Actually, while it is true that algebraic number theory is (in part) the
algebraic theory of numbers, it is just as much the theory of algebraic
numbers. (And its study involves methods that are not algebraic, as
well as methods that are.) So perhaps the ambiguity is not actually so
bad in this particular instance.

Best wishes,

Matthew

The best non-mathematical example I could think of was “Third World War”.

Then again I do have an issue with placing dashes and semi colons in silly places…

I have no intention of taking hyphens seriously. Those who wish to do so I leave to Fowler’s eleven columns. If I attempted to lay down any rules I should certainly go astray, and give advice not seemly to be followed. For instance, the general practice of hyphening co when it is attached as a prefix to a word beginning with a vowel has always seemed to me absurd, especially as it leads to such possibilities of misunderstanding as unco-ordinated must present to a Scotsman. If it is objected that ambiguity may result, and readers may be puzzled whether coop is something to put a hen in or a profit-sharing association, this should be removed by a diaeresis (coöp) not a hyphen (co-op). That is what a diaeresis is for.

I will attempt no more than to give a few elementary warnings.

(i) Do not use hyphens unnecessarily. If, for instance, you must use overall as an adjective (though this is not recommended) write it like that, and not over-all.

But if you do split a word with a hyphen, make sure you split it at the main break. Though you may write self-conscious, if you wish to have a hyphen in the word, you must not write unself-conscious but un-selfconscious.

(ii) To prevent ambiguity a hyphen should be used in a compound adjective (e.g. well-written, first-class, six-inch, copper-coloured). The omission of a hyphen between government and financed in the following sentence throws the reader on to a false scent:

When Government financed projects in the development areas have been grouped.
But remember that words which form parts of compound adjectives when they precede a noun may stand on their own feet when they follow it, and then they must not be hyphened. “A badly-written letter” needs a hyphen, but “the letter was badly written” does not. There must be hyphens in “the balance-of-payment difficulties” but not in “the difficulties are over the balance of payments”.

(iii) Avoid as far as possible the practice of separating a pair of hyphenated words, leaving a hyphen in mid-air. To do this is to misuse the hyphen (whose proper function is to link a word with its immediate neighbour) and it has a slovenly look. The saving of one word cannot justify writing

Where chaplains (whole- or part-time) have been appointed
instead of “where chaplains have been appointed, whole-time or part-time.

The English language was not designed for mathematical clarity. Indeed, most of the English language was not really designed at all – it simply grew. It is not always perfectly clear. Mathematicians must build their communication on top of English [or replace English with whatever is your native or local language], and so they must work to overcome the weaknesses of English. Communicating clearly is an art that takes great practice, and that can never be entirely perfected.
Eric Schechter, Associate Professor
Department of Mathematics
Vanderbilt University

Certainly leave out the hyphens, if you prefer. If questioned, you can always state that it is standard mathematical form. Really, who is going to question a Fields medalist on standard mathematical form! But please, do not leave out the ‘extra’ l in travelling. That is simply a uniquely American spelling.

It’s a rational proposal, but I don’t always stand by it. I wouldn’t insist on hyphenating a phrase that is ambiguous to the layman but not to the specialist if no one else does. Convention trumps rationality.

OT: Is there anything new to report on the “tricks wiki?” I’ve been wondering about that for months, but there’s been no sign of whether the project is even alive, which is disappointing.

My non-mathematical example: California history teacher.

In this example, “California” can conceivably modify “history,” “teacher,” or both. Therefore, a hyphen is called for. “California-history teacher” is a teacher of California history, “California history-teacher” is “a history teacher from California, and “California-history-teacher” is a teacher of California history from California.

I don’t take hyphens lightly. If there’s no ambiguity, I don’t use them!

As for “intermediate value theorem,” “traveling salesman problem,” “twin prime conjecture,” and “minimal surface equation,” I leave these to you mathematicians to determine whether or not they contain ambiguities. (“Three-body problem” is hyphenated by the always-hyphenate-if-the- first-word-is-a-number-and-it-modifies-the-second-word-in-a-three- word-compound rule.)

You need/ought to get a “bot checker”, before the comments section gets flooded with garbage. I’ve had the problem myself.

I go with this. I think convention has a important role to play too — most readers are used to reading the above mentioned titles as proper names. Using the hyphen might throw in some confusion.