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Cons:

  • it takes time. I should rather worry about producing good-quality research and disseminating it through slides and talks, especially now that I am relatively young. Publishing slides and expository material will "help the world" more than an AMS review.

  • it is not something that has a great value for the community. It might be just me, but I find the reviews of little use, considering that the papers already have abstracts. Mathscinet overall is great as a literature database and search tool, but the presence of reviews does not add much to its value.

  • AMS is selling access to these reviews. I am probably getting paid peanuts, or nothing at all (they did not mention payment at all on the invitation e-mail), to help building a corpus that is sold commercially. The prices are not cheap for a single user. I'd rather contribute to a public database.

Pros:

  • I personally do not use often the reviews, but they might be very helpful for other people. Maybe someone else relies on then more than I do (waiting for feedback here).

  • I am afraid to look mean and ungenerous to the eyes of the "math community" if I refuse it. For instance. refereeing for a journal is a time-consuming job, but we should not refrain from doing it because it helps the community; maybe other mathematicians see these reviews in a similar way.

  • it will look good in my CV as an additional "editorial service"; it is somehow a recognition that one is a competent member of the math community.

Overall, the pros do not seem too strong to me, and I realize that they are all about "how people will see me", which is probably a sign that they are flawed arguments. So, unless you guys on Mathoverflow manage to convince me of the contrary, I think I will turn down the offer, at least for now.