Deliberate Ambiguities

Plain language is inherently ambiguous. Its usage in math and science may and does lead to difficulties in communication and learning. Such words as "doublespeak" and "realpolitik" became part of the every day vocabulary. J. Paulos gives (what he calls a charming) example of an ambiguous letter that may have been written by a meek professor who couldn't turn down an importunate request for a recommendation:

You write to ask me for my opinion of X, who has applied for a position in your department. I cannot recommend him too highly nor say enough good things about him. There is no other student of mine with whom I can adequately compare him. His thesis is the sort of work you don't expect to see nowadays and in it he has clearly demonstrated his complete capabilities. The amount of material he knows will surprise you. You will indeed be fortunate if you can get him to work for you.

Surprisingly, one of the quotations on the back cover of the book (perhaps taken out of context) shares the same spirit of ambiguity as the recommendation above

After reading A Mathematician Reads the Newspaper, it will be impossible to look at the newspaper in the same way.

- Philadelphia Inquirer

The book deserves every praise and, for all I know, the reviewer might turn out to be right. But in what sense? Are you going to acquire unusual curiosity towards newspapers or develop inordinate disgust to the mere sight of the fresh print? It does not say.

Virtually every book in my bookstore has a back cover which I dutifully scan for the benefit of the visitors. The back cover to Paulos' book caused me to have second thoughts. As the first step, I went through the back covers of books in my library. To my delight I did not find a lot of deliberate ambiguities. There were just two. The back cover reviews en masse appeared to be informative and sincere. A couple of times I felt in disagreement with an evaluation but, otherwise, I had little to complain about. Here are the two examples I came across.

The first one recommends The Mathematical Universe by W. Dunham (which I consider among the best among popular math books):

... a very special math book, as good as any popular book on the subject since E.T.Bell wrote Men of Mathematics in 1937.

- Los Angeles Times

Am I being too pedantic to insist that unless one has an interest in and experience with popular math books, the quotations says precious little in itself? Furthermore, I heard it said the E. T. Bell in his Men of Mathematics often embellished historical personages by skipping human weaknesses and quite frequent mistakes.

Another quotations recommends the recent book "What Is Mathematics, Really?" by R. Hersh. The passage is by Ian Stewart, an outstanding mathematician and expositor. I hope very much the mistake is the editor's and not Stewart's, whose books I really love. Be as it may, what does the following say?

Reuben Hersh puts the people into philosophy and the philosophy into the mathematics: He will take your mind to places it has never dreamed of.

- Ian Stewart

In the book, there is plenty of information and ideas that, if not altogether original, are selected and combined in an original manner. There are ingenious insights as well. But the same is true of many a book that went into blessed obscurity short time after appearing on bookshelves.

In the book itself, Hersh has this to say:

This book reflects an inside view of mathematical life. It's based on 20 years doing research on partial differential equations, stohastic processes, linear operators, and nonstandard analysis, 35 years teaching graduates and undergraduates, and many long hours listening, talking to, and reading philosophers.

To this I may only remark, that many other authors and mainstream mathematicians with whom Hersh disagrees and who will likely beg to differ from his views, will claim no less distinguished a resume...

(A review of the book by F. Gouvêa appears at the MAA Online site. In my view, a book of 300+ pages that quotes other mathematicians and philosophers several times per page can't be void of content. However, when it comes to his personal views, Hersh demonstrates unusual shortsightedness and arrogance that I would not expect of a person of the statue Hersh appears to claim. His complete disregard for other people's views is quite unprecendented.)

Here's an ad in a window of a real estate agency in Jerusalem, Israel, that caught my eye:

surprising price

A possible ambiguity was pointed out by Jukka Tapani Santala from Finland, and there is another one I came across by accident.


  1. J. A. Paulos, A Mathematician Reads The Newspaper, Anchor Books, 1995

Language of Mathematics, Language of Science and Plain Language

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