How to reduce minor and stupid errors on papers

Question

I am a math postdoc who defended his Ph.D. two years ago.

I have 9 papers and 3 of them are with co-authors. In other words, I am a single author of 6 papers of mine. Two of my papers where I was a single author were published.

Recently, one of my papers was rejected after 8 months because the referee believed: 1) The novelty might not be sufficient for a journal, and 2) the writing contains inaccuracies at places.

I don't have any problems with the first issue as they can have a different opinion. But my problem is the second issue. I found out that all of my papers contain minor problems, such as proving something under compactness assumptions, but not mentioning that, or mix of quantifiers, or using a notation for two objects. Long story short, even though all arguments and proofs are overall correct, there are stupid errors. These stupid errors get my papers rejected from time to time.

What I usually do, when I finish a paper, is not to look at the paper for several weeks, and then look at it again. But again, there are some stupid errors. From time to time, I also ask some experts to look at my papers, but either they don't go through my papers, or they don't look at them very carefully. In general, I found out I shouldn't expect anyone to look at my paper carefully.

One more thing, I know I should work with experts instead of working alone, and I tried, but experts have several things on their plates, and take several years to finish a paper; I don't have that much time due to my short contract. But I have been working with some experts. We finish the result a year ago, but she hasn't finished the writing!

My question is how I can reduce these problems, which I called stupid problems, in my papers?

Answer 1

You are simply noticing a common experience that is pervasive with writers. It is extremely difficult to proof your own work. Waiting a few weeks between edits is a start, but it isn't likely to be entirely effective.

The solution is to have someone else, not involved in the writing, to give you feedback.

The problem is that you have a certain mind-set and a way of thinking. That is natural. When you read what you have previously written you naturally adopt the mindset that you had when you first wrote the work. Thus, when you read over a passage you are all too likely to "see" what you think you wrote, not what you actually wrote. The "correct" version is in your head and you sort of skim over the incorrect version, not seeing the erroneous detail.

It isn't at all that you are unsuited to academic writing. It is that the human mind is very complex and has connections beyond what we experience explicitly at the moment.

Multiple edit reviews of your own will catch a lot of these mistakes, but not all. I've found some incredibly stupid errors in fairly simple math writing. I meant "intersection" but wrote "union". It took several readings to catch it and it was an error that resulted in complete nonsense.

Work with a colleague and offer to pre-review one another's papers and give feedback on issues large and small. They will notice things that you don't.

Not actually writing an assumption (compactness) is a nearly perfect example of this. "Of course, compactness is required."

Reviewers can also do the same, actually, if they know a lot about a subject. The mind can "override" the eyes.

Answer 2

I recognize the problem of others agreeing to review your work, but then not reviewing it thoroughly at all. I'm not sure if you can expect them to review it thoroughly either way...

A quote that may somewhat apply here is: "Ask a programmer to review 10 lines of code, he'll find 10 issues. Ask him to do 500 lines and he'll say it looks good." (-not sure who said this first)

If you ask someone to review a whole paper, they will probably be overwhelmed and find it too much work to review it thoroughly. Maybe you can try asking someone to thoroughly review only a small part of your paper (e.g. only a single proof). Then you can ask someone else to do another part, etc. This is likely less overwhelming and can be done in much less time, making them more likely to do it.

Answer 3

Getting better at proof-reading: The "fresh eye" after a few weeks break is just the start for proof-reading properly. It allows you to actually read what is written (rather than "reading" what you remember writing). But to properly proof-read a mathematical proof, you need to disbelieve it. Put the onus on the text to overcome that disbelief. This will not just help you catch mistakes, but also identify parts of the explanation that need improvement.

Getting other people to proof-read: Reading a paper and proof-reading it are two very different things (see above). The latter takes much more work. If you give your draft to some expert in the area, you may get comments like "This reminds me of this paper here, maybe you should have a look.", but not really proof-reading stuff. (And if they did, I'd feel equally embarrassed about it.)

What you want is to get someone to explicitly proof-read your stuff. Ideally, this person is someone who can understand your paper with some effort, but is NOT an expert in the area. This would naturally put them in the right mindset. You should offer something in return, eg to proof-read their papers.

Getting collaborators: Someone who proof-reads because their own reputation is on the line, too, will probably be more effective than someone doing it as part of a deal. Also, already before the proof is written, the steps of mutually explaining proof ideas to one-another in a collaboration helps identifying the exact assumptions.

You don't need to look for more senior people as potential collaborators. Working with fellow postdocs or PhD students can fill the gap just as well (if not even better).