# Writing a mathematical work in english

this question is less about mathematics, but I don't know else where to ask. I am native to german and have to write my current thesis in english. This is difficult and new to me so i asked my professor, if there is any help to improve creativeness and variety in formulating mathematical sentences in english. His answer was that he guesses by now there should be such literature for mathematical writing in english but he doesn't know any title. I couldn't find any, either.

So here is my question:

Do you know any literature or source for this? (This is not a question about formatting or write down mathematic proofs and results clearly, I am very used to Latex and never had a problem to be unprecise)

If you think this question does not belong here and you know a better place to ask, please tell me.

• want you to use $$\LaTeX$$? if so then there is a guide in the internet to do this – Dr. Sonnhard Graubner Dec 22 '17 at 14:07
• I am using Latex already, my question is more about the competition to write in a foreign language. – Falrach Dec 22 '17 at 14:11
• and about what want you to write? – Dr. Sonnhard Graubner Dec 22 '17 at 14:12
• I think the easiest way is to write. It is very good to have someone read your text. For example two pages per week. In return you read his/her stuff. It is important to be very open minded to feedback and to communicate this to the other person. Only then you both will be able to improve your writing. Also mathstack exchage is a good way to improve your skills. – MrYouMath Dec 22 '17 at 14:17
• In mathematical writing, you do not want lots of "creativeness and variety" in the English. Just use the same mundane phrases over and over again. This is to make it easy to read for those whose native language is not English. – GEdgar Dec 22 '17 at 14:26

This doesn't answer your question (I know no literature source), but it does involve some experience (i.e., a career spent reviewing a fair number of papers written by speakers whose first language is not English.)

I strongly recommend that you write your paper in German, and then translate it, a paragraph at a time, to English.

The organization of thoughts in English, French, German, etc., is pretty similar. I know, because I had to learn to read math papers in French and German back when I did my Ph.D.; after I learned some vocabulary, it was fairly easy.

The reason to write in German first is that you can concentrate on clearly presenting and explaining the mathematics. That's hard to do in any language, so sticking with your first language helps. It's easy to miss (in a comparatively unfamiliar language) that you left out some step.

Step 2 is translation. A really useful thing to do here is to pick up a well-written math book or paper in English. (My general advice: anything written by John Milnor.) Look at how introductory paragraphs are written. When you see

Let $f$ be a function...

appearing again and again, you know (as you translate from French, for instance) that "Soit $f$ une fonction..." must correspond to that. (Google translate, on short fragments, helps a lot here!) You realize that where, in French, you might use the subjunctive, you need to do something else in English, but once you have a pattern/model to work from, it gets a lot easier.

As a final step, get a native english reader (one who's read some math will be a BIG help) to read through the document and mark up/rewrite awkward sentences. The reader should NOT try to understand the mathematics. The goal should be to make sure it reads like English. Your English appears to be good enough that you can tell whether the rewritten sentence says what you meant.

If you do these three things --- write in German; translate to English with the help of model math-writing; get an English speaker to sanity-check the results --- then when I have to review your paper, I'll be a happy guy. Sure, at some points I'll think to myself "What might this sentence have been in German? Oh...NOW it makes sense!"(**) But mostly, I'll find it not so bad to read.

(**) I confess, I can't actually do this for German. Sometimes for French, and sometimes it helps.

Last but not least: include thanks to your English-speaking friend for helping improve the clarity of the document by polishing the English.

• John, I think this is very sensible. – Lubin Dec 22 '17 at 14:25
• I'm a native German speaker myself and I somewhat passionately disagree with this idea. Attempting to do any serious kind of mathematics in German is incredibly frustrating. Developing mathematical ideas is, in my experience, pretty independent of language. Bringing those ideas to paper, however, isn't. And German is a horribly ill-suited tool to do so. (English is far from perfect either but at least it's managable.) – Stefan Mesken Dec 22 '17 at 14:45
• Your English seems pretty decent (although it's "manageable", not "managable" :) ); OP appears concerned with a lack of a sense of speaking idiomatically; your situations differ. As for German being ill-suited to writing math...you may be correct, but I've read several German math papers that seemed fine to me. Perhaps as a non-native reader (I use the term loosely!) I was unaware of how horrible they were. But I did manage to learn the mathematics somehow. My sense is that the AMS translation of Lehrbook der Topologie (I surely spelled that wrong!) was pretty faithful, and I love it. – John Hughes Dec 22 '17 at 15:26
• Sorry, i was travelling so i had not so much time to answer. First I want to say that, although it's not a direct answer on my question, it helps me a lot that you think that this tecnique works. I don't find it hard to formulate mathematical ideas and results in german, so i will try it as you said, but more experimental. Because: I think your argumentation for the first step is ok, but don't forget that I could be a horrible translator, so that the fluent language english can be becomes very "edgy"? to read. <-- | Furthermore, this technique won't help me to improve my english writing skills – Falrach Dec 23 '17 at 15:17
• I agree that you could be a horrible translator. But I'll bet that you're worse at "composing and translating simultaneously" than at "just translating." As for "it won't help me improve my writing skills": you have to decide on a goal. Do you want to produce a good mathematics paper in English, or become a better English writer? I thought that your goal was the first. I think that as a consequence, you'll find yourself doing the second, because when you compare your translation with the "fixes" applied by the native speaker, you'll start to notice patterns... – John Hughes Dec 23 '17 at 15:33