text.
tretretretres is the key?
Posted: Tue Nov 21, 2006 7:04 pm
we're right on both counts - either its supposed to prove the reimann hypothesis or we're looking for something else on the card. either way there is an answer, whether it be to proove the hypothesis in which case we just wait, or until we crack whatever MC want. either way if there was no answer why would there be an answer box? just MHO.
i would suggest we try and solve it another way, at least until there is a definite proof/unproof of the hypothesis by clay institute, even if it takes 10 more years... you never know how MC are thinking. it's worth points so there must be something to it...
Posted: Tue Nov 21, 2006 5:32 pm
Does all this talk imply that the attempts to solve Reimman are coming to an end
Hope not..With all the minds this collaboration has brought together, surely this will be solved one way or another...in the next 25 years maybe! LOL
Posted: Tue Nov 21, 2006 2:42 pm
Maybe Riemann was to point out that prime numbers are important in this game? But we would have figured that out ourselves eventually.
I do have trouble with the idea that this card was designed to not be solvable for points, but as it is out of print, maybe that is the correct interpretation.
Posted: Tue Nov 21, 2006 1:47 pm
While I hate to stop anyone who's having fun brainstorming on this card, I really don't think there is an answer that earns points here.
Remember, this card is from Wave 1 -- i.e. before MC had much, if any, feedback on the cards. I think they made this card as an homage to Earth's great unsolved puzzles -- they never expected any player to actually solve it. That has turned out to bother a lot of people, and I think was the reason the card was taken out of circulation.
I doubt we'll see anything like it in season two, but I think that's what happened here.
That said, I'd love to see a Zen Koan card: (from Wiki) "A monk asked Zhaozhou, 'What is the meaning of Bodhidharma's coming from the west?' Zhaozhou said, 'The cypress tree in the courtyard'." Eat that, Kate Brewster!!!
Posted: Tue Nov 21, 2006 1:15 pm
I must agree with you Aliendial, they must have some form of answer in their database solve area, and despite my best efforts, they just won't impart it to me...lol. There are thousands of people everywhere all trying to get this card solved, and thats the whole point of this game, people collaborating, communities brought together for the common good. Its possible that Mind Candy believe that whoever proves or disproves the Reiman Hypothosis will go to the Clay Institute before doing the solve, thereby giving Mind Candy the time to post up the correct solve?
Posted: Tue Nov 21, 2006 12:45 pm
basil3legs, nobody is arguing that. Except noobs who don't read anything before they post. Those still thinking about this card are brainstorming about the puzzle really being about something else on the card that hasn't been figured out yet. Because we gotta believe there's a way to earn points from this card.
Posted: Tue Nov 21, 2006 7:53 am
I still can't believe people are actually discussing how to prove Riemann to solve this card!! Do you actually believe that should you actually solve Riemann that typing it in the solution box will give a solve for the card? This would mean that they already have the solution - which they obviously don't!!
Get a grip.
If this card is actually currently solvable - i.e. there is something you can type in the answer box to get a solve - it is DEFINITELY NOT a proof of Riemann, unless they intend to make this the solve at a later date when/IF it is ever proved.
Many brilliant mathematical minds have been working on this for some time and have had no joy so do you think you can actually do better? If you do though, I doubt you will be too fussed with the solve for this card having just collected $1,000,000.00!!
I know this isn't actually that helpful but is true!!