Academic integrity [closed]

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.

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.

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.