No mathematician, I agreed to review this book on the basis that I could comment at least on the linguistic aspects. I did have the hope that reading of the etymologies of the words included, I might thereby pick up more mathematical knowledge than I possess, although that has proved to generally be an elusive hope. The book is aimed specifically at mathematicians, although the etymologies and word histories do offer much of interest and value to lexicographers also.
The author is a Professor of Mathematics in the USA, at Allegheny College, and his book is the result of “decades of […] painstaking research […]”. That shows in the (to this non-mathematician) apparently pretty comprehensive coverage of mathematical vocabulary and, certainly, in the accurate etymologies for each word; even more so, in many of the entries where the origins, development and use of a word in English from medieval times onwards is also particularly interestingly demonstrated, selected at random, “antilogarithm […] is a late seventeenth-century offspring of the word logarithm, invented by John Napier in 1614”. I assume that is the Edinburgh Napier of “Napier’s bones” – an early calculating aid which I have seen on display in his eponymous university.
In his preface, Professor Lo Bello states that “this is a book about words, mathematical words, how they are made and how they are used”. In the preface and throughout the dictionary, he is at pains to indicate correct spelling and usage and to deplore incorrect usages, and above all, it seems, hybrid words combining Latin and Greek roots, I suppose he must choose never to watch the television, my classics teacher’s linguistic bête noire in the earlier days of that medium.
I assume, I am told possibly naively, that mathematicians must strive constantly for precision; certainly, that seems to be the case throughout this dictionary. The preface itself widens from an interesting survey of the historical development of mathematical vocabulary into what becomes more or less a diatribe against perceived incorrect usage and terminology. Such opinions recur in various entries, together with the occasional barb against modern teaching (the entry on calculus ends: “In modern times calculus is the standard introduction to the higher mathematics, and it will remain so until innovators sweep it away with everything else”). Among a number of longer entries, I was surprised to find one under “cant”, not a mathematical term at all. The nature of that entry can be summarized by quoting a sentence from it:
In the following paragraphs, I consider the problem of the low type of English usage that has become commonplace in prose written by mathematicians. […] The freefall of English that took place in the twentieth century resulted in the extinction of good style in the language of mathematics education.
Not being a reader of mathematical literature, I would not comment on that, neither would I disagree with many of the other similar comments throughout the book relating to more specific usages. I do, however, quote from the same entry that “The role of a perpetual complainant is as unsuccessful as it is irksome […]”. I would hope that mathematicians will not be put-off using and profiting from this dictionary by finding too many of such “irksome” comments. For there is much of value to be learned by aiming for such accuracy. I might well use the word apophthegm, but am unlikely ever to use apothem; if I came across it anywhere, except here I might unthinkingly assume the latter a strange American spelling of the former. How wrong I would be is explained here by apothem (“the perpendicular distance from the center of a regular polygon to a side”) being derived from the Greek απoΘɛμα (“to place from”) and apophthegm from απoϕΘɛγγɛσΘαι (“to speak out”). The dictionary comprises throughout such detailed and accurate etymologies, primarily from Greek and Latin but also from Hebrew, Arabic and other sources.
Most of the entries comprise a paragraph or two, with a few (Cartesian and Mathematics, for example) comprising essays of several pages. Greek (and some Hebrew and Arabic) words are entered in their original alphabets. The layout of the volume, using bold for headings, italics and smaller indented Roman for more substantial quotations, is clear and elegant. It is apparently only available in a (fortunately sturdy) paperback, or in electronic format.
Until recent times, when the study of classical Greek and Latin have so dramatically declined in Western education, there used to be a sometimes close correlation between mathematics and classics. Indeed, I was once informed, in a job interview of all occasions that the organization liked to employ classicists, as they had good mathematical brains, as it was a job interview I was too polite to ask why they didn’t just employ mathematicians. Here, the two studies are brought back together at the very basic level of vocabulary. Some of the complaints may irk but that should not detract from a fundamentally accurate, clear and very interesting dictionary. It may be aimed at mathematicians, but anybody interested in etymology and the history of word usage will find much of interest here too.
