Family never went to college.
Review system for math publications is flawed and should be replaced by public arXiv comments/checks:
No single reviewer can be sure the proof is flawless and they can easily overlook flaws -- it's only uncovered by continued readings from researchers over time that need to use said results (and in practice it's been word-of-mouth to disseminate knowledge of flaws, which is extremely suboptimal).
Public arXiv comments of the form "I am unsure about step X because of Y" or "I do not see any errors" will allow the community as a whole to assess the work. There is no reason to hide the reviewer w.r.t. journals either, it should be the reviewer working with the authors.
It is ridiculous/disrespectful to have students review papers without compensation nor recognition. Unlike professors, students have no career-security and need to focus on their own work (let alone teach) to achieve that.
Journals for profit with locked subscriptions are parasitic and impedes future research; the above solution removes this.
The arXiv allows versioning so any corrections are coherently documented, whereas a "published paper" does not typically reveal this and you must independently search for errata.
W.r.t. determining one's career, what matters is the assessment/explanation (possible vouching) by the experts themselves without reference to a journal. An administration demanding a number of publications is only amplifying the problem.
