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This post is similar to this one except this is a little bit of a special scenario, I have yet to graduate high school.

I know what you're thinking, oh THIS conversation again, check if it exists, make sure your theorem works, etc. etc.

I have gone through all of this, for over a year I have looked for my theorem online and nothing has come up. I have tried disproving my theorem for over a year, and I have contacted professors and have conversed about this and they all say that it is definitely publishable, but that I should prove it myself. My big worry is that due to my position my ideas can easily be stolen, and I am starting to get a little on edge.

How can I ensure that my ideas are not stolen, Can I provide direct proof that the idea is mine somehow? Should I just publish it without a proof, Can I even publish without a proof? I am kind of stuck at this point.

I have a document that has the theorem on it written in permanent ink, dated, and it is signed by a witness. But what more can I do?

EDIT:

For those curious about my conjecture click here, there are two pages so click next to see the other page.

Feel free to comment

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Eric L
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    For what it's worth, publishing is how you provide direct proof that the idea is yours. – David Z Nov 18 '14 at 07:05
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    I'm already looking forward to learn more about the famous "Lawson Conjecture" and see if it turns into the famous "Clark Theorem" or is rendered false by a counterexample obtained by the famous "Nick S Construction" ... :) – Hagen von Eitzen Nov 18 '14 at 14:25
  • What's the conjecture? – anthus Nov 19 '14 at 08:22
  • @DavidZ it should be noted that publishing in peer reviewed venues is not necessary, there are other ways of publishing nowadays. I'm uncertain about the timestamping and trustworthiness of blogging platforms, but hopefully that will be fixed soon. – Trylks Nov 19 '14 at 10:52
  • For the sake of answering the question (I'm not claiming this is something you should do per se), if you're looking for a way to prove a document exists, you can use Bitcoin's proof of existence ability. – user541686 Nov 19 '14 at 11:21
  • @Trylks yes, that's what I meant. Not only peer reviewed journals but also arXiv or any other means of making the results widely known within the scientific community. – David Z Nov 19 '14 at 11:30
  • @DavidZ I'd say that doing something widely known is not easy nor needed (for "safety", not dissemination). Basically it needs to be accessible and have some trustworthy timestamp that cannot be modified. Blogging platforms would be good enough (IMHO) if they kept a log of modifications to posts (like wikis do). GitHub and such would be good enough (excellent in fact) if the timestamp was set in the server, not the client. – Trylks Nov 19 '14 at 13:35
  • @01000100 I have edited the question so you can see – Eric L Nov 19 '14 at 23:24
  • Making mathematical discoveries that seem true, but hard to prove, is easy, and usually, if this conjecture does not have profound implications, it will be hard to publish. If I find a math problem interesting, I share it, or ask if anyone has an idea how to solve it, on mathoverflow, or a coworker. No-one steals conjectures, but someone might prove it, and publish the proof (stating that it was your conjecture, of course, if they heard it from you) – Per Alexandersson Nov 09 '16 at 21:44

2 Answers2

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The word "theorem" implies that there is a proof. If you do not have a proof, you do not have a theorem. Let's call it a conjecture instead.

I have tried disproving my theorem for over a year.

That's a slightly strange thing to say: how long have you spent trying to prove your conjecture?

Should I just publish it without a proof, Can I even publish without a proof?

It is possible to publish conjectures, but it is significantly harder to do so than to publish theorems. I would not recommend that a young researcher -- especially, a high school student! -- try to do this.

I have contacted professors and have conversed about this and they all say that it is definitely publishable, but that I should prove it myself.

It's no help if I'm not honest, so: this sounds fishy to me. It is often not so easy for (even) a professional mathematician to know what is "definitely publishable": after more than a decade of submitting math papers I find that I still have some things to learn about this. But anyone who is telling you that your mathematical work is "definitely publishable" if it does not contain a proven theorem is either giving you bad advice, or you are misinterpreting the advice.

How can I ensure that my ideas are not stolen, Can I provide direct proof that the idea is mine somehow?

With probability extremely close to 1, professional mathematicians simply do not steal ideas in the manner you are worried about. The "I did something great, but oh no I can't show it to anyone" train of thought is a sad one that amateurs often fall into. Rather, if you do something great, show it to more than one person, and you're fine. One way to do this is just to upload it to the internet in some public or semi-public location. For instance, if you have an account on facebook, just post a scanned copy of the paper as photos. Facebook posts are archived with date and time, so that's that.

I will extend to you the following offer: after you archive your paper publicly on the internet, send me a copy. I will spend up to one hour looking at the paper and tell you one of the following:

  • The mathematical content of your work is such that you should try to publish it. I will then tell you some places you might send it.
  • In my opinion your work is not publishable in a reputable, professional mathematical journal.
  • I am not qualified to judge whether your work is publishable, but I recommend that you send it to third party X.

You should understand that unless the work is very directly connected to my own I will not have the time to help you with it, nor to send more than one email. (I simply can't: I have a lot of other people who are counting on me to spend my time on them. In many cases I am being paid to do so.) But I will give you a professional evaluation of your work so you can (probably) know where you stand.

Pete L. Clark
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    "I have contacted professors and have conversed about this and they all say that it is definitely publishable, but that I should prove it myself." < -- I actually interpreted this as "IF you find a proof, it can probably be published." – Nick S Nov 18 '14 at 02:47
  • Well, I have obviously tried proving it, but I feel it is just as important to try to disprove the conjecture Because if it happens to be false, then I would rather find that out after 2 months of work than trying to prove it for years. – Eric L Nov 18 '14 at 02:50
  • @Nick S: The quote says "definitely"; that sets off my alarm bells at little. I agree that the conditionality of the statement was probably more prominent than the OP is making it out to be. However for a high school student to come up with a new conjecture which, if correct, would be publishable is already unusual and impressive. Until I see the work I would not want the OP to think that as soon as he can prove the result he definitely has a publication. – Pete L. Clark Nov 18 '14 at 02:51
  • "Well, I have obviously tried proving it" This was not obvious to me. I apologize for my obtuseness. – Pete L. Clark Nov 18 '14 at 02:52
  • Also I appreciate your honesty, This has been very helpful. Thank you. Just as a side comment, I didn't mean for the words "definitely" to come into the publishable part, just that if it is proven, it is work that has the ability to be published. – Eric L Nov 18 '14 at 02:53
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    @PeteL.Clark It really depends on the field. In number theory, which I would think is the most common field a student would come up with a new theorem, it is easy for students to discover simple statements which are extremely hard to prove... And not finding it might mean either that it is not famous, or simply that the student didn't know how to look for it. Math theorems are hard to google :) – Nick S Nov 18 '14 at 02:56
  • @Nick S: (I guess you know I'm a number theorist.) Yes, there are a lot of statements in number theory that are easy to conjecture and thus far impossible to prove. However, if someone sent me work making a standard (or less than standard, but not really novel) difficult conjecture like, say, the infinitude of twin primes (not as good an example as it used to be!), then "Yes, that is definitely publishable but you should prove it yourself" is really not a good response. – Pete L. Clark Nov 18 '14 at 03:01
  • @PeteL.Clark Yes, and I agree with a theorem like that. But I think there are few problems in number theory on which I would expect the experts not to spend too much time, and you can confirm/infirm this. Probably not the best example (but as this is not my area, I don't know too many good open problems) but the perfect cuboid problem probably would qualify... Now, if a bright high school student comes and asks me about this, I would not discourage him about looking at this problem, I would think he can learn some things simply by investigating it...... – Nick S Nov 18 '14 at 03:08
  • I wouldn't expect him to solve it, but he would probably learn and discover a lot more by looking at something it looks interesting...... Personally I would make it clear to the student that this is a very hard problem, but someone else might think that this is discouraging the student...... – Nick S Nov 18 '14 at 03:10
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    Sorry for so many comments, but one more comment here, it just hit me. We might also both misunderstand the word "publishable". For us it means in a peer reviewed research journal, but them might have referred to something like Crux Mathematicorum or some similar journal. – Nick S Nov 18 '14 at 03:49
  • Isn't this answer mixing up quite some things? You are making it sound as if the "proof" in "Should I just publish it without a proof, Can I even publish without a proof?" refers to proving the validity of the conjecture, but it would rather seem that in those two sentences, "proof" refers to the proof of ownership of the idea. – O. R. Mapper Nov 18 '14 at 08:00
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    @O.R. Mapper: My reading was indeed that this "proof" referred to proof in the mathematical sense. (This seems more sensible: of course one does not need "proof of idea ownership" in order to publish a mathematical paper; if anything, it is the other way around.) If the OP meant otherwise, I hope he'll let us know. – Pete L. Clark Nov 18 '14 at 15:42
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    @PeteL.Clark: Indeed, maybe I misinterpreted that. My impression was based on the directly preceding sentence "Can I provide direct proof that the idea is mine somehow?" (highlight by myself) – O. R. Mapper Nov 18 '14 at 15:50
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    @O.R. Mapper: Certainly the word "proof" is used in both senses throughout the question, so I think there is reasonable ambiguity either way. – Pete L. Clark Nov 18 '14 at 15:52
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    @PeteL.Clark How can I contact you? – Eric L Nov 19 '14 at 01:53
  • My profile is linked to my homepage. – Pete L. Clark Nov 19 '14 at 02:33
  • @EricLawson: I'm also interested in your idea. After correspondence with Pete, if the result of the discussion allows it, can you update me with the idea also? – justhalf Nov 19 '14 at 06:05
  • @PeteL.Clark The link is in the question – Eric L Nov 20 '14 at 00:15
  • @justhalf It is linked in the question – Eric L Nov 20 '14 at 00:15
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    @PeteL.Clark what ended up happening with this? – Moderat Sep 16 '15 at 01:35
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For mathematics finding a "Theorem" without a proof has very little to no value. With very few exceptions, a Theorem becomes (somewhat) important when it is proven.

The hard part of mathematics is not finding Theorems or statements which seem plausible, the hard part is proving them. And the most important skill as a researcher is finding results which can be proven.

For many Theorems in mathematics, over the years there were many people which discovered and re-discovered that a certain result seems plausible, but no proof. Most of the times noone remembers them, and they don't often care. People usually remember who proved the Theorem, not who discovered first that this could be true.

I wouldn't worry about your Conjecture being stolen, unless you find a proof. And this is probably what those profs suggested: if you want to publish it you need to find a proof.

Also keep in mind that this applies to mathematics, might be different in other fields.

Nick S
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  • Well this is not one of those things that are unprovable, but it is definitely a challenge, But I fully agree with the statements you made. Perhaps I should keep trying to prove it. – Eric L Nov 18 '14 at 02:42