# How to learn/speak “mathematical english”?

Good day!

I was wondering if there is a good way to learn "maths in english". I am studying mathematics in Germany (I am from Germany, so english is not my native language) and have recently started to work with english papers, textbooks etc. Reading them is alright so far, although I had to get used to some sentence constructions (but this was also the case when I started studying maths, as mathematicians tend to have their own grammar, so that is fine with me).

My question aims to writing/speaking "mathematical english". As far as I'm concerned there are (at least) two things I'd like to learn:

1. Get the "basic theorems" right. For example if someone wants to show that there exists a unique solution to $x=\cos(x),x\in\mathbb R$, I'd suggest to use the "Zwischenwertsatz". Using wikipedia I can find that the "Zwischenwertsatz" is the "Intermediate value theorem" and of course I can do that for every specific theorem and eventually learn the translations, but I find it rather annoying to consult wikipedia whenever I want to talk about a specific theorem. I guess I'm looking to suggestions for good textbooks that cover these basics; they don't need to be "good" in a way that they have lots of exercises including solutions, online support or anything like that, but have a "good style" of mathematical writing, which ties to my second point.
2. Get the "style of writing" right. Of course, learning by doing should be a good thing here, but living in a german environment so far I didn't have many chances to write in english. My first attempt to writing maths in english actually happened yesterday here on stackexchange, and it took me quite a while until I was satisfied (and at least thought it to be "readable"), much longer that it would have taken me to write the same thing in german.

Can you suggest anything that I should read/do to achieve this?

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!

Your narrative in English is good.

Two things I would suggest are:

Van Nostrand Mathematical Encyclopedia is available both in English and

German. The key to English version is your German original.. and vice-versa.

A request for time at Chat room with German mathematicians here may help.

As you keep on working at writing you learn slowly, friendly help and

suggestions come in from all. (Things like proper nouns in English are

capitalized, like all nouns in German are smaller issues ..)

• This looks great, thank you! – Hirshy Jun 14 '15 at 10:00
• Also, your written English is better then many Americans. Just do it like @fkraiem says. This is a good place to practice too. Everyone seems friendly and will probably just edit any grammer or translation mistakes rather then vote you down. – JPKowal Jun 14 '15 at 10:04

I think it's no different from learning English in general (or indeed any other language), you learn both by seeing and by doing. The more English-language material you read, the quicker you will "get used to it" and naturally mimic what you have read in your own writing.

As for "chances to write in English", it's really up to you. There's nothing stopping you from writing in English even if it's not required of you (and indeed, if you only ever do things because they are required, that's a problem of its own). You can write up notes of what you learn, or start a blog, for example.

I don't think the names of the "basic theorems" are very relevant, unless you want to teach secondary-school mathematics in English (which is unlikely), so I wouldn't worry about them. The idea is what's important, and often it's not much longer to state than any name people have chosen to give it.

• Thank you for your answer! I hardly ever do anything just because it is required, otherweise I wouldn't even bother to ask questions here. ;) As I was writing my question I thought of your point to just read as much material as I can get, but since all of my lectures, textbooks etc. are in german, I don't know "good" material. And as far as teaching goes, at the moment it is indeed unlikely, but in the future it might be possible (so far I have only taught new students in german, but we have lots of foreign students, so knowing these theorems might come in handy). – Hirshy Jun 14 '15 at 9:55

Maybe this book is what you are looking for: "Writing Mathematical Papers in English" by Jerzy Trceziak. It can be downloaded here: http://www.m-fozouni.ir/wp-content/uploads/2013/07/Writing-Mathematical-Papers-in-English_-A-Practical-Guide-European-Mathematical-Society-2005.pdf