Every collaboration I have had with a mathematical colleague is different; maybe there are some broad types. A couple of my collaborators I met for the first time years after our joint papers were published. In some cases, the work was divided up and each person did his or her part. But the most exciting collaborations are those where the contributions are so tangled up that it is quite impossible to say who did what. A student of mine once described such a collaboration by saying that each of the two authors did 70% of the work. This statement would, I am sure, be angrily dismissed by the administrators who have to assign credit for joint research to individuals; but anyone who has had such a collaboration will know that this is indeed how it is.
I had a feeling of familiarity when I came across an account of the collaboration between Bob Dylan and Jacques Levy which led to the writing of most of the songs on Dylan’s Desire album.
Here is Dylan’s account of the writing of the first song, “Isis”:
I had bits and pieces of some songs I was working on and I played them for him on the piano, and asked him if they meant anything to him, and he took it someplace else and then I took it someplace else, then he went further, then I went further and it wound up that we had this song.
And here is Levy’s account of the same incident:
He had the general feeling of the song but hadn’t got further … so now what? … So the two of us started working on that together. I started writing words, then he would say: `Well, no, how about this, how about that?’ – a totally co-operative venture. It was just extraordinary, the two of us started to get hot together. And we began to work on this thing and we just kept going with it, and we’d stop and we didn’t know where the story was going to go next … we were just having a great time and coming up with one verse after another … and we kept on going until five in the morning and we finished the song … It’s impossible to remember now who did what, it’s like we’d push each other in the sense that he’d have an idea then I’d have an idea until we’d finally got to a point where we both recognized what the right idea was and what the right words were and whether it came from him or me it doesn’t make a difference.
This, incidentally, is from All Across the Telegraph, a collection edited by Michael Gray and John Bauldie, and maybe the best book on Bob Dylan I know.