How to efficiently proofread my own mathematical paper?

Question

The main purpose of this question is to collect some advices to efficiently proofread my own mathematical paper (when there are two authors or more, it is easier since one is supposed to read what the others write). When we write mathematics, there are a lot of not so minor mistakes we can make:

• We omit to introduce a notation.
• Non-uniform notations.
• A sum should stop at n+1, not at n but the last term is not important.
• Etc...

Of course, we would like to limit the number of such mistakes in order to save the reader's (and referee's) time.

• One possibility is to wait a long period of time in order to "forget" and read what is written, and not what we have in mind. Although "hurry for publishing" is very bad, we cannot always wait a lot of time (thesis defense, applying for post-doc/permanent position) and we would like to make the process fast.

• An other possibility is to send a draft of the paper to a colleague. But he may be busy and not read too much into details. Anyway, when we are alone to write a paper, we would like to send to the colleague a document without too much typos and mistakes mentioned in the beginning of the question.

Answer 1

A general technique, applicable not only to mathematical papers, is to list common mistakes, such as the one you noted. Then, you do a revision of your paper for each item on the list: reading only to look at uniformity, reading only to look if you introduce all notations, etc.

I've picked up this tip in the following book and it has worked well so far.

The book also suggest to reduce the familiarity with your text, so you might be able to read it as a "new" reader and thus find mistakes or parts that are not clear. You could do that by putting away the manuscript for a few days/weeks, printing it, changing the font, etc.

Answer 2

Another general technique to reduce familiarity is to read backwards.

Answer 3

Besides, if there is time, a break can help, i.e., not to look at the paper for a weekend, a week etc, longer the better, doing something else, and then reading it afresh. This context switch can help remove the bias of something having known already.

Answer 4

For long papers, one thing that I have sometimes found helpful is to generate a random list of page numbers, and read check those pages in the indicated order. That somehow reduces the problem of excessive familiarity.

Another thing that can be useful for some kinds of papers is to code all formulae in Maple (or some similar system) and check them by automatic simplification or by substituting random parameters.