Can my supervisor steal my theoretical achievements, and publish a paper without me We have solved an important mathematic problem that has not been solved over 10 years. I want to publish a paper about this topic soon, but my supervisor impede me, and he is reasoning that the quality of paper is not good enough. I am concerned that he may publish a paper about the mathematic solution,  without mentioning me as an author, to claim that he is the first person to solve the mathematic problem. Is this action legal?
Collaborating with someone you don't trust is no fun.  I do not speak from direct experience -- I have certainly trusted and remained on positive terms with all of my collaborators.  Yet even under these favorable conditions there are (most) often some conflicts with one's collaborators: e.g. (i) they are dragging their feet / pushing you forward impatiently, (ii) including sloppy and inaccurate / pedantically correct and overly lengthy text, (iii) pushing for publication of a modest partial result / never being satisfied with what has already been obtained, (iv) shooting way too low / way too high in the choice of journal...and so forth.  If I thought that my collaborators truly did not have my best interests at heart...yikes.  This goes doubly when there is a significant differential of power / seniority among collaborators: there can be a fine line between giving your junior collaborator the benefit of your additional experience and insisting that they do things your way.

I'm very sorry to hear that you are worried that your advisor may try to steal your joint work.  If your question is really whether it is in any way ethically acceptable or appropriate for him to do so, the answer is easy: of course not.  However, that you ask shows either great inexperience / mild paranoia on your part or is a sign that the collaboration is dangerously in the "no fun" range.  I looked at your profile and saw that you are a PhD student at a quite reputable research university in the US.  Moreover based on your username I suspect that you are either one of two students with that name in a certain department (not the math department) at that university, each with the same advisor, a young faculty member with an impressive CV.  Obviously I can't promise anything, but in all of my experience a faculty member with a CAREER grant is not someone who would want or need to steal their student's work: not even close, and not on their worst day.  (As an aside, the fact that I suspect that I have identified your advisor whom you are one step away from accusing of stealing your joint work is not great, and you should think about being a bit more circumspect.)

I advise you to concentrate on improving the interpersonal aspects of your collaboration: try to understand your advisor better and vice versa, and try to shore up trust.  If you really can't do that, it's time to find a new advisor.  Though I don't know the situation, based on the fact that you've given no convincing evidence for your suspicions and some other clues, my guess is that you are rather new to research (at least of this kind or at this level) and that as you "learn the ropes" your suspicions will be assuaged.  If you have made a significant mathematical (note: not "mathematic"!) breakthrough, then indeed you should proceed carefully and patiently and not rush into publication.  If the paper is not well written -- according to standards that are difficult to meet or even fully grasp for most graduate students -- that can affect its reception and jeopardize its suitability for publication in a top journal.  

Good luck.