The Princeton Companion to Mathematics is even more nearly nearly finished than it was last time I said it was nearly finished. In fact, this time I can give a date — July 13th — past which it will be too late for me to do any work on it. The book will be printed in September and available in November.
As an example of the important issues we now face, here is a question about hyphens: I’m fairly sure there will be a small but passionate minority of mathematicians who care about these, and a question has come up. I am curious to know what other people think, so I’m not going to say what I think: I’ll just try to present the question as neutrally as possible. And here it is.
Consider the following four phrases: “intermediate value theorem”, “travelling salesman problem”, “twin prime conjecture”, “minimal surface equation”. Do they need hyphens? And how about “three body problem”?
Brief argument in favour: the general rule is that if you have a phrase made up out of an adjective, a noun and a noun then you put in a hyphen. (An example is “brute-force search”.)
Brief argument against: the cases above are exceptions because they are a bit like proper names: the first two words are not really functioning as an adjective that describes the main, third, word; rather, the three words form a single phrase. In addition, the lack of hyphen does not lead to any conceivable ambiguity.
If you buy something like the second argument, can you make it more precise?
Also, if you wouldn’t write the hyphen in “intermediate-value theorem”, do you find it positively wrong and strange looking, or merely not necessary?
In other words, should there definitely be hyphens, should there definitely not be hyphens, or would either decision be acceptable? (To judge from Google, standard mathematical practice seems to be not to put hyphens, but that alone is not a sufficient argument.)
I’ve had a more mathematical blog post planned for months, but it’s still going to have to wait. But once again I’d like to make clear that this blog’s still just about alive and will I hope become more active again before too long.