How to write a research statement for a math postdoc position?
Writing a postdoctoral research statement should not be a huge exercise. Unless you are applying for a major postdoctoral fellowship, I would not necessarily expect a huge research statement. In many cases, in fact, you may not need a research statement at all to apply for a postdoctoral appointment; a cover letter, CV, and list of references may suffice. (When I hired my current postdoctoral associate, those were the materials I asked for.)

Now, that said, your statement should provide a few pieces of information:


A brief description of your current project, and any major research skills or tools you have acquired as a result of your training.
A brief summary of the kinds of problems you would like to study as a postdoctoral associate. If these are aligned with the interests of the group you are applying to, this is even more helpful.


Ultimately, however, when you are applying for a postdoctoral position, you are applying to a specific individual, who will be the one reviewing the applications. What I am looking for is someone who has actually responded to my job posting, not just a job posting. That means I want to see a clear statement that the applicant has thought about what we do in my group, and how her skills will contribute to the project for which I'm advertising. If there's no such indication, I'm much less likely to take the application seriously, unless there are mitigating factors (lots of publications in top journals, strong recommendation letters from colleagues I know, and so on).

Finally, I should also point out that the quality of your written English could be improved. While this might seem to be a minor issue, a poorly written statement can be enough for me as an advisor to think twice about hiring someone, simply because I would worry about my ability to communicate with the candidate. (Furthermore, someone whose communication skills are somewhat deficient will have a harder time finding a position than someone proficient.)