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The deletion of the Math Jokes thread (mirrors: html or pdf), most likely provoked by the meta.MO debate about some specific jokes but not supported by a majority of users, appears to be at least the second time that MO moderation decisions are being based on the perception of outward appearance. (The first, at least to my knowledge, was the deletion of a question about "what image epitomizes mathematics to you" after this image became the highest upvoted answer.)
There are good points to be made against having threads like this on MO; I agree with what seems to be the consensus about them, which is that these are bad questions, relics of a bygone age when MO was still figuring out what it wanted to be. The march of science would not be impeded if they had never been asked.
However, deleting them, in my opinion, requires better reasons than not starting them in the first place. Worse yet is my impression that the deletions are motivated not by pondering what would make MO a better forum but by an (implicit, yet rather transparent) desire to appear maximally professional, polite and smooth to the outside world. And this is not a great goal to set -- even if I assume that outside appearance is nearly as important a goal as inside usefulness (full disclosure: I don't), I believe it is too deceptive a light to steer our ship towards. Consider the likely effects of the deletion of the jokes thread: The jokes thread is no longer publicly visible. But the question debating the appropriateness of the sexual jokes therein remains visible (it's on meta, so there is far less grounds on which it could be deleted). Everyone who cannot see deleted threads is likely to conclude, on the basis of their priors and political leanings, that
either some really creepy jokes have stood undisputed on MathOverflow since 2009,
or MathOverflow has succumbed to outside pressure on a current moral panic and deleted a whole thread based on a few risqué posts.
Either of these paints MO and its governance in a worse light than the thread itself. Meanwhile, no one has stepped in to claim any actual damage from any of the deleted answers. The main forces behind the deletion seem to be "these jokes are unprofessional" and "no one cares for this thread anyway". But the slope is slippery, since we have now set an expectation that even theoretical concerns about unprofessional-looking posts will be met with deletion. Next time it may well hit closer to home, and eventually we'll have to respond with "thanks for your concerns, but our core community believes them not strong enough to delete useful content". The later this happens, the bigger the resulting shitstorm and outrage. In some circles, it is best to never become a fellow traveler, lest you become a traitor once your paths split.
What I've said before is not particularly novel and I expect disagreements to be at where to place our red lines rather than whether there should be any. But with too many different red lines, we'll eventually see the window of conversation narrow even further, since it is easier to get a question deleted than to get it undeleted (math.stackexchange is currently having a similar problem for other reasons). Thus, in the interest of common ground, here are some specific suggestions:
Content that appears to be useful or interesting to a reasonable number of mathematicians (witnessed, e.g., by 10 upvotes, by 5 upvotes and appreciative comments from established users, or by citations from published literature) is not to be deleted barring very grave and specific reasons (e.g., passwords being leaked).
Full thread deletion is to be reserved for threads with no redeeming value whatsoever. Answer deletion is to be reserved for answers that are so bad or unredeemable that downvotes and comments of disapproval don't help.
Vague notions like "professionalism", "appropriateness" and "inclusivity" are not to inform moderation decisions until made precise with more specific arguments. Non-CW posts are to be understood, first and foremost, as statements by their original authors, not as manifestations of the "spirit of MO" whatever it might be; they are furthermore not understood to be targeted at any specific reader unless visibly declared to be targeted. Posts should not be judged on how they would look like if ripped out of context and addressed to someone they were never written for.
Feel free to comment and improve on these points. I regard upvotes as "I agree with the general idea and at least 2 of the 3 suggestions modulo minor issues" and downvotes as "this is going in the wrong direction". Eventually, we'll see if these concerns are worth separating and voting on.