[math-fun] A (non-)proof of the Collatz 3n+1 problem.
Dear funsters, Georg Fischer has an attempt of a proof for the Collatz 3n+1 problem online here: http://www.teherba.org/index.php/OEIS/3x%2B1_Problem He suspects that it contains a flaw, hence refrains from contacting any big-wigs. With his permission I'd like to ask on this list what the problem may be. Any takers? Georg will certainly add the reason for the invalidity of his proof as soon as someone points it out. Best regards, jj
Dear Joerg, I think Claim C8 is unproved: I do not see why a tree cannot attach to itself (and thereby form a cycle). Everything up to that point, as far as I can tell, is valid. Best wishes, Adam P. Goucher
Sent: Monday, October 15, 2018 at 2:23 PM From: "Joerg Arndt" <arndt@jjj.de> To: math-fun <math-fun@mailman.xmission.com> Subject: [math-fun] A (non-)proof of the Collatz 3n+1 problem.
Dear funsters, Georg Fischer has an attempt of a proof for the Collatz 3n+1 problem online here: http://www.teherba.org/index.php/OEIS/3x%2B1_Problem He suspects that it contains a flaw, hence refrains from contacting any big-wigs. With his permission I'd like to ask on this list what the problem may be. Any takers?
Georg will certainly add the reason for the invalidity of his proof as soon as someone points it out.
Best regards, jj
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I'm only part way through looking at the proof in detail, but if this is the only flaw, does the proof show that while there may be other cycles besides 4-2-1, every number eventuallly cycles, rather than going off to infinity? If so, that's still a huge and exciting piece of progress on the problem! Andy On Mon, Oct 15, 2018 at 9:59 AM Adam P. Goucher <apgoucher@gmx.com> wrote:
Dear Joerg,
I think Claim C8 is unproved: I do not see why a tree cannot attach to itself (and thereby form a cycle).
Everything up to that point, as far as I can tell, is valid.
Best wishes,
Adam P. Goucher
Sent: Monday, October 15, 2018 at 2:23 PM From: "Joerg Arndt" <arndt@jjj.de> To: math-fun <math-fun@mailman.xmission.com> Subject: [math-fun] A (non-)proof of the Collatz 3n+1 problem.
Dear funsters, Georg Fischer has an attempt of a proof for the Collatz 3n+1 problem online here: http://www.teherba.org/index.php/OEIS/3x%2B1_Problem He suspects that it contains a flaw, hence refrains from contacting any big-wigs. With his permission I'd like to ask on this list what the problem may be. Any takers?
Georg will certainly add the reason for the invalidity of his proof as soon as someone points it out.
Best regards, jj
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-- Andy.Latto@pobox.com
Like Adam and Andy, I have only skimmed Fischer's presentation. I agree with Adam that I think C8 simply assumes that a segment will attach to another that is not already in its component; I don't see any argument that this is true. And to answer Andy, I think Fischer does not establish that the number of components is reduced to 1, but simply assumes that because the attachment process merges two components, that's the only way the process can end. But of course we start with an infinite number of components, and no matter how long the attachment process continues, there will still be an infinite number. Perhaps I am missing something. The presentation is careful enough and clearly well-intended, and not obviously cranky, so _somebody_ ought to do Fischer the favor of going through it carefully. On Mon, Oct 15, 2018 at 11:37 AM Andy Latto <andy.latto@pobox.com> wrote:
I'm only part way through looking at the proof in detail, but if this is the only flaw, does the proof show that while there may be other cycles besides 4-2-1, every number eventuallly cycles, rather than going off to infinity? If so, that's still a huge and exciting piece of progress on the problem!
Andy
On Mon, Oct 15, 2018 at 9:59 AM Adam P. Goucher <apgoucher@gmx.com> wrote:
Dear Joerg,
I think Claim C8 is unproved: I do not see why a tree cannot attach to itself (and thereby form a cycle).
Everything up to that point, as far as I can tell, is valid.
Best wishes,
Adam P. Goucher
Sent: Monday, October 15, 2018 at 2:23 PM From: "Joerg Arndt" <arndt@jjj.de> To: math-fun <math-fun@mailman.xmission.com> Subject: [math-fun] A (non-)proof of the Collatz 3n+1 problem.
Dear funsters, Georg Fischer has an attempt of a proof for the Collatz 3n+1 problem online here: http://www.teherba.org/index.php/OEIS/3x%2B1_Problem He suspects that it contains a flaw, hence refrains from contacting any big-wigs. With his permission I'd like to ask on this list what the problem may be. Any takers?
Georg will certainly add the reason for the invalidity of his proof as soon as someone points it out.
Best regards, jj
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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-- Andy.Latto@pobox.com
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Side comment: no value of the form 6a+3 can be part of a cycle, so the values 0 mod 3 should not need consideration for a cycle analysis. On 10/15/18 6:23 , Joerg Arndt wrote:
Dear funsters, Georg Fischer has an attempt of a proof for the Collatz 3n+1 problem online here: http://www.teherba.org/index.php/OEIS/3x%2B1_Problem He suspects that it contains a flaw, hence refrains from contacting any big-wigs. With his permission I'd like to ask on this list what the problem may be. Any takers?
Georg will certainly add the reason for the invalidity of his proof as soon as someone points it out.
Best regards, jj
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun .
* Joerg Arndt <arndt@jjj.de> [Oct 15. 2018 17:58]:
Dear funsters, Georg Fischer has an attempt of a proof for the Collatz 3n+1 problem [...]
Thanks to everybody who took time to comment. Now, how should I inform Georg? Suggestion: Anonymously, by forwarding the messages with names stripped off. Just send an email to me (or math-fun) what you prefer individually. He gives his email address on his web page, so I thing it is OK to reproduce it here (in case somebody prefers to contact him directly): dr.georg.fischer@gmail.com Best regards, jj
I personally would not feel comfortable for my comments to be relayed to Dr. Fischer yet. All we have done is to skim the document and look for obvious places where there might be problems. It wouldn't be fair at this point to say, "You haven't proven that the merging operation wouldn't ever link one component with itself," because for all we know he did handle that case in an offhand comment somewhere. (Perhaps Adam is more confident than I am, in which case Adam should contact Dr. Fischer.) Fischer's is a fair try (similar to several other fair tries I have seen, all of which fail in similar ways), and deserves a more methodical analysis. On Wed, Oct 17, 2018 at 1:46 AM Joerg Arndt <arndt@jjj.de> wrote:
* Joerg Arndt <arndt@jjj.de> [Oct 15. 2018 17:58]:
Dear funsters, Georg Fischer has an attempt of a proof for the Collatz 3n+1 problem [...]
Thanks to everybody who took time to comment.
Now, how should I inform Georg? Suggestion: Anonymously, by forwarding the messages with names stripped off.
Just send an email to me (or math-fun) what you prefer individually.
He gives his email address on his web page, so I thing it is OK to reproduce it here (in case somebody prefers to contact him directly): dr.georg.fischer@gmail.com
Best regards, jj
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participants (5)
-
Adam P. Goucher -
Allan Wechsler -
Andres Valloud -
Andy Latto -
Joerg Arndt