How to "work on the essay" as a non-native speaker We received a report on our paper (it's the 2nd version already). The referee writes:


  The proofs are correct. However, I'm not completely satisfied with the style in which the paper is written and the authors have to work more on the essay.


I'm not sure what we can do with that. We are not native speakers and we did our best to use as good English as we can. I'm not sure how we should respond to that, since currently it seems to be the only thing that prevents us from finishing the referee process. We implemented the minor corrections suggested by this referee and as well the remarks by the language editor.

Any ideas how to proceed in such a case, please?
The referee is obviously satisfied with the "scientific" part of the publication but points out the narrative itself. I don't think that your English language skills are the deciding in the factor in that matter. You could write the same paper in your native language, let it someone translate it as it is and still get the same comment. As the referee puts it, it's the style that has issues. You should try to formulate your paper in a way which not only lists the discovered facts one after the another, but attempts to guide the reader's thought process towards your idea and results. Make it more interesting and engaging. Your language should be eloquent, your narrative consistent, your thought flow constant; the paper itself serves as a way to reflect the scientist's mind and as such it does not consist only of definitions, lemmas, theorems, proofs, citations, figures, etc., because a significant part is the skill (or art) to mold them into an article that readers will enjoy reading.

If the problem is really only the lack of English skills, try to write it up in your native language and consult some professional to translate it.

If that is not the case, don't be discouraged, good writing is a skill and can be learned and trained. Unfortunately, I've encountered many students (and some experienced scientists) who struggle with this. I personally blame it on the lack of reading of non-scientific material, like novels, articles, philosophical works, etc. Of course, this doesn't mean that you should style your paper like an adventure novel, but, as I mentioned before, writing is a skill, and it is best honed by being in contact with other well written materials. This way, you'll broaden your vocabulary, improve the ability to express your thoughts through text and, if you focus on English materials, become more proficient in English.