I've certainly not written a text, but I've read a few nasty ones. The best advice I would give an up-and-coming text writer:
1) Before you start writing, think long and hard about who you intend the book for -- Is it for teens? Undergraduates? Graduate Students? PhD wielders? This is something that really matters because of the "mathematical maturity" issue. Somebody that's been studying the subject for 20+ years will be better able to fill in any gaps you might leave (intentionally or unintentionally) in your treatment of the subject matter.
2) Super "symbol-heavy" books are not conducive to getting your message to your audience, although it might feed your ego. I think it is tempting for somebody who'd become so familiar with a subject that they can write a book about it to get carried away with showing off everything they know. If I had a quarter for every time I was reading something convoluted and came across the words 'trivially', 'obviously', 'clearly', etc... I would be a millionaire. Well, maybe not that rich, but I'd have at least $50.00.
3) It seems like mathematics texts come in one of two types:
a) overly symbolic, cryptic, and dense;
b) overly pedantic, example-ridden, boring to read.
4) Many mathematics texts seem to be very "method-driven" and not present the intrinsic subject matter they deal with. For instance, I'm currently reading a book on differential geometry that is extremely dense symbolically (granted, anything with tensors necessitates this to some degree) and the author hasn't bothered to tell my anything about why the hell what he is writing should matter to me: "Ok, I can do this curvature thing, and it's intrinsic, that's nice. So what do I do with it? What motivated the discussion in the first place?"
The above list is by no means complete, but I hope it helps a little. I encourage others to add to my list!
Disclaimer: I am partial to a more conversational reading style, as that is how I write. Don't be too formal in your writing style -- it's already mathematics for heaven's sake!
Best,
Dylan
Let me begin with the disclaimer that by answering this question I do not presume to behold my own writing as a model of the qualities that you admire. I'm answering because I've noticed my comfort with and talent for writing improve markedly as I've matured as a mathematician, and I've often wondered if there is a causal relationship. I believe that for a variety of reasons math and writing are co-productive skills.
First and foremost, learning and doing mathematics invariably requires one to read and write a great deal, and the reading and writing involved can be extraordinarily taxing. As with any talent there is no substitution for persistent, deliberate practice.
Second, good mathematicians and good writers must both develop the ability to use language in a very precise way. Every area of mathematics has its own vocabulary and grammar which one must master in order to become an expert, and indeed many of the great breakthroughs in mathematics are really linguistic revolutions (such as the advent of the formal definition of a limit in calculus). Because of this I've noticed that the writing mistakes which offend me the most are based on imprecise use of words; a common example is when students ask how to "prove a problem".
Third, every serious math student encounters at some point in life the stark contrast between really good and really bad exposition. The most beautiful ideas can feel like tedious nonsense in the hands of a bad writer, and even the most mundane details can come to life in the hands of a good one (of course, a huge part of good mathematical exposition is based on selection of detail). I know that this makes me self-conscious about my own writing, and I wonder if others feel the same way.
These three observations suggest ways in which mathematicians may naturally develop good writing skills, but it's worth noting that the mathematical community as a whole deliberately tries to nurture good writing as well. I never participated in any formal writing workshops, but several of my mentors over the years - particularly my PhD adviser - spent a great deal of time and energy helping me improve my writing.
Best Answer
Guten Morgen,
fellow German here. I was in the lucky position, to have professors in the undergrad courses who started their lectures with a quick review of the last lecture (5 minutes) which was given in english. That way, you started to learn the basic math terminology already in the first semesters. But I also had to look up names of theorems which I also did via Wikipedia. However, what really made me learn the english language (in science) where the lectures given by non-german speakers. This was espacially the case in my Master. I had the possibility to choose my courses rather free, and if possible I took the english version. I have not always written all my exercises in english, but I wrote all the "larger projects" I had to do in english: Reports, Seminar work, Projects, Thesis,... Furthermore, one simply should not be afraid to get all the textbooks in english. If you take an Analysis course, don't restrict yourself to the german textbooks, simply take an english version of it. You can always also ask the professor to suggest good material, they will be happy to do so!
But the most important aspect was already mentioned by fraiem, its learning by doing.
Good luck!