In computer science the first author does the work and is usually a PhD student. The last author is usually the professor that pushed and helped develop the idea, provided funding, and probably wrote or was heavily involved in writing the paper’s abstract, intro and conclusion sections — the bulk of “framing” the work.

But there are exceptions. Some profs are less student-oriented or don’t like delegating so much, and remain “individual contributors” deep in their careers. Those tend to publish nonzero number of first- and single-author papers.

Edit: I’ve noticed that in Theory and Algorithms, profs tend to take first author even though the student slaved out the proofs. That field is kind of an outlier in that it’s close pure math, and I think borrows cultural artifacts from math research.

In a lot of math disciplines, the papers follow the Hardy-Littlewood rule, so the author names are ordered alphabetically [1]. Maybe, that's what you've been noticing. In my area (programming languages, which may be sometimes theoretical but it's mostly a mixed bag), I noticed only one group follow that convention. Others follow the "first author is the main contributor, last author is the advisor" convention you described.

[1]: https://en.wikipedia.org/wiki/Academic_authorship#Authorship...

I double-checked and it looks like you're right, that the Theory papers where I thought the proof took first-author are actually alphabetical.

At least in the fields I've published in, first author does the work (or at least most of it, almost always including writing the paper) and last author secured the funding. Sometimes authors are listed in alphabetical order, in which case one or two are usually listed as "corresponding author". The less-senior corresponding author usually did the work, and the more-senior corresponding author is usually either the one who secured the funding, or a long-term member of the research group who is likely to actually be around to answer correspondence in the future (and who also probably helped out enough to be worth corresponding with).

I think it's pretty field specific. In a lot of CS for example the first author did most of the work and the last author got the funding. The people in the middle may have done varying degrees of work ranging from helping substantially with the implementation, evaluation or writing of the paper to once having read the paper abstract :)

It's definitely more normal in the social sciences for the senior author to be first, so your wife's experience is probably not strange for her field. What people assume about author order really varies a ton between fields.

I think the term you're looking for might be "postdoc" (postdoctoral researcher)? I've seen "recent PhD" a few times as well, seems pretty clear.

In my uni in Belgium, this is the case too. First author does most of the work.