Reviewer asked to move every mathematical proof to appendices for an engineering journal I do research in an engineering subject and my journal reviewer has asked me to push every mathematical proof to the appendix to improve the readability. While I feel this is true, I also think that some of the proofs can be retained, as they are short and not so much mathematical. What is your opinion regarding this?

Right now, I have written this


  We thank you for your helpful comment. We have moved all the proofs
  and the lemmas, which even if removed do not directly affect the
  continuity of reading  and is long, to the appendices. Proofs which
  are not much mathematical in nature and are short are still kept.


Somehow I feel my language is a bit rude. Do you have a better way of putting it? Or should I just move every proof to the appendix? (The journal is almost accepted with only few minor revisions like this)
In all cases I have been involved, together with the revised manuscript a response letter to the editor is submitted, re-iterating the specific comments/issues of the reviewers and explaining the changes made in the manuscript to address these issues. 

What you are describing is typically one of those things that can be explained in the response letter. You can formulate a nice response where you can explain to the editor (who essentially has the last word on whether or not the manuscript will be accepted) that ... 

"while we believe that moving some of the mathematical formulas and derivations to the supplementary will improve the readability and flow article, some are indeed essential in order to give the reader a fair chance to understand the assumptions/model/results/..." 

There are two major benefits of addressing the situation in this way: 


You show that you do not disagree with the reviewer(s). People tend not to complain much when you agree with them. 
You show the editor that you take the matter seriously, have put effort into amending the manuscript in order to improve the situation and also put thought into making the paper easier for the reader, while not losing the important bits.


I would discourage you to use formulations where you decide what does and does not count as long, or what does and does not impair readability. I say this mainly because you are not in an objective position to judge these things. You have written the manuscript and to you, at the time of submission, the manuscript (hopefully) is informative and has a good flow. You have been working on the project for months, maybe even years. At the time you pick it up, you have all the necessary background to understand the paper. The reader is far away from that position. 

Instead consider picking out things that you feel are absolutely critical, in order to understand the essential bits of the work; that is the motivation, the goals, and the conclusions. Everything else could go into the supplementary...



Lastly, does the journal not have any information on how to handle mathematical calculations/proofs etc, on their guidelines for authors? 

Likewise, if you have co-authors what do they think? Your supervisor has some opinions on the matter surely?