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I'm writing up a paper now where I'm the only author and have a stylistic question.

Should I write ''I'' or ''we'' as in ''I/we recall the definition...'' etc. I think this simple example will make everyone understand what I'm talking about.

Or should/can I mix? Is this too confusing. Or simply bad? Or ok?

I feel that ''we'' is maybe a bit too formal and ''I'' gives the paper a certain personal cosy touch. But in certain respects ''we'' is more ''we go through this ordeal together you and I, dear reader'', where ordeal can mean anything in a whole spectrum of things. You know what I'm saying.

So?

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29  
Halmos, writing about mathematics writing, said he prefers "we", but thinks of it as meaning "the author and the reader". But then he remarks not to use it when it really does mean just the author, and quotes one paper as saying: "We wish to thank our wife..." –  Gerald Edgar Jul 3 '11 at 12:22
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What Gerald Edgar said. "We" = "author and the reader", but "I" = "author". Thus "I learned this argument from x", but "we will consider such examples below...". Many people use this rule. As far as I'm concerned, it's the perfect solution. –  JBorger Jul 3 '11 at 12:30
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Well, we don't have strong feelings about the issue. Another option is to side step this, by replacing "We denote the real numbers by $\mathbb{R}$." with "The real numbers are denoted by $\mathbb{R}$" etc. However, this commenter would not suggest that this always a good idea. –  Donu Arapura Jul 3 '11 at 13:57
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In cases such as this, the pronoun is not needed at all: "Recall the definition...", "Denote by $V$ a vector space...", etc. are OK, functioning grammatically as an imperative, which can be read as applying either to the reader or to both author and reader (in which case it's short for "Let us recall/denote ..."). –  Noam D. Elkies Jul 3 '11 at 14:30
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Ok, this seems be getting a little out of hand with all commenting and no answers. I think it could be argued that I got sort of a consensus of what is appropriate. So let's leave this question and go on with our lives :) I suggest we close it now, unless some extremely interesting answer comes up soon. –  Daniel Larsson Jul 3 '11 at 15:13
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In the interest of having an answer and since this is CW anyway:

English is not my native language and (thus) I read several articles/books/chapeters on mathematical writing in English, among others by Halmos, Krantz, and Knuth (et al.)

I do not have the references handy and, since it's been a while, do not recall what precisely they said (and in particular not who said what exactly), but the consesus is definitely 'we' (with exceptions for things like thanks and so on; or, somebody said roughly: one of the rare situations where 'I' feels appropriate is to say 'I could not prove this conjecture' where both 'we' and 'one' seem odd; and also for the 'thanks')

So, I strongly recommend using 'we', in the sense you mentioned yourself (the author and the reader) and using 'I' only if it is a really somehow personal statement.

There is the additional question of using 'the author' instead of 'I' (in the above exceptional cases). Here, I think the situation is slightly less clear. Typically, if I am the sole author I write 'I' as writing myself 'the author' feels somehow strange for me. But, I had at least once a journal that changed this (in the Acknowledgment something like 'I thank..' was change to 'The author thanks...').

In case of multiple authors I am a bit more likely to write 'the authors' (in the exceptional cases) in order not to have two different 'we' (authors and reader as well as just the authors).

Personally, I think an additional advantage of the 'we' (instead of 'I') is that thus articles are written in the same way no matter whether it is single authored or coauthored. To have single authored ones with 'I' and coauthored ones with 'we' seems confusing (well, maybe confusing is a too strong word, but I'd find it at least mildly distracting).

And, finally, how incovenient would it be, one starts a project alone and starts to write a bit of it up, and latter one finds a coauthor...then one would have to change all the 'I' to 'we'.

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