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This may sound like a childish question and for all its worth, very well may be one as I am only 17, but how do I know who to trust with reviewing or looking at my work? The idea of someone stealing someone else's work, sounds so horible I cant imagine anyone doing it, but I am still not very secure on the topic. So who should? and shouldn't I trust? to show work I have done to.

I also often don't know if work I have done is of any value, much of my work, may very well be crap. But if I ever have or create somthing of value, whom do I trust?

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Please give this question a more descriptive title. –  Nate Eldredge Nov 25 '12 at 23:02
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If you publish something in a site like SE it is extremely unlikely that anyone can steal your work. If you do share your work in secrecy with 1-2 people you're more in risk... –  DonAntonio Nov 25 '12 at 23:08
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@Don, I think SE is for asking questions, not for publishing results. –  Gerry Myerson Nov 25 '12 at 23:21
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You may want to ask this on academia.stackexchange.com; but regardless you may want to read mathoverflow.net/questions/43755/… and mathoverflow.net/questions/43755/… –  Asaf Karagila Nov 25 '12 at 23:34
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@boby I don't know of it happening, but certainly there is a fine line between "stealing" and building off something unpublished by someone that supercedes it and then it is no longer relevant. Is that "stealing"? It would certainly be a horrible situation to have happen to you and this actually does happen. –  Matt Nov 26 '12 at 0:44

3 Answers 3

up vote 48 down vote accepted

For better or worse, being unusually concerned about having one's precious ideas stolen is one of the classical hallmarks of a mathematical crank. Therefore if you get visibly protective, the loss of reputation you'll suffer simply because you sound like a crank is likely to outweigh, by far, the very minor risk that you lose the opportunity to earn some reputation because someone took one of your ideas and ran with it.

Part of the equation is that just about everyone who actually does new mathematics always seem to stress how much more productive it makes them to discuss their ideas with an audience. If you can find an audience who are capable enough to be able to make something with your ideas if they (hypothetically) did take them and run with them, chances are overwhelming that they will have too many ideas of their own to give all of them their due. But there's a good possibility that some of them would give you a few minutes of their time to ask the fortuitous question that pushes you in the direction of the eventual solution.

And even if your presentation inspires someone to do some real work on top of yours, it is overwhelmingly more likely that they'll suggest a collaboration than just appropriate your ideas as their own. Doing so is not only the right thing do do -- it is practically without cost to them, because being known as "Jones who published such and such" is not much more prestigious than being known "Jones, of Jones and Smith (who famously proved such-and-such)".

Also, if your ideas are that good, they'll want to stay friendly with you so you'll let them know about your next good idea and give them a chance to collaborate on that, too.

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Great answer, Henning Makholm. You know, this answer was so good I considered posting it myself, but I'm concerned that some of the more prudish elements of this site may not have been able to take the joke... –  Isaac Solomon Nov 26 '12 at 0:45
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Being on the lookout for the occasional dishonest person is not inconsistent with being open and collaborative. Not every person who goes into mathematics is a nice person, and it's inappropriate to brand someone as a "crank" if he wants to make sure not to be harmed by the occasional bad person. You can still be very open with your ideas and recognize a bad apple here and there. It's not common but they can cause damage to people. –  Zarrax Nov 26 '12 at 1:32

Henning Makholm's answer is excellent and I am not sure if I have anything fundamental to add, but I'd like to express my own opinion if only to subject it to some scrutiny and criticism for my own edification.

Mathematics is different from the sciences in that practical applications tend to follow theory by decades or even centuries. On the other hand, scientific developments are rapidly pursued by business and military interests to which integrity often takes a back seat. So I would argue that dishonesty is uncommon in this field, not because mathematicians are somehow intrinsically more honest than scientists, but simply because there is less motivation to cheat. We aren't building hydrogen bombs here and I can't imagine any such thing as an immoral or unethical theorem.

Also, and I think this applies equally to other fields as well, the ability to recognize a good idea is inversely correlated with the intention to plagiarize it. Cheaters associate with their own kind, as do honest people attempting to advance their field.

So on that basis, the idea of having my work plagiarized is something I never worry about.

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Thanks, I appreciate the advice. –  Ethan Nov 26 '12 at 5:51
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Again, I don't really think stealing of ideas is a problem in math, but "there is less motivation to cheat" seems to overlook the realities of tenure at most major universities. You could have a large teaching load, boards, committees, reading course students, advising people, and on and on. In addition to these pressures the human brain is remarkable at rationalizing unethical behavior. Maybe you didn't "steal" that idea because you were close to discovering it on your own and would have got it anyway (or any number of other unintentional excuses). –  Matt Nov 26 '12 at 5:59
    
I'm not an academic so I can't speak from experience but I would presume the same pressures exist to more or less the same extent in other fields? Is there anything that distinguishes mathematics in that regard? –  Dan Brumleve Nov 26 '12 at 6:11

I just want to cite a counter-example to what people written above. Academic plagiarism does exist, and it is better to face it rather than avoid it as something of very small probability. If you were afraid of plagiarism, you can post your solutions/ideas in a personal website/blog or even on arxiv. Then in case others' solution is substantially similar with yours, at least you have a proof online that you did independent work first.

It is very discouraging for a young man/women to work out something himself/herself but found he/she was exploited by others in the end, or wrongly accused that he/she copied other's ideas from somewhere. Consider the outcome of Shengming Ma(he was dismissed from Columbia, and at some point had to work at a subway sandwich establishment), I do not think protecting one's original ideas is what "a crank will do". You should be open to collaborations and discussions, but also cautious of the indecency in academia.

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