What does "communicated by" mean in math papers?

Solution 1:

I'm posting my comment as an answer as Zev and amWhy asked me to do so:

It usually means that John Doe was the editor in charge. That is: John Doe received the submission by the author(s), contacted the referees and informed the board of editors about his and the referees' opinion. John Doe thus takes some sort of responsibility on the paper. His name is associated with it and it's his choice of the referees and his judgment of their opinion that ultimately led to the paper's publication. However, John Doe doesn't contribute a single line to the paper itself. Usually, the communicator is a rather senior and well-established mathematician.

Two journals that systematically use the "communicated by ..." stamp are, among many others:

• Journal of Algebra
• Comptes Rendus de l'Académie des sciences

The CRAS are a journal that (at least historically) belongs to the category that Zev mentions in his answer. However, the Journal of Algebra shows that this is not necessarily the case. The explanation I'm giving tries to cover both cases.

Solution 2:

It appears that some journals that are run by an organization, e.g. the Proceedings of the National Academy of Sciences, historically have only accepted articles from members of the organization; however, to open them up to everyone, there is a formal step where an article accepted for publication that is not authored by a member is "communicated", i.e. "handed off", by someone who is a member. Actually after further Googling it appears that this organization has stopped using this process.

I found this information here.