Mathematics publishing is a soft touch. The publisher usually hasn’t a clue, so they send the manuscript to someone like me to comment on. I used to be a soft touch too
Why do they do it? Academic publishers, I mean, who mix the first-rate with the fifth-rate. Fine manuscripts on very specialised topics have been published for generations alongside compilations of lighter-weight essays, to the general appreciation of the academic community. Reviewed by experts, they are recommended to students and laymen who want to learn more about the subject at hand. Sometimes they sell well, but it’s usually university libraries that buy most copies and essentially finance the whole enterprise.
However, this valuable service is open to abuse by those eager to cash in on the university market by publishing rubbish, perhaps by some college teacher with a silly idea and the determination to turn it into a book that looks on the face of it as if it might appeal to a broad audience.
Mathematics is a soft touch because the publisher usually hasn’t a clue, so they send the manuscript to someone like me to comment on. I used to be a soft touch too. One prominent university press once asked my opinion of a rather dull book using Greek myth to frame some simple mathematical problems (how long would it take to clear the Augean stables given certain conditions? — that sort of thing). I gave a nuanced response pointing out various deficiencies, so the author revised it, and they published it. A waste of my time, but the pièce de resistance arrived a couple of weeks ago, already published: a book by Philip Ording purporting to give 99 variations on a proof, published by Princeton University Press.
Now that could be very interesting, and the title might appeal to university librarians — which, in turn, means the publisher may well break even. For example, there are numerous proofs of Pythagoras’s theorem — just look on the internet — but this was a single equation with two solutions, and the variations were different ways of presenting less than a handful of approaches to solving it (algebra, calculus, geometry) from bare bones to filling in masses of unnecessary details, one chapter for each. One even consists of nothing more than a letter from the author to a retired engineer, and the recipient’s response saying that he did not think his work was relevant. It is a turgid exercise in mathematical piffle.
A good title and wonderful paragraph of blurb may make such nonsense seem appealing to university librarians who cannot be expected to be specialists. But in the long run, they do nothing to enhance the reputation of the publisher. They deserve to fail.