If you have access to MathSciNet and are in the mood for some good laughs, head over to Kimball Martin’s collection of Exceptional MathReviews. He introduces his collection as follows:

Were you ever looking up papers in MathSciNet and you found one that especially made you smile or laugh? And were you ever wishing that MathReviews were sorted by amusement factor? Well, we did. In fact, it is a long-standing game among many mathematicians to find the most amusing or worst MathReviews they can.

As a gesture of humanitarianism, I’ve compiled a list of what I take to be, for one reason or another, exceptional MathReviews of which I have been made aware. A review may merit listing by being unexpected, witty, scathing, humorous or otherwise deviating considerably from the run-of-the-mill reviews. It may be either good or bad, called for or uncalled for, but it should be in some way exceptional.

Here are a few of the reviews (or snippets of reviews) that I found while browsing the list.

Spike Milligan wrote of a certain poet that he tortured the English language, yet had still not managed to get it to reveal its meaning. Trying to fathom the paper under review is similarly frustrating.

It is hard to imagine in a single paper such an accumulation of garbled English, unfinished sentences, undefined notions and notations, and mathematical nonsense. The author has apparently read a large number of books and papers on the subject, if one looks at his bibliography; but it is doubtful that he has understood any of them… What is amazing to the reviewer is that such a thing was ever printed.

Not every text containing mathematical formulae or terminology may be considered as a scientific work. Sometimes it is a mere imitation. My impression is that this is exactly the case of the paper under review.

The author adds three introductory sentences to a paper of G. P. Whittle [Discrete Math. 54 (1985), no. 2, 239; MR0791665 (86j:05047)] and changes the word “principal” to “fundamental”. He also adds an acknowledgement to the referee but fails to add an acknowledgement to Whittle for writing the original paper.

This paper seems to the reviewer to contain no mathematics.

The author asserts that “this book is written by an amateur for other amateurs, but we amateurs won’t mind having the professionals reading over our shoulders”. The reviewer, a professional, would like to benefit from whatever insights the author may have. However, he has not been able to see through the blizzard of unusual (and largely unexplained) notations and formulas that fill the 274 hand-written pages of this book. If the author has a message for professional mathematicians, he will have to try again, using a language that is not a personal secret.