One pesky problem that seems to pop up when I write or review papers is the “minor algebra error due to space constraints.” You have some theorem and then you go back and redefine x to be 2 y instead of y/2 and then suddenly stuff is off by a factor of 4 everywhere, but that doesn’t matter for the result per se — it’s just some constant floating around. This is of course an issue with conference papers, since they have strict page limits, and you end up shortening proofs to sketches, but it also happens while revising journal papers. One of the jobs of the reviewer is to check that the algebra works out, which becomes tedious if all the algebra is in fact correct but the paper skips 5 lines of simplifications and you have to go and work it out yourself.

Which brings me to the modest proposal : when submitting a journal paper, put in all the algebra, with a little footnote saying that you’ll omit the intermediate steps in the final version. This way, the checking for correctness becomes almost mechanical. Sure, it may make the submitted manuscript look bloated, but then the time saved can be spent on checking the structure of the argument. As an added benefit, the writer will be forced to explore the full ramifications of changing the notation around. Of course, this wouldn’t be possible (probably) for conference papers, but would it help for the journal process?