I am a graduate student and am into 2 years of PhD. My current specialization is in signal processing. During this period, in my spare time, i came up with an idea which seems to be a research problem in Mathematics which hasn't been investigated till now in Mathematics literature. I am so much interested in this research problem and added to my already existing bent towards Mathematics, i want to study and work in Mathematics full time in order to solve this problem, which could give a wide scope to do futher work in Mathematics. I could post this problem as a question on Math.SE, but even if someone is able to answer, I think i may not be in a position to appreciate the proof/answer. Moreover I really am interested in solving this problem myself. For this purpose I want to approach a Mathematics Professor who could upon looking at the research problem would be interested in it (hopefully) and be able to offer me a position (may be PhD or some form of internship) to work under his guidance in order to solve this problem.
In this regard, What are the possible and best ways to approach a Mathematics Professor who would be interested in offering me such a role to work in Mathematics. I really do not want to publish/post about the research problem in a public forum until I solve it completely. I'd appreciate your advice whether positive/negative in this regard.
I am currently in Electronics and Communication Engineering Dept. and all my previous studies and degrees are from this Dept.