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The intention of this community wiki is to aid in learning another language in the restricted topic of mathematics. It does matter whether one wants to learn another language for mathematics or use mathematics as a stepping stone into another language. This post focuses only on the written aspect of the language.

For each language, there is a a small description, which includes its difficulty and pay-off, and a list of works to help learn it, which includes one or two grammar books and several works written in the language, which are accompanied by a description that includes their difficulty of reading. If it is a historical paper or it difficult to find in print, then a link to it will be provided if one is known. Since this is more about learning the language, works that are easier to read are preferred, although very famous works might also be mentioned, and, in the case of ancient languages, an exhaustive list list of all mathematical works in this language is ideal. Works that include a heavy amount of mathematics, but whose main topic is not mathematics but a related field, such as physics or astronomy, are sometimes acceptable, especially in the case when they are written in dead languages.

Some General Tips:

  • Often, dictionaries and translators do not translate mathematical vocabulary well. A good way to go about this is to use Wikipedia by switching the language of the page.
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    $\begingroup$ Maybe it could makes sense to move the info about specific languages to answers. $\endgroup$ – quid Jun 16 '19 at 17:45
  • $\begingroup$ @quid Personally, I think that having it written in the non-answer format would make it a bit more organized and polished. But, for the most part, it doesn't matter to me, and, as a worst case scenario, I think that it would still be about the same quality. $\endgroup$ – Eudoxus Jun 16 '19 at 18:21
  • $\begingroup$ When I was at university, long, long ago, there was a course: Russian for mathematicians. It aimed to teach you enough to read a mathematics paper in Russian but no more. $\endgroup$ – badjohn Jun 16 '19 at 19:50
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    $\begingroup$ Should Japanese be added. $\endgroup$ – badjohn Jun 16 '19 at 19:51
  • $\begingroup$ @badjohn If you can contribute to any language, then feel free to add it to the list. $\endgroup$ – Eudoxus Jun 17 '19 at 14:47
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Portuguese

In the recent years, developing countries in the Southern Cone have gained an unprecedented importance in global mathematical research, spearheaded by Brazil's Instituto de Matemática Pura e Aplicada (IMPA) which recently hosted ICM 2018 and is home, among many others, to Artur Ávila, the first Latin American to receive the Fields Medal for his work in dynamical systems.

Being a romance language, there may be difficulties in learning Portuguese for the native English speaker, but in the case of Spanish speakers it is quite the opposite: both languages are similar enough to the point that Spanish and Portuguese speakers can understand each other symmetrically with little trouble (this is evident e.g. in tourism and there's even a related linguistic phenomenon named "portuñol").

Another Portuguese-speaking country is Portugal. Brazilian Portuguese and Portugal's Portuguese only have slight differences (e.g. words for verb tenses, and cultural differences in what constitutes a formal voice).

General Resources:

  • (I do not know of any introductory texts aimed at English speakers, sadly.)

Mathematical Resources:

  • One of IMPA's explicit aims is to build a specifically Brazilian mathematical literature, and thus many books regarding all sorts of subjects (from first year undergraduate mathematics up to cutting-edge research monographies) are available. They are distributed by the Sociedade Brasileira de Matemática (though shipping options don't seem to be available...).
  • Recordings of IMPA lectures, colloquiums and events are available at their YouTube channel and are an excellent resource to improve listening skills.
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    $\begingroup$ Angola and Macau also speak Portuguese $\endgroup$ – Danilo Gregorin Jul 5 '19 at 15:35
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Sanskrit

  • Yuktibhāṣā by Jyesthadeva (This is possibly the first text that covers the foundations of Calculus)
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Russian

What resources are there for learning Russian math terminology?

(Note. This post has three sources for guides to Russian mathematics. Are all three good? If you have read these, feel free to clear up the issue by either explaining how each plays a role or deleting one or two.)

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  • $\begingroup$ All three books assume a certain level of Russian (if you can read texts, you're good) but generally, they start with a reminder of the basic phonetics and grammar while introducing the verbs and nouns used in mathematics (e.g. "to differentiate"). A friend of mine who knows Russian and is also a mathematician read a newer edition of Glazunova's book and she says it's good. $\endgroup$ – B. Núñez Jul 3 '19 at 22:17
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German

Learning German as a native English speaker is more difficult than the romance languages on this list, but easier than the rest. It shares many common roots as English. Its grammar is a bit of an obstacle. If your intention is to read historical works, then German has a high payoff. Many 19th Century works were written in German.

  • English Grammar for Students of German by Zorach, Melin and Oberlin (grammar book)
  • Analysis 1 by Forster (This is a modern textbook. It is not particularly well written, but, since it relies heavily on mathematical notation, it is relatively easy to read.)
  • Untersuchungen über die Grundlagen der Mengelehre by Zermelo (If you are familiar with the axioms of Set Theory, then this paper is on the easier side of historical papers in German to read.)
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French

This is one of the easier languages to learn as a native English speaker. Many of its words are recognizable by most English speakers, and its grammar is similar to the grammar of English. It also has one of the highest payoffs. Currently, more mathematical works are being published in French than any other language except for English.

  • Essential French Grammar by Resnick (grammar book)
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Chinese

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