Choice of personal pronoun in single-author papers

Very rarely is 'I' used in scholarly writing (at least in math and the sciences). A much more common choice is 'we', as in "the author and the reader". For example: "We examine the case when..."

One exception to this rule is if you're writing a memoir or some other sort of "personal piece" for which the identity of the author is particularly relevant.

Now let me quote Paul Halmos (Section 12 of "How to Write Mathematics"):

One aspect of expository style that frequently bothers beginning authors is the use of the editorial "we", as opposed to the singular "I", or the neutral "one". It is in matters like this that common sense is most important. For what it's worth, I present here my recommendation.

Since the best expository style is the least obtrusive one, I tend nowadays to prefer the neutral approach. That does not mean using "one" often, or ever; sentences like "one has thus proved that..." are awful. It does mean the complete avoidance of the first person pronouns in either singular or plural. "Since p, it follows that q." "This implies p." "An application of p to q yields r." Most (all ?) mathematical writing is (should be ?) factual; simple declarative statements are the best for communicating facts.

A frequently effective time-saving device is the use of the imperative. "To find p, multiply q by r." "Given p, put q equal to r."...

There is nothing wrong with the editorial "we", but if you like it, do not misuse it. Let "we" mean "the author and the reader" (or "the lecturer and the audience"). Thus, it is fine to say "Using Lemma 2 we can generalize Theorem 1", or "Lemma 3 gives us a technique for proving Theorem 4". It is not good to say "Our work on this result was done in 1969" (unless the voice is that of two authors, or more, speaking in unison), and "We thank our wife for her help with the typing" is always bad.

The use of "I", and especially its overuse, sometimes has a repellent effect, as arrogance or ex-cathedra preaching, and, for that reason, I like to avoid it whenever possible. In short notes, obviously in personal historical remarks, and perhaps, in essays such as this, it has its place.

You can download the pdf of Halmos' complete essay.

Authorial "we" is quite common, even in single author papers (at least in math and related fields). The explanation I've heard is that it should be read as both the writer and the reader (as in "we now prove...", meaning that we two shall now prove it together). Some people find it awkward, and insist on "I", but this is unusual (and I've heard of referees demanding "we"). In cases where "we" is truly nonsensical (for instance, introducing a list of people being thanked), people who avoid "I" either find an alternate phrasing or refer to themselves in the third person ("The author would like to thank...").

In single-author papers, I think consistency trumps any particular rule or style. As the Haimos essay suggests, you can achieve whatever style you choose; you just need to make sure that it makes sense.

For instance, don't switch back and forth between "I" and "we," or between active and passive constructions too close to one another. Make the use of "I" and "we" clear to indicate active participation in the project (for instance, for assumptions or approximations made, you choose that—unless it's something everybody does).