Family never went to college.

Professors should remove illusions from (under)graduates about pursuing a PhD (i.e. they should not do it with an expectation of staying in academia, and forgoing the opportunity cost of financial stability and control over where they live city/town-wise).

Review system for math publications is flawed (everyone knows this) and should be replaced by public arXiv comments/checks:

1. 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, horrible!).
2. 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!
3. 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.
4. Journals for profit with locked subscriptions is parasitic and impedes future research; the above solution removes this.
5. W.r.t. determining one's career, so far (empirically) it doesn't matter whether you have publication in journal X unless X is effectively the "best" in the relevant field, but that can be assessed/explained by the experts themselves without reference to journal X. The above solution will remove the illusion that you benefit from many sub-mediocre/trivial results (instead, such results should still exist, as they get posted to arXiv and potentially used in future research).