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For people with "hands-on" experience in mathematical research, what languages are the most beneficial to learn? I know that many graduate programs require some degree of non-native lingual proficiency, so what would be the pros and cons of pursuing various languages?

(I realize that this question is a bit broad; please ask if anything needs to be specified.)

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Aside from english, I've heard of french, russian, and german being common languages that people learn in Ph.D math programs, but I don't have any sources. The biggest reason I see is in order to read more literature in your subject, since there will be some situations in which papers are only submitted/written in a foreign language. –  Hayden Jun 17 at 0:37
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See also: mathoverflow.net/questions/8056/… –  Dan Piponi Jun 17 at 0:44
    
Besides English, I've found French and German most useful research-wise. –  Andres Caicedo Jun 17 at 1:25
    
If you study set theory, then Hebrew is a good candidate too, at least in the next couple of years. –  Asaf Karagila Jun 17 at 1:27
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Haskell, Fortran, C, C++, Java, BASIC, the Wolfram Language, MATLAB. –  Doug Spoonwood Jun 17 at 1:35

3 Answers 3

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Most US-based PhD programs have, as a requirement for the degree, at least having reading proficiency in one of: French, German, Latin, Russian or, increasingly, Chinese. The first few for obvious historical reasons. In fact, except for Chinese, the impetus is predominantly historical nowadays; internationally, most cutting-edge mathematics is being published in English.

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Latin? Is there really a PhD program that accepts Latin? –  kigen Jun 17 at 2:21
    
@kigen Some math history programs will. And probably some math programs in general will, also. Many programs have a loosely-worded requirement such as "proficiency in one of X languages, or a suitable substitute to be accepted by the department." Until the 19th century, almost all serious scientific writing was done in Latin. Although those works have been translated and disseminated in English or other languages, there is still some value in being able to read the original text. –  Arkamis Jun 17 at 3:05

Not sure it is an answer... let's try!

If you search to learn a new language just to enhance your efficiency to do research, I think you're loosing your time. Even in countries that had a strong tradition of writing in their own language (France, Russia), most publications are in English nowadays. Important books in Russian are quite quickly translated into English. The material contained in old articles can be found in more recent work (in my specific topic, everybody quotes a certain article in German by Hopf, by I guess few people read it). Except for history or philosophy of mathematics, the mathematical benefit of reading the original paper is very low. But learning a new language is time-consuming! If you want to be an efficient article-reader, use that time to read maths in a language you already know.

The only reason you should learn a new language is the same as non-mathematicians: learn it because you are genuinely interested in it! Of course, one interest could be being able to read the work of your favorite mathematician in its original form, but don't expect a huge impact on your career. At least, learning a new language may ease your collaboration with foreign coworkers, but it is kind of an indirect impact.

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French for sure. Opens up a whole wide world. Much more opportunities. Non-francophone countries accept to do business in English.

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