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#1 2006-07-28 05:40:19

se7en
Member
Registered: 2005-12-25
Posts: 28

Riemann hypothesis

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basically I just asked for an explanation of the Riemann hypothesis

Last edited by se7en (2006-07-31 05:53:58)

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#2 2006-07-28 06:39:54

ben
Member
Registered: 2006-07-12
Posts: 106

Re: Riemann hypothesis

se7en wrote:

and now I want to prove the Riemann hypothesis. The problem is, I don't really even understand the Riemann hypothesis. smile

Kinda stuffed, aren't you? I would say it's  a tall order, to put it mildy, to prove a hypothesis you don't understand.

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#3 2006-07-28 06:48:41

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: Riemann hypothesis

Can you show us the proofs for Fermat's Last Theorem and the Goldbach conjecture?

Edit: Oh, and do you understand what the Riemann Zeta Function is?


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#4 2006-07-28 07:24:40

se7en
Member
Registered: 2005-12-25
Posts: 28

Re: Riemann hypothesis

post deleted

Last edited by se7en (2006-07-31 05:54:51)

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#5 2006-07-28 08:16:28

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: Riemann hypothesis

Fermat's Last Theorem isn't on that list.  Why can't you show that one?

Most math, such as Fermat's Last Theorem and the Golbach Conjecture, is not about plugging numbers in at all.  So your description of a way to solve any algebra problem by an algorithm is nonsensical.  I'd still love to hear it though.

And besides, if you told us it'd be on these pages.  Even if MathIsFun took down the website, they are cached by google and no one can change that.  Furthermore, you can save it yourself.

But as I said, Fermat isn't on the list for prizes and it's already been solved.  So please, do show us your proof.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#6 2006-07-28 08:17:33

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: Riemann hypothesis

Oh, and I forgot, if such an algorthm is is valid, you would be the most famous mathimatician ever.  Money isn't really worth much when you have the whole world and all of history at your feet.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#7 2006-07-28 08:19:38

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: Riemann hypothesis

As for the Riemann hypothesis:

Let a be a complex number such that a is not a negative even number.

If zeta(a) = 0, then Re(a) = 1/2, or rather, the real part of a is 1/2.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#8 2006-07-28 08:42:57

numen
Member
Registered: 2006-05-03
Posts: 115

Re: Riemann hypothesis

Ahh, one of the Se7en (7) millenium prize problems...

So you plan to solve them all, eh? Best of luck to you, you'll most definitely need it wink


Bang postponed. Not big enough. Reboot.

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#9 2006-07-28 08:54:42

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: Riemann hypothesis

Well, se7en has been here for over 7 months (and less than 8, so I didn't just use that number to be funny), so I think his/her username and the number of open problems is just a coincidence.

Edit:

Hitchhiker's Guide to the galaxy: [taking place an a completely foreign world] Zaphod Beeblebrox was on his way from the tiny spaceport on Easter Island (the name was an entirely meaningless coincidence - in Galacticspeke, easter means small flat and light brown) to the Heart of Gold island, which by another meaningless coincidence was called France.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#10 2006-07-28 09:44:28

Zhylliolom
Real Member
Registered: 2005-09-05
Posts: 412

Re: Riemann hypothesis

He may not want to show the proof of Fermat's Last Theorem because he says his algorithm can solve all of these problems. So if someone sees the algorithm in the proof he posts for Fermat, they could take it and adapt it to the Goldbach Conjecture, Riemann Hypothesis, and other big problems.

I'm sorry, but I'm very reluctant to believe all of this. If you have such an algorithm, it must be extremely creative and original to be on a high school level (I assume it's there because you ask for the Riemann hypothesis to be explained in "terms a high school student can understand") and not have ever been caught by the countless mathematicians who have lived ever since our "high school level" mathematics have been around. I mean, just imagine how many mathematicians there have been who have tried to find a simple proof to Fermat's Last Theorem. If you've really managed to prove these great problems, big congratulations to you. I've been working on them this summer but I haven't gotten too far. I was hoping to solve mabye one, many moons from now... maybe if they do get solved, I can still prove them in another way. Man, if this is all true, I guess my chances for mathematical fame in this lifetime are gone, everyone in this era would instantly be downsized, and the greatest problems will have already been solved, so what could I do after that!?

Is Ricky's explaination good for you? He laid out the basic hypothesis for you, but we don't know how much you need to know for you to be able to use this algorithm.

(Hey Ricky, congratulations on post 1000)

Edit: He has 7 posts too, this is pretty insane. April 1st was a while ago though.

Last edited by Zhylliolom (2006-07-28 09:45:18)

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#11 2006-07-28 09:52:16

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: Riemann hypothesis

(Hey Ricky, congratulations on post 1000)

I noticed I was up to 995 this morning, but I had completely forgotten about it till now. Thanks!  And it just had to be my luck that I quoted HHGG in my 1000th post... Guess I'll just have to wait till my 10000th post to make it a more meaningful one.

I have a distinct feeling, since se7en is in highschool, that (s)he does not quite know what it means to rigorously prove something in math.  I know I sure as heck didn't.  So what I would like is for se7en to prove the two following problem, and please, no one help him:

1.  Prove that if a divides c and b divides c, then ab divides c.

2.  Prove that if gcd(a, b) = 1, then lcm(a, b) = ab.

My reasoning behind this is that if you understand what it takes to prove these two problems, then you understand how hard it is to prove something like the Goldbach conjecture.

Oh, and se7en, if you are willing to post your Fermat proof, you can just ignore the above.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#12 2006-07-28 10:17:16

Zhylliolom
Real Member
Registered: 2005-09-05
Posts: 412

Re: Riemann hypothesis

I was hoping you'd make it this morning, I was waiting in the shadows ever since I saw you at 989 a day or two ago, and I saw you were at 995 thi morning too.

I'm a lowly high schooler too, and I have the same feelings you do, Ricky. They don't emphasize proof at all here. Even in mathematics competitions they're real light, I can do a terrible "proof" (sometimes I don't even feel like it shows anything at all, but I have to submit something) and they're perfectly fine with it. Then when I started reading up on vector spaces and topology and the like, I wasn't breezing through, as there aren't as many "exercises and problems" in these topics as there are "prove theorem 6.2.7". It's a lot different from calculus or "high school math", where you mainly solve exercises but rarely prove anything (I don't think I've ever had to do a real proof for any math assignment). Anyway, I guess the idea here is that if se7en is a high school student, it is unlikely that he has much experience with proofs unless he has unique or special math classes, or he does them in his private studies.

Just a brief semi-off-topic question while I still have it in my head: does anyone know of a good book that is a good aid in constructing proofs? Kind of like a guide to proving theorems. I've never been formally taught this kind of stuff and I find it pretty essential. I think I'll go look up some stuff on Wikipedia and see what I need to learn.

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#13 2006-07-28 11:55:56

George,Y
Member
Registered: 2006-03-12
Posts: 1,306

Re: Riemann hypothesis

I would rather trust him.  I  derived the principle of Bayesian Statistic by Bayesian theorem once, only to find there were more books published than my textbooks.

Zhyllioliom, you need a Logic book or a Critical Thinking book. And if you are not a firstborn, bonus.

Just recall Cantor was a medival logic studier before he constructed Real Numbers.


X'(y-Xβ)=0

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#14 2006-07-28 12:07:13

George,Y
Member
Registered: 2006-03-12
Posts: 1,306

Re: Riemann hypothesis

By the way, what is Ferman's last theorem?

Goldbach conjecture???
I think it is something familiar to me, since a mathematician of my country has proved a part of it, or made some progress.
Does it have any relationship with a hypothesis concerning complex numbers?

Nonetheless, just inform you everyone here that recently a philosopher of my country claimed to have proved 4 Color Theorem within 3 sheets of paper. I'd rather believe him, for
1 He claimed only 1 proof.
2 He claimed using his "advanced" logic
3 the two above suggests he at least  did work to prove, though probably incorrectly.


X'(y-Xβ)=0

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#15 2006-07-28 12:19:20

Zhylliolom
Real Member
Registered: 2005-09-05
Posts: 412

Re: Riemann hypothesis

Fermat's Last Theorem: For n ≥ 2, x[sup]n[/sup] + y[sup]n[/sup] = z[sup]n[/sup] has no solutions for nonzero integers x, y, and z. Looks simple, but it's extremely tricky to prove. I'll include a copy of the only proof currently in existence. It'll make your head spin.

The Wiles paper: http://math.stanford.edu/~lekheng/flt/wiles.pdf

Goldbach Conjecture: Every even integer greater than 2 can be written as the sum of two primes. Once again, a very simple and easily understood statement, but to this day nobody has supplied a correct proof.

That would be incredible if someone solved the Four Color Theorem in such a concise manner. I was actually reading up on it today, and I have the following facts to offer: the first proof of the theorem was a proof by exhaustion with 1,936 cases. Today the lowest is 633 cases.

Edit: Sure, I've also derived results independently from my studies of mathematics only to later discover that somebody else had already established such discoveries many years before me, but these problems are on a completely different level. Mathematicians have been struggling with them for hundreds of years. It is highly unlikely that these problems would be solvable on a high school level, and even less likely that the same process could be used to prove all three of these legendary problems. But there's nothing we can really do yet; until we see the proofs we have no idea whether the algorithm or its application to these problems is correct, so for now all we're doing is assuming the most reasonable case. Anything is possible, but distinct events are on varying levels of possibility.

Last edited by Zhylliolom (2006-07-28 13:03:51)

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#16 2006-07-28 22:51:46

se7en
Member
Registered: 2005-12-25
Posts: 28

Re: Riemann hypothesis

post deleted

Last edited by se7en (2006-07-31 05:56:11)

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#17 2006-07-29 04:35:16

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: Riemann hypothesis

I have to say that I don't believe a word you say, but I eagerly await that day.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#18 2006-07-29 05:05:25

ben
Member
Registered: 2006-07-12
Posts: 106

Re: Riemann hypothesis

se7en wrote:

Ricky: Sorry, as Zhylliolom mentioned, if I post any of my proofs I'll be revealing my METHOD of proof and someone could take it and use it to prove the Riemann hypothesis, and basically every other problem in maths, and I'd be left with nothing to prove.

My poor young friend, you have a very warped view of the way the academic world works. For your information, it is not a market place. If you really have something (my doubts are even stronger that Ricky's) the custom among academics is to share and be generously congratulated by those with the ability to recognize the worth of your work.

I am cautious about doing that until I've proved at least one of the millenium prize problems. (I want that million Dollar prize. )

This may be an acceptable motivation in your street, but I can absolutely assure you that you would have to travel a long way to find an academic who shared it.

Incidentally, as what I have is an actual ALGORITHM for proving stuff, proving any given proposition reduces to a purely mechanical procedure. Something that even a computer program could carry out. Just imagine the possibilities! Never again will there be open questions in mathematics.

This is just silly. The 3 problems you claim to be solving (Fermat, Golbach and Riemann) are all problems in number theory. Do you really think that proofs in number theory carry over to, say topology, manifold theory, Lie algebras, differential forms, exterior algebra, Clifford algebra...? Because they don't.

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#19 2006-07-29 09:23:02

Zhylliolom
Real Member
Registered: 2005-09-05
Posts: 412

Re: Riemann hypothesis

Ricky wrote:

I have to say that I don't believe a word you say, but I eagerly await that day.

Eagerly await the day there's no open questions in mathematics? What? I don't know if that's what you're referring to, but I wouldn't like a world like that. I don't think it's very possible either, so I guess I don't have anything to worry about. It would be a sad day when us mathematicians are left with nothing to prove. If I can't get a job in 10 years after going through college for math because R-66Y can not only calculate faster than me but prove anything and do it without asking for a salary, I'll be pretty upset.

ben wrote:

...topology, manifold theory, Lie algebras, differential forms, exterior algebra, Clifford algebra...

I love it when you talk dirty wink. But you're right, this thing would have to be more than insanely good to be able to solve ANY problem in ANY mathematical field. It's already impossible enough that it could solve 3 of the greatest problems in history related to number theory.

Last edited by Zhylliolom (2006-07-29 09:23:52)

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#20 2006-07-29 23:15:56

se7en
Member
Registered: 2005-12-25
Posts: 28

Re: Riemann hypothesis

post deleted

Last edited by se7en (2006-07-31 05:57:24)

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#21 2006-07-30 00:19:42

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,529

Re: Riemann hypothesis

Good on you, se7en.

It is normal for people to be skeptical in the mathematical world. Many "proofs" come unstuck. And many times people "discover" things that have been discovered many times before. But it is important to give it a try, and if nothing else your knowledge will grow and that can lead to great things. And dicoveries DO get made, of course.

(I have a couple of theories in computing I have yet to expand on ... I should work on them one day)

And the world of Science is famous for being conservative. Einstein's most famous paper on special relativity was titled "On the Electrodynamics of Moving Bodies".

Also Crick and Watson's paper on DNA was titled "Molecular Structure of Nucleic Acids: A Structure for Deoxyribose Nucleic Acid" which contained the famous line "It has not escaped our notice that the specific pairing we have postulated immediately suggests a possible copying mechanism for the genetic material."

Anyway, Riemann Hypothesis on wikipedia: http://en.wikipedia.org/wiki/Riemann_hypothesis


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#22 2006-07-30 00:24:31

se7en
Member
Registered: 2005-12-25
Posts: 28

Re: Riemann hypothesis

post deleted

Last edited by se7en (2006-07-31 05:58:09)

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#23 2006-07-30 02:17:38

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: Riemann hypothesis

Computer applications exist for expressing and solving problems in all the fields of mathematics you have mentioned, and indeed in all of mathematics in its entirety, and as you probably know, computers perform operations such as addition, subtraction, and so on, in terms of the logical operations AND, OR, XOR and NOT.

Computers don't solve problems.  They run solutions.

But anyway, the point is that a problem in Clifford algebra could be expressed in terms of AND, OR, XOR and NOT. (Actually, you could just use AND and NOT. We say that AND and NOT forms a FUNCTIONALLY COMPLETE SET, and this is known as the interdefinability of the logical operations.)

Actually, NAND is all you really need.

Any problem in maths could be expressed in terms of the logical operations.

Can you show that to us?  For example, ohh, let's say, the Poincare Conjecture?

Eagerly await the day there's no open questions in mathematics? What? I don't know if that's what you're referring to, but I wouldn't like a world like that. I don't think it's very possible either, so I guess I don't have anything to worry about. It would be a sad day when us mathematicians are left with nothing to prove. If I can't get a job in 10 years after going through college for math because R-66Y can not only calculate faster than me but prove anything and do it without asking for a salary, I'll be pretty upset.

If there comes a time when I get the choice between making a key discovery in math that will in the end help the world, and keeping my job, I'm going for the discovery.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#24 2006-07-30 03:03:53

se7en
Member
Registered: 2005-12-25
Posts: 28

Re: Riemann hypothesis

post deleted

Last edited by se7en (2006-07-31 05:59:15)

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#25 2006-07-30 03:08:12

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: Riemann hypothesis

Fine, then how about this simple one:

If a | b and b | c, then a | c.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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