How to respond to threats by disgruntled, powerful former collaborator I am a mid-career mathematician. I have had a long-term collaboration with a well established, influential,  and recognized senior mathematician. We wrote many papers together for the last ten years and the first papers have been the fruits of a real collaboration and exchange of ideas. However, in the last papers, there was no collaboration anymore and I have been the only one to work on the problems and solve them, even though the papers were cosigned.

About 3 years ago I sent a note to this professor with our two names on it, proposing a project and proving a result in a given framework. She/He has been sitting on the file since then, without any kind of input. 

One year ago, during a discussion with other collaborators, this project resurfaced and we, the new collaborators and I, obtained a series of very interesting and deep results in another framework. We developed methods which were completely different from  what I sent to the professor. With my new collaborators, I eventually posted a paper on Arxiv in the summer 2017.

A few days ago, the professor to which I sent the file 3 years ago came back to me with insulting emails and threatens to tell the mathematical community and my new collaborators that the project originates from her/him (which is not true) and that I have been deceitful. 

I  made the ethical mistake of not informing this professor of my new collaborations and my new collaborators of the existence of this file that I sent to the professor. However, the intersection between the note sent to the professor and the final paper is very small and I have often felt bullied by this professor and wanted to distance myself from her/him. Since this professor is  influential, the situation is very distressful.

What would be the best way to handle the situation now ?
Right now, given the lack of details (and maybe you don't want to add more), it's hard to say what to do.  One thing that would be good to know is: what are you actually worried about?  If you are tenured (I guess mid-career means this), you don't need to worry about that.  What sort of influence does this person actually have?  Disputes happen from time to time, and if your collaborator is a jerk and people know this, they may not pay much attention to their rantings.

That said, my suggestion is to reply with something along the lines of:


  Sorry we neglected to mention my preprint with you.  That project came about independently, and I should have told you about it earlier.  I've added an acknowledgement and a reference to that preprint.  See attached.  Other comments welcome.  By the way, what do you want to do with our preprint?


From my point of view, it makes sense to mention your preprint from 3 years ago in your newer paper, and being generous with acknowledgements costs you nothing.  (Presumably you've had discussion about related things, which, even if your colleague did not actively contribute to your understanding of things, may have been helpful in some ways.  Though again, I don't know the specifics, so you have to decide this.)

Even if you can win, no one wants to get into some big fight about who had what idea when, so if there's a reasonable way to mollify your colleague, it's probably worth it.  Admittedly, your colleague doesn't sound reasonable, but if you add an acknowledgement and reference to that preprint, I imagine most people would think you behaved ethically even if your colleague goes on a rant-page.

You should also discuss this with your present coauthors before doing anything.