Instructive examples of elegant, clear, rigorous, terse, but "non-dull" mathematical prose

Question

On the "About" page of the Mathgen project one can read:

"More seriously, I think this project says something about the very small and stylized subset of English used in mathematical writing. This program only knows a handful of sentence templates, and yet I think its writing style is not far off from many published papers. You could argue this is bad (shows a lack of creativity) or good (makes papers more accessible to those with a limited knowledge of English), but I think we could stand to pay more attention to our writing styles, instead of unthinkingly relying on stock phrases."

Starting from these considerations, I would like to ask a more general question on mathematical prose: could you point out some examples of "great" mathematical writing that you've came across over the years from which an undergraduate can learn how to write mathematics well (while understanding the content)?

I will define "great" as follows:

• showing masterful expertise;
• engaging, but rigourous and precise (as opposed to chatty and friendly but unclear and imprecise);
• elegant, terse (by which I mean polished, smoothly elegant, and to the point, but not brusque or abrupt or devoid of motivation), clear.

Note (1): I've read A primer of mathematical writing, which gives some sensible advice on writing in general, but I was looking for some actual examples of good mathematical prose.

Note (2): I guess that many of you will mention Rudin, so I would like to say that I'm already studing his book.

Answer 1

I nominate Halmos. All of his writing is good, but you might look in particular at "Finite dimensional vector spaces".

Answer 2

Pick up an issue of SIAM Review. I admit that I haven't read every article in every issue of late, but I cannot recall an article with less than "very good" writing, and most are excellent.

Answer 3

There is a book by Bott and Tu called 'Differential forms in algebraic topology' which I think satisfies your criteria. In particular, you say it should be engaging and that is what I remember most about when I first read this book.