Writing assignments in mathematics are always dreaded by the students as writing math is much more difficult than writing on topics in other subjects. There is also the fact that students who are good with science subjects are not usually very good with words. This makes the task of writing even more difficult for students who are studying math. The tough part, mostly, is not that of forming the hypothesis or proving it. What students find difficult in a math research paper is the part of explaining the theory to the audience and conveying the same, effectively.
Effective writing requires the base of a thorough knowledge. But it will be wrong to say that people who have a good grasp of the subject can convey it easily. You might have noticed that not all who knows can teach. If you are not one of the lucky ones who can easily transform your thoughts into words, you must learn the skill at the earliest, even if you are a math student. You will not be able to handle the writing assignments without knowing how to present your ideas.
You must appreciate the fact that the person at the other end does not have a clue of what you are talking about. Hence to be able to write your math research paper comprehensibly you must go back to the starting level of your theory. Starting from the beginning you must explain it clearly and through a step-by-step procedure. Since you would have stated your theory in the introduction, your audience will be aware of what you are aiming to prove. So starting from the beginning will not throw them off the track. Instead, it will help them grasp it in a better way.
Mathematical formulas and theories are fascinating. You must present your theory in such a way that would capture the beauty of your theory. Readers or audience of a math research paper would expect nothing less than to see a wonder unraveling in your research paper. You must not disappoint them. Your writing must be legible and easily comprehensible to the reader. Once you have finished preparing the rough draft, get someone else to read it in order to find out whether they can follow your words. Do not take the intellectual level of your audience for granted. Explain the theory in as much detail as possible.
Math is a very organized subject. Hence all points mentioned in your math assignment should be clarified to the reader. Mentioning any aspects or points vaguely will not be appreciated by the audience of a math research paper. They will be expecting clear and precise explanation and presentation of the theory or mathematical problem. Do not include irrelevant points as it will distract the reader and make the research paper lose its focus.
Writing mathematics is not easy. But writing math impressively is extremely difficult. You must practice effective writing in math even if you are good enough with your words, if you wish to write an impressive math research paper. Taking a look at research paper samples also would be helpful in understanding the pattern.