Pure mathematician here. I've written several letters for graduating PhD students, for folks finishing one postdoc and looking for the next, and for visiting professors at my university looking for a tenure track job at a liberal arts college. I've also read thousands of such letters when we are hiring.
Broadly speaking, I agree with the answer the OP linked to, that there is an expectation to explain the person's results. There are several reasons for that. First, presumably a senior person is better at explaining the results in terms the hiring committee can understand (thanks to the experience of grant writing for example). Second, it's important to show an understanding of the candidates work, before commenting on its quality. Third, the candidate will likely have some unpublished preprints and the hiring committee wants an opinion about the quality of those and the level of journal we can expect them to be published in.
My template is as follows:
This is a letter of recommendation for X. X is a talented and personable young man who is currently in the final year of <>. For the past three years, I’ve interacted with X via ... X is a strong researcher, an excellent teacher, and a great colleague. X's research touches on several areas that have lately been attracting a great deal of attention, including ... I am very enthusiastic about X’s research, so let me start with that.
The basic idea of algebraic topology is ... X's research connects to these questions via ...
Here you have 2-4 paragraphs explaining the big ideas, X's specific papers, where they were published, and the quality of the preprints. Usually candidates have at least one thing published, and I can say that their preprint should be published in an equally good journal. I try to emphasize that X is a good writer, well-organized, has a track record of bringing things to fruition, is likely to be grant funded, and has lots of promising ideas that are likely to lead to many publications over a productive career.
If I only know about X's research then I conclude with something like:
In summary, X is a bright and talented mathematician, who has already proven many excellent results and has plans to prove many more. In my conversations with him, I’ve been impressed by how quickly X digests new mathematics, with his creativity in solving technical problems with slick arguments, and with his meticulous attention to detail in his writing. I think this skill will serve him well in publishing and grant-writing. X’s research is strong for a homotopy theorist just finishing his first postdoc. In a postdoc with you, I am confident he would produce several high quality papers, could plug in to others’ existing research program, and could expand his expertise in the direction of ... I recommend him to you without reservation.
One might also get a recommendation "in the strongest possible terms."
Because I'm at a liberal arts college, if the candidate is apply to such a place, I include a paragraph about undergrad research projects, reflecting my conversations with the candidate, their interest in such research, and the fact that they have good ideas for suitable projects. If I have seen them give a talk, then I include a paragraph about their teaching abilities like:
Turning now to teaching, service, and colleagueship, it seems clear to me that X is ready for either a research postdoc or a tenure track job at a small liberal arts college. While I’ve never seen him teach, I have seen him give several seminar presentations, and all have been clear and well-prepared. He is an engaging speaker, with excellent board work, and he has won several teaching awards. His teaching statement echoes our discussions over the years, with his emphasis on active learning, empathy, being approachable, encouraging students, and helping students build up their confidence. I note that one course X taught, .... X's empathetic, relational, and encouraging approach greatly helped his students in this course succeed. X is also an excellent departmental citizen. He served as a peer mentor for new TAs, helped in the summer training for incoming TAs, has run reading groups and helped with the seminar, and stepped up to supervise undergraduate research even in the middle of the COVID pandemic.
I modify this and fill in the blanks based on what I know from the teaching statement, CV, and conversations with the candidate. Most likely you will have a separate teaching letter and there's no real expectation to have teaching mentioned in a research letter, but I do it because it might help a little bit, coming from someone like me at a place known for an emphasis on quality teaching.
Then I put it on letterhead, include my email address, sign it, and send it on time.
I agree with opinions in the comments to the OP that, if you were drafting your own letter, you'd want to leave the subjective judgments to the senior person. It's a real shame if the senior person isn't willing to write the letter themselves, because I think it adds a lot of value to have a second perspective on the research, other than what is already in the research statement. Having the candidate write both seems pretty suboptimal.
