1. Preparation. (Some actual work is required here. It is salubrious to remember that in the field of mathematics, referees must work through the mathematics of the article under review with pencil and notepad and, yes, with some concentrated brainpower.)
a. I skimmed the article.
b. I read it through carefully.
c. I read it through twice or more.
d. I have checked my objections.
i. Example: Could the author overcome an objection by simply photocopying the appropriate page of a dictionary?
ii. Or, worse, could the author overcome an objection by simply calling attention to the article itself? (You aren’t still at 1a, are you?)
2. The approach, up or down.
a. Did I learn from reading this article? An answer of “yes” might suggest that the author knows as much as or more on the subject than the referee, should steer you toward approach 2c, and, in the best of all possible worlds, would make section 4, below, completely unnecessary.
b. Does the article state and substantiate a thesis? An answer of “yes” should steer you toward approach 2c.
c. My goal in writing the evaluation is to help make it a better article.
d. My goal in writing the evaluation is to show the editor that the piece is beyond redemption.
3. Writing the report.
a. Have I begun the report by writing a fair restatement of the article’s objectives?
b. Have I evaluated the article in terms of these objectives?
c. Have these goals already been achieved? Remember, a “no” answer here is a positive. This may be difficult; if its job has already been done, the article may seem “correct” and in accord with good doctrine rather than redundant. A “yes” answer should actually steer you toward 2d. In fine, beware of finding yourself asking, “If it’s right, why hasn’t it already been done?” (Yes, a respondent actually said it.)
d. Have I let the article focus on these objectives, or do my requests force the article to veer into other directions? Remember, you are not the author.
e. Are the requests and objections I pose arbitrary? This question is meant as a cross-check on 3b and 3d.
4. Checking the tone.
a. Would I have expressed myself this way to the author’s face?
b. Is the tone of the response written from a point of view of omniscience? This entry could be read, perhaps by a referee, as a desideratum. It is not. “Yes” is the wrong answer to most questions in this checklist section.
c. Is the tone sneering?
d. Is it patronizing?
e. Will any of the observations be taken as an insult?
f. Have I used the phrase “let alone the . . .”?