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I was recently attempting to solve one of the more known, already proved, problems in mathematics when I stumbled across an observation I thought might be worth digging into further.

Unfortunately I have only been able to verify my observation up to a small few numbers but I am convinced that it holds true for all numbers? How or why, if I knew the answer I would be asking you guys how to go about submitting a proof :).

Anyway my question is, How do I submit my conjecture for a review, knowing fully well that it's just a conjecture and if it really does have some value a person reviewing it might claim it?

I do expect a certain degree of honesty from the committee members but in case I do not want to take any such risks, what is the best way to have my conjecture reviewed by knowledgeable people in the field without risking losing the "ownership" to the conjecture?

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    $\begingroup$ Honestly, as with virtually any other endeavor, losing ownership of your idea (in this case, conjecture) is the last thing you should be worried about. I assure you that virtually every mathematician worth their salt has enough ideas of their own that you needn't worry about them swiping one of yours. $\endgroup$ – Steven Stadnicki Nov 12 '14 at 22:37
  • $\begingroup$ Computers should let you verify for more numbers. Mathematica gives free trials, for example. And you'd want more than "it's true up to 11, what do you think?" if you want a professional to take it seriously. $\endgroup$ – zibadawa timmy Nov 12 '14 at 23:44
  • $\begingroup$ Hi Steven, thank you for replying. I did not mean any disrespect to any mathematicians out there whatsoever, my only concern is I just have a "conjecture", no attempt at a proof, and no consequences of the "conjecture" or any potential solutions in mind which would make my case a much weaker one as opposed to someone with in depth knowledge of the field and potential consequences of either the validity of the conjecture or its proof(s). Hi Timmy, thank you for replying. The computer program's run time increases exponentially as i keep cranking up the numbers!! But, I do agree with your point $\endgroup$ – joubin Nov 13 '14 at 0:26
  • $\begingroup$ If you can back the conjecture up by a substantial amount of calculations, why not post it on MO or MSE, possibly under your real name, along with the data? If this came up while investigating a well-known conjecture, chances are your conjecture already exists, which doesn't demean it in any way, to the contrary, or has already been solved, or the claim can easily be debunked, or is a worthwhile new problem. In any case, I think everybody would benefit from this approach. $\endgroup$ – Olivier Bégassat Nov 13 '14 at 3:04
  • $\begingroup$ Hi Olivier, I agree with your substantial calculations suggestion but what if what your are arguing has got to do with non-existence of a certain set of solutions and existence of a certain set? The existence part is always easy to prove. Find a case that satisfies and your are done. On the other hand non-existence becomes very open ended if you are trying to back it with computations only and not logic. $\endgroup$ – joubin Nov 13 '14 at 17:49
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It honestly depends on who you talk to and how interesting and possibly tractable your conjecture is perceived to be. Usually a paper with only a conjecture in it will be rejected unless it's extremely well written and successfully explains how monumentally interesting it is. Every mathematician already has problems they are working on, and it's hard to convince someone to drop everything and work on something else unless it's extremely compelling.

In terms of ownership, that's always iffy and there are no guarantees about who will be remembered in a hundred years for thinking of what. It's extremely common for people to get it wrong. If it's marketable, though, you can try to get a patent. Plagiarism is unfortunately not illegal, it is merely reprehensible.

That said, there's no harm in telling people your conjecture if it's pure math. There are a couple of reasons for this:

  1. Pure math very rarely wins you fame and fortune. It might get you some fame, but only in a very small community, and it can get you some grant money, but it's not worth killing for.

  2. It's been observed that math is, at least compared to many other fields, generally honorable. Stealing other people's ideas is greatly frowned upon. If two people are working on the same thing and they find out about each other, and they decide not to collaborate, it's common for one of them to stop working on it so they don't tread on the other's territory.

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  • $\begingroup$ You could also give a (notarized?) copy to your lawyer to keep as proof of when you put the idea down. $\endgroup$ – zibadawa timmy Nov 12 '14 at 23:39
  • $\begingroup$ Hello Mat, thank you for replying. I do not see any monumental consequences (i have little idea though) of either a proof or its solution. Although it does have a lot of historical importance but having gone through answers to some similar questions on this forum, I have come to the conclusion that (a) I am not a mathematician, not even in the amateurish league, so just because i have found an interesting link to a famous problem does not merit it being "nomenclatured" a "conjecture" and (b) you need a "big" name to try and fail to prove it for it to become intriguing or interesting enough!! $\endgroup$ – joubin Nov 13 '14 at 0:34
  • $\begingroup$ @joubin I'm interested in knowing what the conjecture is. $\endgroup$ – Matt Samuel Nov 13 '14 at 0:42
  • $\begingroup$ Hi Matt, letting it out would defeat the very purpose of this post wouldn't it :). $\endgroup$ – joubin Nov 13 '14 at 2:31
  • $\begingroup$ @joubin See edit above. $\endgroup$ – Matt Samuel Nov 13 '14 at 2:46

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