Division of Labor:
Should one Collaborator be filling in all the details and typing up the Project?
The culmination of a successful collaboration is often a written manuscript that will be submitted for publication. There are many ways to produce the final paper that explains the results of your collaborative research. Sometimes, the first author does all of the initial writing and drafts of the paper are passed back and forth to all collaborators for their input and modifications. There are some specific advantages to this strategy, including that writing in this way makes it easier to maintain consistency in writing style and flow. One disadvantage to this approach is that it often takes many, many drafts to satisfy all contributors to the paper. This is especially true for interdisciplinary collaborations where the final paper must not only meet the basic standard of advancing understanding but must also communicate the mathematical component and its interpretation effectively to the intended scientific audience.
Another approach for writing a collaborative paper is for each person to write up the motivation, explanation and results of their specific contributions. This works well in some cases, but can lead to the criticism that the final paper lacks, “one voice”.
The best way to decide what writing approach to take is to have a specific conversation about this as the collaboration is progressing and before it is time to begin the writing process. Whatever approach you choose, be sure that authorship accurately reflects the contributions of those involved.
The role of each collaborator should play to his or her strength. Sometimes one person is stronger technically and another is better at generating ideas. If not all the authors are native English speakers, one that is should do a final read through for grammar and usage. All collaborators, however, should feel they have made a real contribution to the mathematics. If one person feels they have not made enough contribution, or others feel someone has not held up his or her end, a prominent thank you to that person might be better than putting his or her name on the paper. If removing an author creates an uncomfortable or awkward situation, it is better to share the credit and not collaborate in the future.
When coauthoring with a person in a nearby field, one may wish to write two papers: one with the theorems whose proofs rely on one field written by the coauthor in that field and one with the theorems whose proofs rely more on the other field written by the other coauthor. Suppose the coauthoring is done to solve a major problem in field X using field Y, then the field Y paper is published first and the field X paper applies in. This makes the refereeing process much easier. When coauthoring with people in one's own field, I find swapping the file around works well.
I do know some young American mathematicians who felt too much of the write up process was left to them with very little assistance from a foreign or senior coauthor. Explicitly asking the coauthor to contribute more to the write up process or to write up a certain section of the paper, sometimes addresses the problem. Sometimes the coauthor is a disorganized person, who needs to be asked to tex up smaller pieces. In the end, if you decide to do the whole write up just to get the paper out, either don't coauthor with this person again, decide you don't mind doing the write up or make it very clear that completing the write up on your own was a one time event. I've had a coauthor where I did the write up because I was on sabbatical and he wasn't, but he later wrote up our second joint paper. If you do decide you like doing the write up, keep in mind that you can use this as a selling point with some future collaborators, but it only works as a selling point if you become known as an excellent writer. See also IIIB The absent coauthor.