I heard that learning basics of French and German, especially in order to read mathematics, is not difficult. It's verified by my experience of learning French: it's much easier to read mathematics than any other kind of material, even that of physics. It seems to me that, duolingo is enough for basic French to read mathematics. Now I'm planning to learn some German to read mathematics in German. I need suggestions to indicate how to begin with. My aim is to read mathematics, and no more is needed (provisionally) such as listening comprehensions and writing skills.

PS: I'm now a graduate student major in mathematics, and by mathematics, I mean, mathematical thesis and textbooks for undergraduate/graduate students (such as old-fashioned van der Waerden's books on algebra, or Hilbert's Zahlbericht, which is recently translated into English).

  • 4
    American universities used to have requirements to be able to read mathematics in e.g. German, I assume that they also had classes teaching that. Maybe you can find out what material they used.
    – Carsten S
    Commented Jan 11, 2016 at 10:45

6 Answers 6


There are great, advanced, modern specialized textbooks in German. Consulting just one of them in your specialty field will help you immensely. The icing on the cake would be a book with an English translation.

As a first example, in algebraic geometry/commutative algebra one has Kunz's Einführung in die kommutative Algebra und algebraische Geometrie, translated as Introduction to Commutative Algebra and Algebraic Geometry.

Similarly in advanced number theory we have Neukirch's Algebraische Zahlentheorie, translated as Algebraic Number Theory.

As a last example, in differential topology Bröcker-Jänich's Einführung on die Differentialtopologie has as translation Introduction to Differential Topology .

There are similar examples in most branches of mathematics.

  • 1
    +1 for Bröcker-Jänich, just because I like the book ;)
    – Carsten S
    Commented Sep 5, 2016 at 9:46
  • Dear @Carsten S: I'm glad to read that we both are fans of that very pretty book :-) Commented Sep 5, 2016 at 9:48

The requirements for mathematics texts in German from the point of view of the vocabulary are small for modern texts, somewhat higher for older books. However, I think the main task you will have at the beginning is to understand the particular jargon mathematicians use all the time. For that it might be useful to look into books which are meant for future maths students who have the standard knowledge from school. There are many such books -- one example is Jürgen Wagner: Einstieg in die Hochschulmathematik. Once you are a bit familiar with the mathematicians' communication style, things will become easier, since the special terminology most often is quite similar to English via Latin- or Greek-derived words.

  • Thanks for the answer. I've edited my original post to include some backgrounds. I don't know whether these mathematical jargons in German are literal translations of those in English, and since that book hasn't been published yet, I cannot preview the content...
    – Yai0Phah
    Commented Jan 11, 2016 at 16:55
  • @FrankScience Okay, now I understand better what you are doing. The book by van der Waerden is one of the genuine classics and compared to modern texts very nicely written. Sorry, I did not notice that the recommended book is not yet published. You can try another one by Joachim Hilgert instead, see springer.com/gp/book/9783642375491 . Commented Jan 12, 2016 at 8:27
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    Thanks. Now I won't be afraid of Faisceaux algébriques cohérents, say, and I can read whenever I want. I hope I'll be happy with Vollstandigkeit der Wuschen Relationen zwischen den STIEFEL-WHITNEY- schen Zahlen differenzierbarer Mannigfaltigkeiten in the same sense.
    – Yai0Phah
    Commented Jan 13, 2016 at 9:57
  • @FrankScience Have fun. Commented Jan 13, 2016 at 10:02

It is said by some that the book of E. Landau "Grundlagen der Analysis" is one way to learn German for mathematics.

I've found one German edition at my university's library which has in the end a short vocabulary list of German words and their English equivalent.

But I believe that even with an online dictionary, you'll be fine.

ps: I'd suggest you to read his Differential and Integral Calculus book as well which I consider it equally classic.

  • Welcome to the site. Some good recommendations.
    – Tom Au
    Commented Sep 1, 2016 at 3:59

This is exactly what I have been doing for several years now. My goal has been to read many of the classics of math (Gauss, Moebius, Euler, Courant, Hilbert, etc.) in German (or French). Noting (!) of course that Gauss and Euler wrote in Latin .. older translations were into German or French (similarly for example for writers like Galois, or Abel, which I have been able to find in German only).

Here are some of my suggestions.

I like this dictionary: German-English Science Dictionary (Louis DeVries and Leon Jacoley). It's a lot faster to look up mathematical vocabulary in it than a more complete dictionary (of course you will also need that as a last resort).

Start with something that is either easier (an introductory text), or that is harder but is something you are very familiar with, so in either case you recognize the topics and in some cases the theorems and the development are immediately recognizable to you.

In the case of some of the more famous works (Disquisitiones for example), you can also obtain an English translation to use when you get stuck (amazingly, Disquisitiones did not appear in English until the 1960's!). In my area of interest I have also found both German and English versions of Hilbert, Courant, and others.

I have been pleasantly surprised overall at how much easier it is to actually read German when limiting myself to math. I would have difficulty carrying on a conversation in German, or reading a newspaper, but I have for example read most of Moebius' Astronomy book (an introduction to the subject), and pieces of several other works including Disquisitiones, and feel that I have been able to comprehend these just fine, albeit slowly at times.

It's a fun project! Just think: In some cases you are understanding a book written in German better than a native speaker would because you understand the math, even though you would (well, I don't know about you, but I know I would) get lost in a supermarket. Good luck with it!

  • Pretty natural that math is much easier than daily conversation. But for the supermarket, it's incomprehensible to me because I think that one only needs to figure out what these nouns mean, a work which could be easily accomplished by a dictionary or a machine translator.
    – Yai0Phah
    Commented May 21, 2017 at 15:29

You have two tasks.

The first is to learn a couple hundred of the most "basic" German words, including the differences between der, die, and das, that is the various gender forms of "the"; and related grammar such as noun endings and verb conjugations. These will be your connecting words. This will get you to the level of "A1" on the Common European Framework of Reference for Languages (CEFRL).

Your second task to is acquire a specialized vocabulary in Mathematik, probably several hundred words. Many bilingual texts or math dictionaries will do the job. This task will be easier than the first one because there will be many "cognates" in German of French and English words that you already know.

When you are done, you will be an "idiot savant" in the German language; a "B2" in your specialized field (upper intermediate with modest expertise), and an "A1" (rank beginner) outside it on the CERFL scale.


Since the other answers have already addressed the main aspects, I will only add a specific advice.

Be aware that for many mathematical concepts, German has two words:

kontinuierlich = stetig

Limes = Grenzwert

Variable = Veränderliche

Funktion = Abbildung

Konkatenation = Verknüpfung

Sequenz = Folge

disjunkt = elementfremd

perfekt = vollkommen (field theory)

One coming from Latin, the other with a German root. Sometimes this equivalence extends to non-mathematical language, sometimes it doesn't. The Latin version most of the time coincides with the English terminology. Which version is more standard is arbitrary. For example, Variable is more common than Veränderliche, but Folge is more common than Sequenz.

In older works, like those you intend to read, chances are higher you will encounter the non-standard version of the term. This should however, make it only more interesting.

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