Is it common to make seniority distinctions between coauthors of a paper in math?

Question

Twice now, I've read a paper written by a prominent researcher and some other "younger" researchers, e.g. instead of being superstars they're merely professors, I guess. In the text, he is referred to as the "senior author", e.g. in sentences that read like "In [4], the senior proved this result which is relevant to us because..."

I was a bit shocked, to be honest, essentially because I had never seen something like this in (pure) mathematics. In my mind there was always the implicit assumption that all others contributed approximately equally to the paper, which explained the alphabetical ordering of authors in (almost) all papers.

How common is this? Have you seen this before, and if so, how often?

Answer 1

Is it common to make seniority distinctions between coauthors of a paper in math?

This is uncommon. However it seems less unusual to refer to something one of the authors did, e.g.:

In a previous result [2] by one of the authors, it is shown that ...

or:

This builds on prior work of the first author [3], namely, ...

As Andrés E. Caicedo says in the comments, I would assume that this is just a way to refer to one of the authors, similar to the above statements. That is, this is not a way to imply that they are more important, or contributed more to the paper. (If anything I would assume the senior author contributed a little less :) ) It may be a small gesture of respect, formality, or acknowledgement to the mentor of the work, but nothing more.

In my mind there was always the implicit assumption that all others contributed approximately equally to the paper

Yes, this is indeed the implicit assumption. Moreover, referring to an author as the "senior" author does not really contradict this.

Answer 2

I'll guess that this is pretty uncommon, but the situation itself is a bit uncommon. Perhaps it is just that the senior professor is mentor to all of the others and they want to honor the person. It may well be that one person produces a key result that the others then explore, develop, and they put it all together.

I did something similar (maybe even more rare) in my doctoral work. For one of the key theorems, the thesis and later publication, contains a proof by my advisor. I had an alternate proof, but his was more interesting and had potential for new insights into the field. My proof was more pedestrian. So, while I was actually sole author, his proof is contained in the paper and credited there to him.

But, I think you are correct. In pure math, a paper with several authors has a basic assumption that all contributed in such a way that it is impossible to rank who contributed "more" than others and so authors are listed alphabetically. Even if one person has an idea "first", others can be key to the exploration and development of the idea. Even "small" insights can have a big effect. It saves a tremendous amount of grief. I've been told that in applied math, different standards apply.

But honoring special contributions is also fine when it happens.

Answer 3

It seems rather unusual, and I consider it bad style to use a descriptor that readers will not be able to figure out unless they consult the list of references. (With "first author" you can at least get a reminder by looking at the running header.) It is, of course, possible that the first author is indeed the senior author, and in the context of the journal that might be an acceptable synonym.