How to avoid research getting stolen by professors?

I've made solid progress on a problem in mathematics, and hopefully once I get it to be something publishable I'll publish my work. I'm currently in a course somewhat related to the problem, and my professor (whos quite good by the way, I wasn't surprised to find he teaches at MIT as well) works in the field he teaches. I'd like to bring it up to him, maybe get a little more direction taking my half result to a fully baked result, but I've already made material progress to a solution that I haven't seen done anywhere else. It would be a mildly big deal within the field to get this all the way, and I don't want my progress nabbed by someone who could finish it quicker/without my involvement. He seems like a good guy, and he's ridiculously strict about honor code (he's like the gestapo during exams) but I've heard too many stories to not be mildly cautious. Thoughts?