TITLE: Plagiarism in the community
QUESTION [16 upvotes]: I am a graduate student thinking about some stuff.
1) If I have an idea for a result but it is not yet complete, is it advisable to mention it to others (especially more experienced people)? Is it possible that he/she will take it, develop it quicker than I do and publish it? How should one behave in these situations?
2) Is there a rule of thumb about when (and how) to mention your ideas to others in the community?
3) How often does it happen that a student's idea is hijacked by a more experienced mathematician?

REPLY [6 votes]: To be honest, I don't like the question very much, but I will answer it by
plagiarizing, I mean quoting,  Hailong's succinct answer:

"There is a nonzero risk.
  But the rewards ... far outweigh the risk". 

To be more explicit, talking to an expert might save you a great deal of effort and
pain, as in "Look at this paper", or "Try this", or more importantly "Here is a counterexample..." It is possible, and there are some famous examples, to solve a
hard problem without discussing it, but this is an exception, especially for someone
at your stage. 
Anyway, you should discuss the specifics with advisor. Unless that's the person
your worried about. In which case, you should switch advisors, or perhaps professions...

REPLY [5 votes]: The math community is rather small, bad people are known (and there's only few of them),
stories about them circulate.
Just ask around: "Do you think that it's a good idea that I go talk to professor X?"
If professor X happens to be an (one of the very few) unethical mathematician, people will warn you against talking to him/her.

REPLY [3 votes]: Ask yourself: do you want to be part of a community, or do you want to do math by yourself in the woods?
There is no wrong answer: doing either is a fine and potentially rewarding lifestyle, but giving up on the community means giving up on both the positives and negatives that it brings, and most answers here make clear that the positives outweigh the negatives.