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I'm curious what languages contribute the largest fraction of published research mathematics. That is, for a given language the percent of new research being published in that language. I'm especially curious to see how you come up with such numbers.

From some googling I managed to get a very crude estimate of total publication volume: 28643 arXiv articles in 2014. Looks like arXiv sometimes has articles in other languages but I can't search by language.

Edit: Thanks S. Carnahan for pointing out that I could search the full text by common words from different languages!

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    $\begingroup$ Don't forget that non-anglophone countries have repositories, too, for instance HAL (France), SciELO (Brazil/S. America more generally) $\endgroup$
    – David Roberts ♦
    Commented Sep 24, 2015 at 2:47
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    $\begingroup$ The claim "they're always in English as well" is only true of the abstracts, not necessarily for the articles. As the page you linked indicates, if you search the comments for language words, you may get information about the article language. $\endgroup$
    – S. Carnahan ♦
    Commented Sep 24, 2015 at 2:54
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    $\begingroup$ Ah, great idea @S.Carnahan and thanks for pointing that out! $\endgroup$
    – Whosyourjay
    Commented Sep 24, 2015 at 3:18

2 Answers 2

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This question has no definite answer if time frame is not specified. The situation in 20s century changed very quickly. In the first half of the century, German and French dominated. (More German than French). In the second half, it is clearly English, and one does not need any research to see this. But English dominates more and more. In the 1970-s and 1980-s about 1/3 of all papers was published in Russian. (I did count this. There was a Russian counterpart of Math Rev, using Cyrillic for Russian papers, so it was easy to count). Not anymore. Until the late 70s, most German papers were published in German. Not anymore. My guess would be that in 21st century an overwhelming majority of publications are in English, and there are some in French and Chinese. Proportion of other languages is negligibe.

EDIT. In the discussion, mostly arXiv is discussed, so you probably mean very recent papers. I follow the arxiv since its inception, and my impression is that less than 1% of all papers are written in French or Russian. I have not seen any in German or other languages, including Chinese.

EDIT2. One also has to specify what kinds of books and papers are we talking about. Of course, textbooks and lecture courses are published in every language. Because TEACHING in most countries is in the native language, especially undergraduate teaching. Same applies to many publications intended for more general audience, publications related to education and history, popular mathematics etc. In the arXiv they are in the sections "History" or "General math". All non-English papers on the arXiv that I know are in "History". I will not be surprised if statistics from the arXiv will be very different from that in Mathscinet, even if one restricts Mathscinet to the recent years when arXiv exists. In fact arXiv is not a good representative for the whole mathematics. In some areas, almost all papers go to the arXiv, in other areas, only a small proportion.

EDIT3. OK, in Mathscinet they indicate the language:-) Since 2000: 70K in Chinese, 66K in Russian, 21K in French, 5K in Spanish and Japanese each, 4K in German and Italian each, 1K in Portuguese. Out of 1,358,623 total. Zentralblatt seems to have a similar feature but I could not make it work.

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  • $\begingroup$ I would imagine Portugese and Spanish are present for South America. I don't know the quantities, though. $\endgroup$
    – David Roberts ♦
    Commented Sep 24, 2015 at 5:18
  • $\begingroup$ It is present, of course. See my EDIT2 $\endgroup$
    – Alexandre Eremenko
    Commented Sep 24, 2015 at 5:20
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    $\begingroup$ Thanks @AlexandreEremenko this is an interesting answer. As you surmise, my interest is mostly in new content. If you could somehow estimate the fractions by language of historical content though, across all time, I'd love to see it. I don't think arXiv is representative but I couldn't find really any representative source. Here's an example of papers in Chinese: papers on Acta Mathematica Sinica. $\endgroup$
    – Whosyourjay
    Commented Sep 24, 2015 at 5:38
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    $\begingroup$ @Whosyourjay: Actually Mathscinet is a better source, if you restrict the year range. And has a much superior search possibilities. $\endgroup$
    – Alexandre Eremenko
    Commented Sep 24, 2015 at 5:41
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    $\begingroup$ @Igor Khavkine: It seems that it still exists: viniti.ru/pro_ref_el.html $\endgroup$
    – Alexandre Eremenko
    Commented Sep 25, 2015 at 16:27
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I researched the language distribution using the Web of Science. Since your interest was in new content, I restricted the search to the period 1985-2015. The total number of mathematics articles in that database is 882565 for this period. Here is the breakdown by language:

[1985-2015]

The Web of Science goes back to 1945, so I also made the search for the entire period 1945-2015. That gives a total of 1120170 mathematics articles, with this breakdown by language:

[1945-2015]

Finally, for the last ten-year period 2005-2015 the breakdown (for a total of 459213 mathematics articles) is

[2005-2015]

It is clear that the coverage of Web of Science is not representative for Asia, but for the European languages I would expect it to give a reliable breakdown.

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    $\begingroup$ Now I can't help but wonder what those two papers in Danish are. $\endgroup$
    – Tobias Kildetoft
    Commented Sep 24, 2015 at 6:53
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    $\begingroup$ Or the one in Latin (or the four in Welsh!) $\endgroup$
    – David Roberts ♦
    Commented Sep 24, 2015 at 7:20
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    $\begingroup$ Talking about papers written in Latin, I did have to struggle with that one: math.univ-toulouse.fr/~schechtman/defin-nova-preprint.pdf $\endgroup$
    – André Henriques
    Commented Sep 24, 2015 at 11:26
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    $\begingroup$ I find it suspicious that Japanese is conspicuously absent from all the lists, when it is tied with Spanish in Alexandre's list. Does WoS not have a category for Japanese? Then again, Chinese is also significantly underrepresented compared to Alexandre's data, so perhaps WoS is more Euro-centric. (Oddly enough, the selection process link is translated into ten European languages, plus Japanese (but not Chinese), even though there are apparently no Japanese articles in the database.) $\endgroup$
    – Mario Carneiro
    Commented Sep 25, 2015 at 9:32
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    $\begingroup$ If I remember well, Clifford Truesdell who founded Archive for Rational Mechanics and Analysis, decided that the accepted languages would be English, French, German and Latin. He himself wrote a paper in Latin ! $\endgroup$
    – Denis Serre
    Commented Feb 9, 2019 at 10:32

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