I discovered that Yu Zhang has a total of 22 reviews in MathSciNet, 19 of which consist of verbatim quotes of abstracts of papers or prefaces of books. A good example is the review 2000h:60086 of [R. Durrett, "Stochastic spatial models," SIAM Rev. #41 (1999), 677-718], since the review has a direct link to the exactly identical abstract on the journal website. Interestingly, authors (not) reviewed by Zhang include some of the best known mathematicians in the field, R. Durrett, G. Grimmett, T. Liggett, etc.
The only reviews which are not obviously direct verbatim copies of the abstract or passages of a preface are given below with numbering as in Yu Zhang's list of reviews on MathSciNet. Only item 19 (review 97j:60191) contains an evaluation of a result, i.e., more than just a list of the results from the paper.
Jane Kister, an associate editor at Math Reviews, in a reply to Doron Zeilberger's Opinion 24 justified the increase in non-reviews of short articles. However, the Yu Zhang phenomenon defies justification, other than the possibility that, due to the incredible volume of reviews, it escaped everyone's attention, except mine, that is.
An e-mail from Allyn Jackson of the AMS (but who otherwise has no
relation to Math Reviews other than an article in the Notices of the
AMS) suggested that verbatim Math Reviews were not unusual, so I
decided to do some more further investigating.
The statement that verbatim abstracts are not unusual did not
seem valid, in the sense that I conjectured that most verbatim
abstracts would usually be found on unsigned reviews, by which I mean
a review which does not have a named reviewer, and was therefore
constructed by Math Review editors by copying the abstract of the
paper. (Reviews having a credited reviewer will be denoted as "signed
I therefore did a MathSciNet search for the word "summary" in the
search field "anywhere". This returned 360,053 items. I then proceeded
to examine the first 200 items. Of the 200 items, 6 were papers with
the word "summary" in the title or in the body of the review. The rest
were all papers with reviews consisting of verbatim abstracts. Of these
194 items, there were exactly 19 signed reviews. Thus, a cursory
estimate shows that about 10% of verbatim transcriptions are signed
reviews. This survey seems to justify my belief that verbatim
signed reviews are unusual.
The above search produced another interesting result. One of 20 the
listed reviewers, Gil De Oliveira-Neto, has 60 reviews. After perusing
the first 20 items in the list of his reviews, I can report that 17 of
these reviews consist of verbatim abstracts. This shows that the Yu
Zhang case is not unique.
I recently noted that this year marked the passing of Robert
A. Rankin. As far as Math Reviews, he is special for having reviewed
his own paper 10,509b [Rob Alasdair Mac Fhraing, "The numbering of
Fionn's and Dubhan's men, and the story of Josephus and the forty Jews
(Gaelic)," Proc. Roy. Irish Acad. Sect. A. #52 (1948),
87--93]. Indeed, this is explained by the fact that this is the only
Gaelic paper as well, Rankin wrote it using his Gaelic name, and was
then asked to review, as he had been the only reviewer to put Gaelic
as a second language. I hope that this story is correct--MathSciNet
does not recognise Rankin as being author. In any case, are there any
other examples of self-reviews, I wonder.
Allyn Jackson reports that this story is recounted in the
memoirs of Ralph Boas, who was then the Math Reviews executive
director. In his review Rankin included a note saying that he was
author of the article.
Since this story appears to be well known, at least by
former Math Reviews executive editors, MathSciNet should be able to
recognise Mac Fhraing as Rankin, which it doesn't.