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# Mathematical writing

One of my goals with participating in this category theory course (other than the obvious) is to improve my writing, particularly my mathematical writing.

Earlier today How to Write Mathematics, Halmos was posted on Hacker News. It's 22 pages, but fairly easy to read and contains a good bit of guidance. Much of it is "obvious" as the author points out in the preface, but sometimes what's obvious isn't well understood or connected in our minds.

For those who, like me, haven't been writing a lot of math over the years this could be a useful or at least informative read. Since, based off the introductions, many of us are not professional mathematicians, and even fewer are mathematicians by education, this may be helpful.

I'm sure John Baez and others can offer additional advice or pointers to other resources similar to this one (or even counterpoints to some of Halmos' statements).

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edited April 2018

Of course, even more important than getting advice on writing is to read lots of good writing. This is harder in mathematics than if, say, you were an aspiring novelist, since badly written novels don't generally get published. In mathematics, it often happens that a paper that contains exactly what you want to learn is also badly written. It's important to realize that even "professionals" can write poorly, and some professionals in the mathematical sciences never learn the skill of writing well. But, looking for good mathematics writers and paying attention to their style is really helpful.

You seem to have already found one of the best mathematics writers I know (he's teaching this course!) so you're on the right track there. ;-)

One fairly recent resource does come to mind: the Princeton Companion To Mathematics. The articles' authors are written real experts in their subfields, but also selected by the editors for their clear writing skills. And, I think Timothy Gowers personally helped improve the writing on many of them. It's a great book. The Princeton Companion To Applied Mathematics, is also good, and it contains a good article on writing mathematics, written by Gowers.

Comment Source:Good thing Halmos's paper is "easy to read" -- never trust any hard-to-read advice about writing! :D Of course, even more important than getting advice on writing is to _read_ lots of good writing. This is harder in mathematics than if, say, you were an aspiring novelist, since badly written novels don't generally get published. In mathematics, it often happens that a paper that contains exactly what you want to learn is also badly written. It's important to realize that even "professionals" can write poorly, and some professionals in the mathematical sciences never learn the skill of writing well. But, looking for _good_ mathematics writers and paying attention to their style is really helpful. You seem to have already found one of the best mathematics writers I know (he's teaching this course!) so you're on the right track there. ;-) One fairly recent resource does come to mind: the [Princeton Companion To Mathematics](https://press.princeton.edu/titles/8350.html). The articles' authors are written real experts in their subfields, but also selected by the editors for their clear writing skills. And, I think Timothy Gowers personally helped improve the writing on many of them. It's a great book. The [Princeton Companion To Applied Mathematics](https://press.princeton.edu/titles/10592.html), is also good, and it contains a good article on writing mathematics, written by Gowers. 
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I once wanted to write a paper about why most papers on mathematics are badly written, and there's a draft of it here:

I think it's a great title, and I think there are some ideas worth developing here - but I never finished the paper, perhaps because the TeX file was called boring.tex.

Comment Source:I once wanted to write a paper about why most papers on mathematics are badly written, and there's a draft of it here: * [Why mathematics is boring](http://math.ucr.edu/home/baez/boring.pdf). I think it's a great title, and I think there are some ideas worth developing here - but I never finished the paper, perhaps because the TeX file was called boring.tex.
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edited April 2018

I'm not sure if I've managed to actually work any of the insights into my writing but I found Steven Pinker's "The Sense of Style" to be an interesting read (though not aimed at mathematical writing directly).

Its also something I wish we'd spend a bit more time on in technical disciplines in general. I sometimes get the feeling that I've spent more time discussing american vs british style suggestions than larger questions of style and whether whats being written is actually communicating ideas effectively. Which I find worrying. So thanks for the suggestions on other resources. Without having read all the way through (yet!) I get the sense I'll be very sympathetic to John's points about effective narrative techniques.

Comment Source:I'm not sure if I've managed to actually work any of the insights into my writing but I found Steven Pinker's "The Sense of Style" to be an interesting read (though not aimed at mathematical writing directly). Its also something I wish we'd spend a bit more time on in technical disciplines in general. I sometimes get the feeling that I've spent more time discussing american vs british style suggestions than larger questions of style and whether whats being written is actually communicating ideas effectively. Which I find worrying. So thanks for the suggestions on other resources. Without having read all the way through (yet!) I get the sense I'll be very sympathetic to John's points about effective narrative techniques. 
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edited April 2018

Deirdre McCloskey wrote on Economical Writing (4 odd pages), some of which is specific to economics, but a lot of it is probably quite useful to mathematics too. Plus, she is very entertaining and opinionated.

Comment Source:Deirdre McCloskey wrote on [Economical Writing](http://www.deirdremccloskey.com/docs/pdf/Article_309.pdf) (4 odd pages), some of which is specific to economics, but a lot of it is probably quite useful to mathematics too. Plus, she is very entertaining and opinionated.