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I am a scientist writing my first manuscript with a substantial amount of mathematical methodological documentation.

I am using LaTeX, but this is not my question.

I would like to find a list of usage rules similar to Strunk and White. I can follow the practices that I see in my field, but it would be helpful to know the underlying rules and recommendations that will help me explain mathematical concepts in a reproducible and understandable way.

Thanks!

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I like how that book I mentioned was so good, it showed up in the answers as well... :D –  J. M. Dec 13 '10 at 17:28

5 Answers 5

up vote 13 down vote accepted

Here's what is in my shelf, in the order in which I picked them up:

  • Mathematics into Type (Updated Edition). American Mathematical Society, Providence, RI, 1999, ISBN 0-8218-1961-5. It includes what the usual submission/refereeing process is, how to mark manuscripts, how to space symbols, in-line equations, and display equations (and how to break long equations across lines). It does not discuss matters of style (how a mathematician usually says certain things), however.

  • Handbook of Writing for the Mathematical Sciences by Nicholas J. Higham. Society for Industrial and Applied Mathematics, Philadelphia PA, 1993. ISBN 0-89871-314-5. It includes a section on Mathematical Writing (Chapter 3) and one on English Usage (Chapter 4), as well as tips on organizing a paper and the like. I'll add that Chapter 2 ("Writer's Tools and Recommended Reading") contains a wealth of references.

  • A Primer of Mathematical Writing. Being a disquisition on having your ideas recorded, typeset, published, read, and appreciated by Steven G. Krantz. American Mathematical Society, Providence RI, 1997, ISBN 0-8218-0635-1. One full chapter devoted specifically to mathematical writing ("How to State a Theorem", "How to Prove a Theorem", "How to State a Definition", etc).

  • Paul R. Halmos. How to write mathematics. Enseign. Math. 16 (1970), pp. 123-152. A very good read, cited by every other work mentioned above. Also available on the web, as a quick google search will reveal; e.g., here.

  • How to write mathematics, corrected edition, by Norman E. Steenrod, Paul R. Halmos, Menahem M. Schiffer, and Jean A. Dieudonné American Mathematical Society, Providence RI 1981, ISBN 0-8218-0055-8. A reprint of four papers on writing mathematics, including Halmos's paper mentioned above.

  • Writing Mathematics Well: A Manual for Authors by Leonard Gillman. Mathematical Association of America, 1987, ISBN 0-88385-443-0 (page ix reads: "This manuscript was prepared by the author on an Apple Macintosh with the help of Mac$\Sigma$qn, a program for symbols and equations"; how times have changed...)

  • Mathematical Writing, by Donald E. Knuth, Tracy Larrabee, and Paul M. Roberts. MAA Notes no. 14, The Mathematical Association of America, 1989, ISBN 0-88385-063-X; this is a bit of an odd duck, in my opinion. They are the class notes for a course on mathematical writing taught by Knuth.

There are other, more general guides; I keep a copy of Fowler's "Modern English Usage" and the "Oxford Guide to English Usage" always available, as well as a copy of the Chicago Manual of Style (14th edition) and of Strunk and White at home (recently joined by Eats, Shoots and Leaves: the zero tolerance approach to punctuation by Lynne Truss; now I can tell my students that the semi-colon was invented by the same guy who invented italics). Mary-Claire van Leunen's A Handbook for Scholars (revised edition) is a classic as well. But these are not specific to mathematics, and a lot of the advice has to be actively disobeyed to follow standard mathematical phraseology or uses (many a copywriter unaccostumed to mathematics has choked on "a Green's function").

Added: I don't think you will necessarily pick up the traditional jargon/cadence of mathematics from any of the above sources, however. That's something that is picked up by osmosis, through hearing and reading a lot of mathematics. But this even happens across fields, not just across disciplines; one can often spot that someone is new to a particular field within mathematics by how he or she phrases certain statements, which is at odds with the usual practices of the sub-field in question. But the advice you get in any of the above (my recommendations, in no particular order, are Highman, Krantz, and Halmos for writing content, and Mathematics into Type for final preparation of the manuscript for submission, especially if you are submitting to a mathematics journal) should carry you through.

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Shouldn't "Green's" have an apostrophe somewhere? ;) –  J. M. Dec 13 '10 at 17:29
    
"That's something that is picked up by osmosis, through hearing and reading a lot of mathematics." - agreed. You learn to write like "them" by reading "them". –  J. M. Dec 13 '10 at 17:31
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@J.M. Oops. Quite so. In fact, it's "a Green's function" that is in the anecdote related by Krantz, of a copy-writer to told him it must be changed to "the function of Mr Green". –  Arturo Magidin Dec 13 '10 at 17:32
    
I understand where the copywriter's coming from, but I'm still snickering... –  J. M. Dec 13 '10 at 17:36

An excellent reference is

  • Krantz, Steven. A primer of mathematical writing. AMS (1997).

It covers much more than just papers, and I recommend it even to people with some experience. (There is a more technical book by Krantz in the same vein that treats books more extensively, "Mathematical publishing, a guidebook".)

Another excellent source, particularly because of Halmos's essay, is the short pamphlet

  • Steenrod, Norman; Halmos, Paul; Schiffer, Menahem; Dieudonné, Jean. How to write mathematics. AMS (1973).

Finally, some colleagues have recommended the following as well:

  • Higham, Nicholas. Handbook of writing for the mathematical sciences. SIAM (1993).

Hope this helps!

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And if you have time, you should watch J.P. Serre's lecture "How to Write Mathematics Badly" for what not to do.

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I enjoyed that talk a lot. –  Raphael Dec 13 '10 at 18:11
    
@Willie: +1. I really appreciate the video link. –  Jack Jul 18 '11 at 3:02

This may not be exactly what you're looking for, but Tao has good advice and includes on his page any other source I would consider referencing.

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See this previous post.

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