### Halmos on Writing Mathematics

#### Posted by Simon Willerton

Over in a discussion at Math Overflow I was reminded about Halmos’ great article on writing mathematics, which I highly recommend to all graduate students (or anyone else, for that matter).

- P. R. Halmos, How to write mathematics, L’Enseignement Mathématique, Vol.16 (1970) [31 pages, 3.3MB]. Individual pages are available for those with slow connections.

This caught my eye because I am in the middle of teaching an undergraduate course on how to present mathematics. As I flipped through Halmos’ article I realised that I discuss just about everything in it in my course. I had forgotten that I’d actually read the article, but I think that it had a lasting effect on me. Undoubtably, much of what is said is also said in most of the books on mathematical writing, however Halmos says it all rather well.

I won’t quote any of the article as I don’t want to focus on any one bit – it’s all great – instead I will give you the 2,000 year old quote that I start my course with. It’s by Marcus Fabius Quintilian, a Roman rhetorician, and seems as relevant now as it would have been then.

We should not write so that it is possible for our readers to understand us, but so that it is impossible for them to misunderstand us.

De Institutione Oratoria, Book VIII, 2, 24 (ca. 95AD).

## Re: Halmos on Writing Mathematics

It’s sound stuff. The main thing I found to disagreee with was that he seems to work under the assumption that readers read from beginning to end. (He doesn’t

saythat he assumes this. I just got that impression.) This assumption is wonderfully simplifying when it comes to solving the problem of how to structure your book, paper, etc., but totally unrealistic.