I think your summary is accurate. I treat MO as more like a seminar, precisely because it is in print. Whatever you write is preserved for posterity, which makes me take it reasonably seriously. (But I may be something of an outlier in this regard; I'm not sure.)

Best wishes,

Matt

What about here on Mathoverflow? Of course I'm not asking for firm-and-fast rules, but for etiquette advice. Part of the question is: Is MO more like a department tea or a seminar? (I've recently decided to treat MO as a seminar and Meta as the tea afterwards, but that's not great, because at tea I talk a lot more about math than about running seminars.) Another part of the question is whether the fact that everything is in print makes a difference?

I agree that behaviour (3) is fine. I think that behaviour (1) is like any personal foible: we all have them, we all try to overcome them, and we all hope that others will be forgiving of us!

Regarding behaviour (2), I think that when discussing math over drinks, it's perfectly fine to cite other mathematicians' opinions as reasons to think a certain way; others may or may not agree (on various levels --- on whether your advocated position is correct despite the endorsement you are referring to, or perhaps even on whether the mathematician you are quoting truly believes what you claim they believe), but that's fine --- I think that anyone discussing things over drinks realizes that such discussions are informal and not to be taken too seriously.

In a paper, on the other hand, I wouldn't engage in behaviour (2) unless it can be converted into behaviour (3). One can write passages of the form "it is believed that ..." or "it is expect that ..." or "it seems possible that ..." and then make citations, either to regular papers, or to material of type (3), but my own view is that one shouldn't go further in the type (2) direction than this in one's writing. (The biggest issue, even more serious than others not being able to verify the claims being made about a third party's beliefs, is that you don't want to speak for another person in your own writing: perhaps they have changed their mind, perhaps you misunderstood them, perhaps they haven't put their belief into print for a reason, and so don't want you to do so either, ... .)

If you do want to explain a certain point of view or opinion on how things can go, and your confidence in your belief is bolstered by knowing that it is shared by another (perhaps well-respected) mathematician, what you can do is just explain your point of view, and then in your acknowledgments section you can thank said mathematician for useful conversations, which helped you to clarify your point of view on material xyz, or maybe just for useful conversations on the topic of xyz.

A middle ground between conversation over drinks and a paper is a seminar talk. I can imagine people engaging in type (2) behaviour in that context; I've surely seen it, and probably done it myself. But on the whole it's probably best avoided, for the same reasons that one would avoid doing it in print; the circumstance is sufficiently formal that people should be allowed to speak for themselves (i.e. through citing their work), rather than via hearsay. But again, if you want to, you can certainly make an acknowledgment in a seminar talk, e.g. by saying "I learned the following [example, way of thinking, point of view, technique ...] from mathematician A".

I hope that this is some help.

Best wishes,

Matt

I know that I do the following:

1. I sometimes "name drop" in the purely gratuitous "I'd like to show off that I have met or am otherwise connected to some famous person". I don't have a good reason for doing this, and I'm sure it is an unhelpful and problematic habit. I hope I'll grow out of it.

2. I often would like to share some opinion, which is not a "result" that could be in a paper, but I want to lend it some more credence. If I have a reason to believe that some famous (in the sense of mathematically well respected) mathematician also shares this opinion (or maybe disagrees with it), then I like to bring up what that I think they think something. This, I think, has a fair amount of intellectual and academic value: well-respected people are well-respected for many reasons, but often some of them are reasons for also respecting their opinions.

3. I occasionally cite unpublished work / personal correspondence / personal conversation. I would never rest a proof on such facts --- I'd always want to reprove them in a publication. But I definitely do want to give credit where credit's due.

I assume that 3. is non-problematic, except that I should always make an effort to find any publication by the same person with substantively the same ideas. I believe that 1. is problematic, but I don't have a great strategy for fixing my own behavior beyond being aware of it. (And I don't think I "name drop" that often.) My secondary question is to gauge how problematic y'all find behavior like 1.

My primary question is about "name dropping" in the form of item 2. above. Namely, there's some gray area, and I want to know how to navigate it. Are there things one should look out for? Ways to site opinions of respected mathematicians that don't come across as type-1?

I think that such a discussion would make very valuable reading for "young mathematicians" like myself. So I'm asking it not just for me --- for example, I've seen many websites with "advice for young mathematicians", but none that adress this question. I don't think that this question is appropriate for the main MathOverflow: it is too discussiony, subjective, doesn't have a single correct answer. But if you disagree, please say so, and I'll (or you'll) post a Community Wiki question about it. I do think that the question is appropriate here on Meta, because it is at least in part about professional behavior over on MO.

Thanks,

Theo JF (not to be confused with the other MathOverflow Theo, so I need to get into the habit of including my initials when I sign things)