Article submitted and clearly referee cannot understand basic premise-What to do? I have submitted a mathematical investment article to a new journal (maybe two years old), based on the suggestion of the editor-in-chief, whom I had sent it to earlier, and who claimed he liked our article very much. A version of the article had been sent to a number of individuals, one or two senior mathematicians who are very capable, and a number of these people had good suggestions and helped us find appropriate extensions. Basically, it has been read a good many times and many people seem to think it important and well-substantiated.

So, we formally submitted the article to this new journal, partly because we cited an article that appeared in the journal last year, and partly because we thought it appropriate given that our article was at the junction between mathematics (probability), theoretical statistics, and algorithmic investment. 

The referee report came back and it was clear that he understood the importance of our goal, but it is also clear he had no idea about the underlying mathematics. It was accepted (rejected?) conditionally. Conditionally on redoing the entire paper  (i.e., even the report recommendation was wishy-washy).

Basically, he said that the basic premise of the paper was incorrect, and if we revised it, he would accept it. It was also clear, the referee was not capable of understanding the math in the paper or hadn't bothered to do so. The error in his review was so basic, that any grad student in math should know it--the sum of two (or any finite number of) Guassian random variables is a Gaussian random variable. 

I have two basic solutions:


Write a nice letter to the referee, spelling out exactly why we have already addressed his concerns in the paper and that perhaps we could spell this out more explicitly, showing him how.
Submit to another journal, and write to this first journal's editor-in-chief, questioning the quality of his referees (who may be capable in terms of 'investments' but no in terms of 'mathematics'). Perhaps it was not a mathematical enough journal, anyway and is not the most appropriate for our submission. Then again, it could be that this new journal has growing pains.


My tendency is not just option 2, but to be somewhat more ballistic.

Edited question:
I am asking, given the combined experiences of academics in this forum, there must be creative means of dealing with this problem which are deemed to be more successful. I'm sure going balistic feels immediately rewarding but doesn't help one bit in achieving our goal of getting published quickly. 

Is there a way to both educate without belittling someone who seems really lacking in basics in the topics we cover in our paper? Is there a subtle way to suggest that the referee may be ok for non-mathematical papers but not appropriate for any paper with more serious math?
I understand how you feel, but what you propose in solution 2 does not sound productive. I try to see (after the initial phase of being dissapointed and annoyed) the reviewer as a potential reader of that journal who is gracious enough to spent more time on your article than most readers will. Apparently, my article wasn't clear enough at a point, and that is something that needs to be fixed. It is easy to think something is too basic it needs no explaining, but there are a great many such basic facts; many more than anyone can remember... I suggest you take the same approach.