D.H.J. Polymath is the assumed collective pseudonym for the authors of a number of papers which have arisen as a result of the polymath project initated by Gowers. Presumably, since it is a matter of open record, one can go through and identify the participants and their various individual contributions.
But what is it that mathematicians on the street think when they answer this question? The answer is that D.H.J. Polymath is equivalent to T.Gowers, T.Tao, et. al. I don’t claim that this is an accurate reflection of the contribution of the participants, but simply the perception in the community (as far as I have gauged through a number of conversations). Credit for joint publications can be a tricky issue at the best of times. In this case, the people responsible for making the decision to choose a pseudonym are presumably those for whom receiving credit is the least relevant. I find myself sympathetic to the remarks made by T.Brown in the mathscinet review of the first polymath paper:
This reviewer would have preferred to see, rather than the pseudonym “Polymath”, a list of authors. In other fields there are papers with a hundred co-authors. Why not in mathematics a paper with twenty or thirty co-authors, with extra credit for the person(s) who wrote the exposition?
Since I’m currently reading through the Polymath8 draft from A to Z, I can probably say a few words…
There seems to be two issues: (1) absence of designated authorship in a Polymath paper; (2) the fact that people might associate the idea with Tim and Terry (apologies for using first names…) I think these issues are independent.
The first does not (as far as I know) arise from a definite policy (e.g., Polymath4 ended with a published paper with clearly identified authors) but from a consensus decision for each paper, and there is always a web page detailing who has participated in the project at the level expected of a co-author (on the honor system). For myself, I see this as a different style of mathematical work, and I am happy to go through this type of experience at least once.
The second point is probably a real issue, but anyone who understands that Polymath is used to speak of completely independent projects, and who knows even vaguely some examples, should understand that the participant’s list will vary a lot, and therefore that attributing the corresponding mathematical results to Gowers and Tao without discrimination makes little sense (in practical terms, it is obvious to me that Polymath8 would have taken an immensely longer amount of time — and would quite likely have turned awry and lost the name of action — without the momentum and work of Terry). Ultimately, if the idea of Polymath projects survives, any direct connection with the first ones will disappear, and this will become much less important.