Does writing matter a lot in research? I am a PhD student (mid stage) and my work includes the use of mathematics. I try to learn as much as possible. I am facing a problem: I spent enough time on the mathematics required for my research, and according to my research supervisor I am good at understanding proofs, theorems, etc. at an intuitive level, but in writing I still have some work to do. Many times I try to write things and, although I think I am not that so bad, there is still a problem to be resolved.

Question: Is writing in research so very important? I have seen some research papers of some star people whose writing does seems to be very impressive to me (although I may be wrong).

Edit: Please note that I don't consider myself a star: that's why I am asking this question. I am trying my best to improve my writing skills and it has improved to some extent, but to me it appears that I may not get that much better at writing. Let me tell you a story: once during my PhD I worked with a professor other than my supervisor, and then we got some result so he ask me to write a paper. I took 4-5 days write a paper 8-9 pages long, then he told me that I wrote in a cryptic manner. (This happened in my first year.)
Writing matters a lot, and a lot of the time probably most PhDs (and even postdocs) face a steep learning curve. This curve is particularly bad in a field where writing is your tool, such as Philosophy. Even when analysis takes the form of symbols, in mathematics and logic, it is essential to convey your ideas clearly. Clarity is particularly problematic for young researchers, because of our tendency to hide behind pretension. Pretension, confusion, clunkiness must be removed for your ideas to come through.

Overcoming these issues is not essential to get an inexperienced researcher to approve of your work, but any researcher worth their salt will know when what you say is bullshit, or when what you say might have value but is unclear. I say this as an experienced, but not necessarily a good, writer. My writing has often been criticised and quite rightly too. I wish I had learned to write better earlier, is my point and the advice I give.

Because writing is important, there is a second question. How to focus on improving it?


Read good writing.  
Read a book on good writing, I recommend Joshua Schimel's Writing Science. 
Once you have written, wait, and then go back and read it. And then edit it. You will read it from the perspective of another person and hence realise why writing is so important and partly what you need to do to improve.