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I recently got a tenured (yes, permanent) faculty position in mathematics. During my PhD and postdoc, I collaborated with the same people on some projects, one big and one small, but most of my time was spent on my own, single-authored projects.

This clearly worked, however I now feel like I am missing out. I see all these people at conferences interacting, breaking ground on new knowledge together and having rewarding time working with other people. How do I get to that point?

Not to fall into stereotypes, but I am unfortunately a bit socially awkward, which does not help. I can go out and have fun with other young mathematicians, but walking up to someone and starting talking about a topic of collaboration seems to be out my reach. It never goes further than "I have a question", listening to the answer, and going back to talk with my friend-colleagues.

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    By "tenured" do you mean "tenure track"? – Mad Jack Jun 20 '18 at 3:49
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    @MadJack No, I mean tenured. Well, "tenure" per se does not exist here (it's mostly a North American concept). I mean that I cannot get fired easily. I would need to kill a student or set the building on fire. And I am free to research whatever I want. – user94113 Jun 20 '18 at 12:04
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The best way to start I know of is to quietly pick some small problem somebody else is stuck with (requires no social skills whatsoever, just being reasonably open-minded, flexible, and being willing to listen more than to talk), solve it, and communicate the solution to that person. That will open him up immediately and more often than not a bigger collaborative project will ensue.

In general, keep in mind that most people are willing to talk about what interests them and are quite reluctant to think of what you are interested in, so learn to work on whatever comes your way rather than only on what you specialize in and let it be the other person who chooses the topic and the direction of the collaborative research. Just go with the flow and enjoy the ride. Note that every time you think of or collaborate on something you haven't tried before it is you, who benefits most by gaining new tools and ideas, and the entry cost is usually not very high: most of the time people are stuck on something that can be easily explained in "mathematical common" and requires just a fresh pair of eyes to figure out.

In summary, rotate the table: create the situation when other people will seek you to ask questions.

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    I appreciate the effort, but I would recommend that you try saying your last sentence out loud, perhaps ask a colleague what they think of it. It's offensive. And English is not my native language, so I am not certain why you would call me a "pig". – user94113 Jun 20 '18 at 16:59
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    @user94113 I don't think I ever called you a pig. My apologies if you had any reason to think so. All I'm saying is that you do not need to care much about the impression you are making on other people as long as you do not start behaving in totally unacceptable ways. I have said that sentence out loud many times with no offense meant or taken by anyone (English is not my native tongue either). Apologies again if you misinterpreted the intended meaning. – fedja Jun 20 '18 at 20:49
  • Ah, the classic "I apologize if you misinterpreted what I said" non-apology. I say "I am a bit socially awkward", you reply "you can stay as "socially awkward" as you desire" as if it was a choice of mine. Then you finish up with "just don't be an outright pig", which apparently means "do not start behaving in totally unacceptable ways"; what the hell gave you the impression that I behave in totally unacceptable ways? In what world in your reply, basically calling me a weirdo, acceptable? Just because you and I are anonymous does not mean you are not talking to an actual human, you know. – user94113 Jun 21 '18 at 2:02
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    @user94113 I cannot change the past. All I can offer you is an apology, which I did. Whether to accept it or to reject it is up to you. – fedja Jun 21 '18 at 2:38
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Going to mathematics conference talks, there are often two types of open problems that speakers present:

  1. The speaker can't do it. Avoid these; it's far too much effort to join in and make a worthwhile contribution.

  2. The speaker could do it, but hasn't done it. This is possibly because of lack of time, or their prioritizing other papers, or possibly they find some particular aspect unappealing (e.g., tedious) to work on. (Sometimes it's because they are not familiar with programming.) Often this type of work is pioneering in nature, and there's lots of room for scope.

    The speaker is probably presenting this problem at the conference in the hopes of collaboration; that someone will say "I can do that!".

I recommend keeping an eye out for this second type of talk. Work on the problem they state, and email the speaker after a few weeks to show what progress you've made. Even if it's minor progress, the speaker will likely have the familiarity to proceed from there.

It's not guaranteed, but I feel they'll be thrilled that someone (anyone!) is interested in their research problem.

This is especially the case when you're working on the aspect of the paper the speaker is less excited about (they get to work on the part they like; and you do the rest).

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    and ideally - it isn't so much choosing to do something both parties find tedious to start a collaboration. Think strategically as to whether your interests and expertise complement. What is less exciting or difficult for the collaborator is more exciting and fun for you (and vice-versa). – Carol Jun 21 '18 at 15:52

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