Starting to Collaborate Again: looking for the Warning Signs
Christina Sormani: I'm not really sure I can best answer this question, but no one else has volunteered. The setting here is one in which someone has just been through a mathematical divorce. For some people this is simply a matter of never coauthoring with the particular mathematician again. For others, there can be some difficulty facing the idea of coauthoring with anyone again.
The easiest path to take would be to publish with a trusted prior collaborator or work alone for a little while. That may or may not be feasible for everyone. Some people will react with an overarching statement like "I will never work with a ---- again". This can be very damaging as the blank can encompass an entire gender, or a nationality, or a subfield of mathematicians or an age group. In fact, I will admit that sometimes people give advise of this sort, even advise so terribly damaging as to suggest avoiding coauthoring with men or never to work with a senior mathematician. The people giving this advise are often not mathematicians. Since many people do not feel comfortable discussing mathematical divorces with mathematicians, they get advise from non mathematicians.
At some point, a little distant from the divorce, it can be helpful to review what went wrong and to see if there was anything you could have done differently. Someone told me recently about needing to switch thesis advisors because his thesis advisor considered him to "be an idiot". This is similar to a mathematical divorce and certainly collaborations have broken up over such treatment. I spoke with the student and found out he asked some rather trivial questions. I suggested that he ask other students the easy questions, and to consult wikipedia and textbooks. With his new advisor, he restricted himself to more serious questions. I realize, of course, this is a typical grad student/advisor scenario and doesn't apply so often to a mathematical divorce. A discussion with a mathematician about a broken off collaboration might reveal something about how you can alter your behavior. Perhaps you could be more assertive or you could be a better listener. You may feel you did too much of the work and a third party could point out that in fact it seemed not so unbalanced after all. Perhaps your coauthor was rewriting all the proofs you gave him because you weren't writing them rigorously enough or had poor grammar. Or perhaps the collaboration fell apart primarily because the problem was too difficult and no progress was being made. It is often hard to tell on your own what went wrong.
Of course, in many cases, you don't need to alter your behavior. You may decide that you don't wish to alter your behavior and look instead for collaborators that accept you as you are. If your conflicts arose from debates over rigor, you may wish to scout the prior published work of potential coauthors and see if you feel their work is written in a style similar to yours, or if you are willing to work with their level of rigor. If your collaboration broke up because you were stuck writing everything up and proving all the details, you may specifically discuss sharing this work with future potential collaborators. Or perhaps you don't want to do the write up at all: you could find a coauthor who wants everything in his own words in the end. If you decide that you prefer playing certain roles in your collaboration, you can look for coauthors that wish to play complementary roles. If you decide your collaboration failed primarily due to the conjecture you were pursuing, you might even consider coauthoring with the same mathematician again on a different project.
I realize I've postponed the most difficult kind of mathematical divorce: one which involved theft of a result. If work has been stolen from you or if you somehow felt you had to abandon a project and lose all credit, you may be afraid to trust someone again. As I mentioned above, working alone or with prior trusted collaborators for a while may be a safe course to take for awhile. You might also ask people to recommend someone especially trustworthy that you could work with. Once you have established that you are working on a project with someone, you need to trust that person with ideas related to that project. You do not need to talk to that person about other ideas of yours. In fact a collaborator might assume anything you discuss is part of the joint project. But you do need to trust the collaborator with ideas relating to the joint project.