I'm developing a paper right now based upon some of my preliminary results, and I'm attending several conferences to present and get some feedback on my results from other experts in my field. A thought occurred to me that because my work is yet to be published, I there is a potential for others to steal my idea and publish before I get a chance.
I'm probably over-thinking this, and there is little chance of it actually happening. But I'm curious how frequently this happens in scientific domains. Do people go to conferences to steal ideas? If it does happen, how can I best prevent it from happening? Obviously, I want to share my ideas with the world, but I don't want to lose a chance to take an idea into fruition. What should/shouldn't I share about my research before it is published? Should I simply wait until my paper is accepted before I go on the conference circuit?
My field is computational science (not to be confused with computer science).
As some comments note, answers will vary dramatically by field, but it seems better to have a bunch of answers for different fields to one question, instead of having people ask the same question a dozen times for different fields.
For math, if you're talking about a completed, submitted paper that hasn't been published yet (say, because it's still being refereed), you should feel free to talk about it; the submission date proves your claim on the result, so it can't really be stolen at this stage. (Also, you already put it on the arXiv, so it's already public, right?)
Suppose you're still writing the paper, but the results are completely solid. There are good reasons to tell people about the result: you may be want to discuss ideas for how to build on your paper, you may want to give people a head's up that the theorem is coming---say, so they can use it to prove things themselves, and you may want to establish a partial claim on the result in case someone else is doing the same thing. There are also good reasons not to tell people: even though you're really awfully sure the result is solid, there might still be mistakes; routinely announcing results well in advance of the paper can negatively affect your reputation; someone could use your ideas to write their own paper faster. (There's an interesting phenomenon where once people know a theorem is true, it becomes easier to solve; sometimes a problem is open for a long time, and then abruptly solved multiple times in a short period.)
Taking these together, I'd advise not to announce a result until the paper's finished unless there's a strong reason to do so. This is particularly true early in your career, when it's more likely that you'll mistakenly believe a proof was really-definitely-totally finished. (I was given this advice when I was in grad school, and while I haven't followed it 100% of the time, I've never regretted following it.)