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In various conversations with my mathematical colleagues, I noticed that the expression "your field might be related to my field" should not always be understood literally. Namely the other person does not always invite me to work on a joint project unifying the two fields. In some cases, I noticed the possible relation seems to be too vague to really work on it.

Am I missing something, and should this expression be interpreted more broadly?

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    Really, we can't impute much to the true meaning of the phrase without more context. Please tell us the context and the gist of the earlier dialogue. If nothing else it may entertain us.
    – user104446
    Commented Jan 12, 2023 at 14:12

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It is somewhat baffling to me that you think the literal meaning of "your field might be related to my field" would be "let's work on a paper unifying the two fields". The literal meaning is simply that "there might be connections between the two fields". This might just be small talk, but often the person you're talking to is interested in learning more and exploring if there exist connections between the two fields. If such connections come up during conversation (or later, after thinking about it more) and seem promising, it might lead to some project, which might be a joint one. Often, as you've found, the possible relation is too vague to be worth pursuing at this time, and nothing happens except that you two had a chance to socialize and maybe learn something useful.

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    I had a chuckle since this reminds me of the joke (Family Guy probably?) where a guys says "Hi" and the girl immediately responds with "I have a boyfriend".
    – DKNguyen
    Commented Jan 11, 2023 at 19:24
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    @DKNguyen, ah, yes, exactly on the mark. :)
    – paul garrett
    Commented Jan 11, 2023 at 22:11
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    To extend on the 'small talk' bit: "your field might be related to my field" can be a segue to "so you should listen as I tell you about my field/my work". There's no guarantee that this conversation leads to the connection between the fields, it's just an opportunity for them to talk about something important to them with someone they think will listen.
    – Bryan Krause ♦
    Commented Jan 12, 2023 at 1:42
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    'It is somewhat baffling to me that you think the literal meaning of "your field might be related to my field" would be "let's work on a paper unifying the two fields".' - I must say that, when I read the question title, the very first thought that sprang to my mind was indeed: "Ah, presumably, the person saying that wants to suggest (checking possibilities for) a collaboration."
    – O. R. Mapper
    Commented Jan 12, 2023 at 13:17
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    @Anyon: No, I wouldn't have said it's the "literal" meaning. More like "the pretty straightforward (or so I thought) subtext of that statement".
    – O. R. Mapper
    Commented Jan 12, 2023 at 14:44
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The expression your field might be related to my field is an expression of interest.

How many interests do you have? I hope plenty. Do you have time to pursue all of them? I am sure not.

General rule: no one has free time or free money to give out.

Namely the other person does not always invite me to work on a joint project unifying the two fields.

Well, the few cases that they invited you to work on a joint project are the best opening to future collaborations that you can achieve. Spend some time (ideally as much as you want, practically as much as you have) to investigate if something meaningful can come out from the collaboration.

It seems to me that you are expecting that everyone has infinite time to collaborate with "just met" random people working in a maybe related field.

Play down your expectations, keep the door open to collaborations, always interpret expression of interest as a "broad" expression of interest and not as a promise of collaborations.

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