Let me share some more gears/evidence. I believe something a little more interesting happens than what you’re saying (which is definitely one piece of the puzzle).
(1) It’s fun to look at how the audience organizes itself during math talks. The faculty almost always sit in the front row, point out mistakes more directly (“You mean this” instead of “Is this correct?”), ask questions more often (and with less hand-raising), and sometimes even feel comfortable to answer questions in the speaker’s stead. I suspect this is a social role that everyone learns through attending enough seminars.
(2) Faculty have access to a lot more privileged information about other mathematicians than everyone else. They are on editorial boards, hiring committees, admissions committees, conference organization, awards panels, etc. I got a confidence boost after peer reviewing my first couple of papers, the transition to faculty is this x10 in terms of data to train on and notice you’re being underconfident.
(3) Professors spend a lot of time with their research groups/PhD students/undergrads compared to in the company of other faculty, so they aren’t doing as much comparing themselves with other faculty as you would think. At least in mathematics, it’s generally preferred for faculty at the same university to have research interests as far as part as possible (to cover a breadth of fields), so each professor interacts a great deal on the day-to-day with their group of undergrads/grad students/postdocs. Meetings with other faculty are mostly logistical, with the possible exception of a handful of close collaborators. This is probably even more true in fields where a professor is literally a head of their own lab and the PI for all research that happens in the lab. I think status feelings tend to work on the level of “people you interact with most on a daily basis” instead of “people you intellectually compare yourself to.”
Let me share some more gears/evidence. I believe something a little more interesting happens than what you’re saying (which is definitely one piece of the puzzle).
(1) It’s fun to look at how the audience organizes itself during math talks. The faculty almost always sit in the front row, point out mistakes more directly (“You mean this” instead of “Is this correct?”), ask questions more often (and with less hand-raising), and sometimes even feel comfortable to answer questions in the speaker’s stead. I suspect this is a social role that everyone learns through attending enough seminars.
(2) Faculty have access to a lot more privileged information about other mathematicians than everyone else. They are on editorial boards, hiring committees, admissions committees, conference organization, awards panels, etc. I got a confidence boost after peer reviewing my first couple of papers, the transition to faculty is this x10 in terms of data to train on and notice you’re being underconfident.
(3) Professors spend a lot of time with their research groups/PhD students/undergrads compared to in the company of other faculty, so they aren’t doing as much comparing themselves with other faculty as you would think. At least in mathematics, it’s generally preferred for faculty at the same university to have research interests as far as part as possible (to cover a breadth of fields), so each professor interacts a great deal on the day-to-day with their group of undergrads/grad students/postdocs. Meetings with other faculty are mostly logistical, with the possible exception of a handful of close collaborators. This is probably even more true in fields where a professor is literally a head of their own lab and the PI for all research that happens in the lab. I think status feelings tend to work on the level of “people you interact with most on a daily basis” instead of “people you intellectually compare yourself to.”