I received a letter from Mathematical Reviews inviting me to be a reviewer. Before I make my decision, may I ask what are the possible advantages and/or disadvantages of being a reviewer?
For background, MathReviews are reviews written by mathematicians of published mathematical papers and typically describe the content of the paper. Such reviews are available on the online database MathSciNet.
Here are some reasons to do it
Writing reviews forces you to read some papers that are not in the focal point of your interests. Since there is no decision to take, I find it less time-consuming and stress-generating than refereeing a paper.
A good review is a service to the mathematical community: it allows mathematicians to find relevant papers and decide wether a paper is worth searching for and/or reading.
You get paid $8 for each review that you can use to buy books from the American Mathematical Society.
Your name might appear in MathSciNet as a reviewer next to some nice authors and nice papers ;-)
Here are some reasons not do it:
Reading a paper and writing a review takes time.
You are not anonymous. If you are not careful enough in writing your review, you might upset some authors.
Here are some tips to have a good experience:
You can set up a limit of the number of papers that you accept to have at once. Set it a reasonable level for your workload.
Choose carefully the AMS classifications that you are interested in. A poor choice can lead you in reviewing papers that do not interest you. (Afterwards, if you receive many uninteresting paper, you should consider mentioning that you are not interested in their AMS classification.)
Reviewing a book takes much time. Think carefully about it when asked.