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It seems that knowing French is useful if you're an algebraic geometer. More generally, I've sometimes wished I could read German and Russian so I could read papers by great German and Russian mathematicians, but I don't know how useful this would actually be. What non-English languages are good for a generic mathematician to know? Are there specific languages associated to disciplines other than algebraic geometry?

(This question is a little English-centric, but I figure it's okay because this website is run in English.)

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How about making this community wiki, and asking people to attempt sorting languages by importance within each discipline? –  Andrew Critch Dec 7 '09 at 1:10
Every time I read the title of this question, I see "What are non-good english languages". –  Harry Gindi Dec 7 '09 at 11:11
Hungarian, of course –  Gil Kalai Dec 7 '09 at 13:04
Perhaps the title would read a bit smoother if it said "Which non-English languages are most useful for mathematicians to know?" –  Steve Flammia Dec 7 '09 at 22:21
It's too late to change the vote, but I would have downvoted it simply because it's as vague as saying: "Which countries should I visit to read mathematical resources from libraries?" or something similar. However, imho, it would have been an excellent question if it was geared towards learning a language that may illuminate the structure of mathematics within context of grammar, including and not limited to programming. –  Sniper Clown Jun 9 '12 at 21:56

20 Answers 20

C and LaTeX. Speak them like it's the mother tongue.

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C? I thought we were mathematicians, not computer scientists. –  Harry Gindi Dec 7 '09 at 10:16
Probably Magma, Sage etc should replace C. (or maybe for some others, mathematica, matlab etc) –  Ho Chung Siu Dec 7 '09 at 14:31
If you're going to choose a language like C which is really only useful for computational programs (and software design, but I assume most mathematicians don't do too much of that), you might as well say Fortran rather than C. It's still the language of choice in most hard sciences. –  Logan Maingi Jun 5 '11 at 6:20
C and Latex--hear, hear! –  drbobmeister Jun 8 '12 at 22:41
Knowing some programming language well is probably useful. But C, specifically, needn't be it... –  Sridhar Ramesh Jun 9 '12 at 0:14

I'm with Deane here: I think learning foreign languages is not a very mathematically productive thing to do; of course, there are lots of good reasons to learn foreign languages, but doing mathematics is not one of them. Not only are there few modern mathematics papers written in languages other than English, but the primary other language they are written (French) in is pretty easy to read without actually knowing it.

Even though I've been to France several times, my spoken French mostly consists of "merci," "si vous plait," "d'accord" and some food words; I've still skimmed 100 page long papers in French without a lot of trouble.

If nothing else, think of reading a paper in French as a good opportunity to teach Google Translate some mathematical French.

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While I mostly agree with the sentiment here, one can get tripped up badly on the wording of some conditions. I recall pulling my hair out in graduate school reading some paper in French that claimed that something-or-other "ne depend que" something else, because it really seemed to depend on it. I eventually figured out what that construction meant, and all was well. –  Ramsey Jan 31 '11 at 17:16
Yes, but that means you have good reading French, even if you don't speak it. To access mathematical literature, you don't need to speak the language well, just read it well. –  mike3 Feb 15 at 6:51

Just a comment, there are thousands of excellent Chinese papers written in journals which never get translated to english. Being able to read both is definitely good if you are willing to put work into researching.

[EDIT: Douglas S. Stones] I've been learning Chinese for roughly three-and-a-half years now and I feel it has been given an unfair treatment so far in this question. So I will add a few reasons why I found learning Chinese has been valuable as an early mathematician.

a. There are many talented Chinese researchers that are looking for international collaborations (here's my first: http://portal.acm.org/citation.cfm?id=1734895).

b. Merely restating a result (that has been published only in Chinese) adds something to a paper that others can't easily match.

c. I can pronounce Chinese names at conferences without sounding like a goose to the Chinese speakers in the audience (e.g. "Wang"). These are some of the most common surnames on the planet.

d. In learning Chinese, you make your knowledge work for you -- you actively find papers in Chinese, etc.

e. There was an argument about traditional vs. simplified Chinese, i.e. not being standardised. It's pretty easy to switch between traditional and simplified (and pinyin) on a computer (I admit this becomes more complicated if you only have a hard copy or a scanned copy, but there are ways such as OCR or simply drawing the unknown character into appropriate software). For many characters, the traditional and simplified characters are quite similar. [Side note: If I redefined "English", "German", etc. to be "European language 1", "European language 2", etc. then "European" would not be standardised. Why would you want to learn "European language n"?]

f. There are native Chinese speakers everywhere!

That being said, learning Chinese (as with any language) requires a certain temperament and a long-term commitment. But it is easier now than it has ever been in the past thanks to online learning tools. My favourites are ChinesePod, Skritter, dict.cn, DimSum Chinese Reading Assistant (but there are plenty of others).

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It may be a shame that my motivation to learn Chinese (Mandarin, I assume) for this reason will probably always stay low. Without knowing some of the language, and with institutions seeing low demand to subscribe to anything academic in Chinese, my own opportunity to come face-to-face with the language and its usefulness in math will probably remain identically zero. –  alekzander Dec 14 '09 at 4:00
I know essentially nothing about what is happening mathematically in China, but I would be interested in hearing about it. Do you know any good source of general information? –  Neil Strickland Feb 1 '11 at 10:29
My curiosity about general information comes from that China's population no. and educational advances make it a candidate for an autark science community (not only in mathematics). Perhaps there exist already math analogues to this observation by a friend?: "Few people notice that square blocks are so wide, there must be something secret in the middle, not visible from the street. And indeed in Chinatown, there are secret buildings behind buildings, notknown even to census workers. census.gov/srd/papers/pdf/ev91-06.pdf –  Thomas Riepe Jun 5 '11 at 7:22
BTW, very much of what I heard about how technology and sports are organized in China sounds like Luhmann's sociology set into practice. So one can wonder if that is the case in sciences too, in which case "applied Agnotology" could be a theme: uni-bielefeld.de/%28en%29/ZIF/AG/2011/05-30-Carrier.html –  Thomas Riepe Aug 7 '11 at 22:30

My impression is that the vast majority of mathematical articles written in the last 20 years are in English and that even foreign mathematicians try to write their better papers in English. It is, for better or worse, the only way to maximize the number of people who will read your paper.

So the only real need to read in a language other than English is to be able to read older papers. Which language you need depends pretty strongly not only in which subject you are interested in but the specific topics. For algebraic geometry, French can be very useful, but Italian can be, too. In differential geometry, the two languages that arise most often are French, German, and Russian. It really depends on whose work you want to read.

Overall, French is the most common language after English, because French mathematicians have been the most reluctant to switch to writing in English. For example, it is nice to be able to read the Seminaires Bourbaki.

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Not sure if it's only older papers- see for instance Deligne's preprints: math.ias.edu/~phares/deligne/preprints.html. –  Akhil Mathew Dec 7 '09 at 1:43
I agree that French is the most useful out of the "big three" non-English mathematical languages (French, German, and Russian); most important papers by Russians get translated, and most Germans write in English now. I wonder to what extent this has to do with how much the educational systems in various countries push learning English. –  Michael Lugo Dec 7 '09 at 5:03
Honestly, I think it mostly has to do with French nationalism. Another important factor is the size, strength and tradition of French mathematics. The only country with a comparable history is Germany, and their mathematical community was gutted by the Nazis, with many of their best mathematicians emigrating to the US. Similarly, the post-USSR exodus of mathematicians to the West has taken a lot of the wind out of the sails of Russian as a language for mathematical papers. –  Ben Webster Dec 7 '09 at 19:03
To add a frenchman's perspective: yes, many big papers still regularly appear in french (e.g. Ngô on the fundamental lemma). It's not easy for me to explain why. The main reason probably is that the way english is taught in France is definitely not efficient enough as Michael guessed, so that many french scientists and mathematicians really do struggle with english (I've heard dozens of examples). Another reason is a form of active resistance to english seen as American hegemonism (it is not so much pro-french, as pro-diversity). But anyway, better online translators will solve the problem. –  Thomas Sauvaget Dec 8 '09 at 16:03
I'd like to upvote italian for algebraic geometry too, as in algori's answer below. And, if some humor is allowed, I'd say that in conferences it is always useful to know the speaker's mother tongue in order to understand his/her English... –  quim Dec 10 '09 at 15:26

French, German, Russian. It's a pity English dominates so much. French reads beautifully. (Also if you read older papers by Hadamard, Stieltjes or Levy, the first thing you'll notice is their extreme honesty (they don't use difficult terms, they define everything, they don't try to make their arguments appear difficult) also calculations are not condemned nor indulged with (they often just write an equation and say in words how the rest of the computation goes)).

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As the great mathematician Groucho Marx said, English is the lingua franca.

Ha, ha, ha. :-)

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If your field is complex analysis then Finnish might be your language of choice. In fact, this book talks a little about how Fred Gehring learnt Finnish in order to work on quasiconformal mappings.

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Hungarian. No, really!

I have read a couple of very nice expository papers in Hungarian, but that's not what I mean. Being able to speak Hungarian has been socially very helpful at conferences (I work in combinatorial number theory). Hungarians are instantly warm and trusting toward other Hungarians, and as a non-Hungarian speaker of Hungarian, I am close enough.

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Hungary,of course,has a deep and rich tradition of combinatorialists and graph theorists,Kevin.I've been told by several friends that Hungarian is a lot easier to learn if you first learn German because the 2 languages are quite similar.Is that true in your experience? –  Andrew L Jun 5 '11 at 19:43
@Andrew L : Hungarian is a Uralic language instead of an Indo-European one, and is thus unrelated to any major western Eurpoean language (an exception being Finnish, though I have been told that understanding one doesn't help that much in understanding the other). In particular, knowing German won't help you at all with Hungarian. See the wikipedia page for more details : en.wikipedia.org/wiki/Hungarian_language –  Andy Putman Jun 6 '11 at 21:18
There are also many papers on Discrete Geometry written in Hungarian. –  Samuel Reid Jun 8 '12 at 22:42

It surprised me that nobody said to learn the language of your better half... if s/he is not a native English speaker. That way, you have a better family, which is one of the precondition to have a better research life, I guess.

As a Japanese, I would say learning Japanese might help you a bit, because there are many nice math textbooks in Japanese by Kodaira, Sato, Jimbo etc. Yes some of them are translated to English but some of them have not been.

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The Japanese school should have a much better lobby in the "western" part of the mathematical world... –  user5831 Apr 28 '12 at 19:51

I'd say that in general (especially for algebraic geometry, but I really do mean in general) French is probably the way to go. Sure, there've been a lot of influential German-speaking mathematicians, but before 1820 or so they mostly wrote in Latin, and many of the important papers since then are available in translation.

In my experience, though, if you just want to read mathematical papers, it's not that hard (for a fairly well-read native English speaker) to pick up the basics of either French or German, since we have so many words derived from both. Of course, if you want to be able to write or speak the language, that's a different matter, but you can get surprisingly far with a dictionary and practice. (Note: This does not help with Bourbaki or Grothendieck.)

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I have to upvote the second half. I think I've accepted the fact that learning a new language for reading is excessive. (Opportunity cost high, likelihood of forgetting high, frequency of usefulness low.) Instead, I tend to make fairly quick progress whenever I try to read, and a (paper!) dictionary quickly finishes the process. Reading math is slow, anyway. –  alekzander Dec 7 '09 at 16:13

A quick examination suggests that articles in French continue to appear in Annals and Inventiones with some regularity, though much more frequently in the European Inventiones than the US-based Annals. I think this quite strongly supports the position that French is a useful language to be able to read. On the other hand, neither of these two journals seems to have published anything in German, or indeed any language other than French or English, for quite some time. Germany's other major journals, Mathematische Annalen and Journal für die reine und angewandte Mathematik, also do not these days seem to publish articles in German in practice. Russian and Chinese are certainly very active mathematical languages in their countries of origin, but unlike French, major works in these languages seem typically much more subject to translation.

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Inventiones is not France-based. –  Chandan Singh Dalawat Jan 30 '11 at 15:44
Oops, my bad. Out of curiosity, which country is it based in (if this concept even applies these days)? –  Ian Morris Jan 31 '11 at 13:23
Deutschland(=Allemagne=Germay). $$ $$ –  Chandan Singh Dalawat Feb 1 '11 at 7:15
Or indeed "Germania", as I must refer to it from my present location... –  Ian Morris Feb 1 '11 at 10:19
Some points on translations. For journal papers, these are usually done by people not understanding the subject, so they tend to introduce many little errors which make reading painful, if not too painful or critically misleading. Virtually none of the English translations are freely accessible; virtually all original Russian journal literature is, mathnet.ru (with the exception of Doklady, and of the last 1-3 years for some other journals). Math books published in Russia, including translations from Engish, French and German, usually cost about 5−10 US dollars, and never above 25. –  Sergey Melikhov Feb 1 '11 at 18:42

Of course it's great that today we have a scientific koiné, but I only disagree with the idea showing here and there that studying a language is a waste of time, even for the sake of studying Mathematics. Mathematics, as a human mind's product, has a cultural aspect, that of course is not relevant from the theoretical side, but that I would really regret to miss. There's a French style in doing mathematics, a German style, an Italian style, a Russian style, and so on, and being able to appreciate their features and differences is really a wonderful piece of human studies. Also, I suspect that knowing a bit how the various traditional schools work in mathematics help us a bit to learn how to think better. Btw, as far as I knonw, one of the last important journals that published in several languages, Latin included, was the Archive for Rational Mechanics and Analysis at the times of Clifford Truesdell.

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I not a native English speaker and thus my intervention here is a bit odd, to say the least. Growing up behind the Iron Curtain I learned English, but I discovered that as a mathematician it is more useful to learn Russian, simply because the Soviets translated all the influential books and articles into Russian. Often, the Russian translations would be better than the original because the translators, influential mathematicians themselves, would correct possible errors and would add illuminating footnotes and appendices.

To this day I cannot read German, but I can read Grauert's or Brieskorn'article in Russian. Today though, English is the lingua Franca of Science, so for a youngster it is more profitable to concentrate on Math.

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For the 19th and early 20th century literature: French, German, Russian, Italian. Earlier, Latin. For the future... maybe Chinese. But it seems that new mathematics will be in English for the next decade or three at least, and after that machine translation (and hand-held cybernetic assistants, if not direct mental interface) will eliminate the need for spending lots of time learning a language.

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I was feeling you until you said, "direct mental interface." –  Harry Gindi Dec 7 '09 at 15:36
Is that when your direct tactile interface shut down? –  Tom LaGatta Jan 25 '10 at 16:53

Italian can be quite important if you are doing projective algebraic geometry. For example there is someone I know who would often set up a Master's project like this: take paper XXX (in Italian) and prove the main results rigorously using modern language.

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Italian also seems to be good for history of mathematics. –  Paul Taylor Apr 11 '13 at 10:30

I'm inclined to suggest Russian for dynamical systems, ergodic theory and control theory. However, a lot of the original papers have been translated by AMS to English in '50s and '60s. That is not to say that some of those translations are easy to come by, though.

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It's worth keeping in mind that there are many levels of language competence and you don't need to be able to carry on a conversation or read great literature in a given language to read most math papers. Personally, with a dictionary (or Google) on-hand, I can follow a French paper or book in my area just fine, albeit much more slowly than I read in English, and I've never formally studied French. I would think the situation is similar for most well-educated Anglophones, though I think many are too intimidated to give it a try.

On the other hand, I can't even get started with Russian since I don't know the alphabet.

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It might work for theorem-proof-theorem-proof style texts, but don't tell me I'll be able to follow a verbose explanation of motivation and ideas in French just by googling for the words. –  darij grinberg Feb 1 '11 at 10:23
You're right, it depends a lot on the style of the text. Google Translate can help a lot for more verbose texts if you're reading something in electronic form. (I don't claim that's perfect, either, especially since it can get badly confused by technical terminology.) It also depends a lot on how good a writer the author is. One of my favorite textbooks is written in German and is quite verbose, but the writing is so clear that I find it easier to read than many English-language texts at a similar level, although English is my native language and my German is very rusty. –  Mark Meckes Feb 1 '11 at 14:50
You do know much of the Russian alphabet: most letters look like the corresponding ones in Greek. –  Noam D. Elkies Apr 28 '12 at 19:35
"Much" I agree with; "most" I think is inaccurate. –  Mark Meckes Apr 29 '12 at 1:22

Not really an answer, but a suggestion on how to go about finding an answer while keeping a modicum of objectivity.

Although the vast majority of papers on international journals are in English, some of the journals accept papers in other languages. Check the top journals in your favourite area and see which languages they accept. Most of the time it's only French and German. This may be historical or, as in the case of Springer journals, possibly geographical.

In my experience, I've found French to be the most useful language after English for contemporary papers and also, together with German, for older (say, late 19th, early 20th century) papers. Older than that and I find that there's a problem of mathematical language, regardless the natural language into which the mathematics happens to be embedded.

Alas, my mother tongue (Spanish) has very little mathematical literature :(


I noticed the CW suggestion after I had started typing the answer. So to restate, French has proved the most useful to me, and the topics are Differential Geometry and to some extent Lie theory. A close second is German, on the same topics. My main research topic, though, is Mathematical Physics and this seems to be almost all in English.

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Well, there's those funny lecture notes on point-set topology that I talked about here: mathoverflow.net/questions/7957 :D –  Alberto García-Raboso Dec 7 '09 at 1:18
Yes, and they are indeed hilarious. I was talking mostly about research literature. Of course there are nice textbooks/notes/... in a variety of languages, even Spanish :) –  José Figueroa-O'Farrill Dec 7 '09 at 1:21
Jantzen's Moduln Mit Einem Hochsten Gewicht is a '79 text which I would still love to read, and which I think has no (English) translation available. –  alekzander Dec 7 '09 at 7:28
You'd be surprised just how much work is published only in french even nowadays. –  Harry Gindi Dec 7 '09 at 9:39
Yes, Jantzen's paper is a classic and so is Gabriel's paper on the ADE classification of quivers with finite type representations. Both from about the same time, I think. Also, now that I think about it, at least on a couple of occasions I wished I could read Russian. –  José Figueroa-O'Farrill Dec 7 '09 at 15:08

German, I guess, because many important languages have been developed by German and Swiss mathematicians. Words like Eigenvector, Eigenvalue, Eigenfunction, Ansatz, Nullstellensatz, Entscheidungsproblem, Vierergruppe,... and the like speak for themselves.

If you want to read Einstein, Riemann, Hilbert, Gödel, Cantor,... to name but a few you have to learn German (which is quite similar to English, by the way, because they share common roots. Both are so called Germanic languages).

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Actually -- and I'm sure I'll get flamed for this -- I don't consider English a truly Germanic language. For almost every word of Germanic origin in English, there is also a word of Romance origin with a similar (but nuanced) meaning: hard/difficult, easy/facile,... In a way this is what makes English such a rich language. –  José Figueroa-O'Farrill Dec 7 '09 at 15:05
José- I certainly hope you don't get flamed, but at the same time I think you've taken a very superficial (good Latin word there) view of what makes languages similar. It's true that English has taken a lot of its software from French and Latin, but the operating system is still Germanic. For example, English speakers tend to be absolutely horrified by the French or Spanish verb systems (¡¿conditional progressive?!), whereas the German (or better yet, Dutch or Danish) system is fairly familiar. –  Ben Webster Dec 7 '09 at 15:31
On the other hand, the argument that this will lead to it being easy to learn enough German to read math papers is, well, wrong. Math words, for the reason that José pointed out, are actually much more likely to be cognate in English and French than in English and German (space, espace, Raum, for example), so my skills reading French math papers might still be better than mine reading German ones, even though I've had two years of college German, and never studied French. –  Ben Webster Dec 7 '09 at 15:41
Speaking some German, my experience is probably useless here, but the only German texts I can consistently read without much difficulty are math texts. On the other hand, I can almost understand the gist of French texts while knowing "no" French. –  Cory Knapp Dec 7 '09 at 19:15
@Ben: Point taken. However I would still argue that in some ways English is not like German or Dutch (I don't know any other Germanic language to any extent) in some structural ways. For instance in the position of the verb in the sentence. In that sense it is much more like French or Spanish, whereas in the position of the adjective it is more like German. At any rate, one thing I've noticed since I started learning Japanese is that ALL the Western languages I know and about whose differences I used to agonize, are virtually the same :) –  José Figueroa-O'Farrill Dec 7 '09 at 19:40

Pietro Majer's comment about style reminds me of another aspect of language and translation. When I took the basic graduate course in algebra, one of the textbooks was the second volume of van der Waerden's "Modern Algebra" in English translation. Some years later, I got (as a present) both volumes in the original German. I found the German much more enjoyable to read, and I don't think it was just because it was not a required textbook. Van der Waerden's writing style is great, and I think much of it got lost in the translation.

While I'm at it, let me mention an example where more than the style got lost. Some years ago, I saw, on our university library's new-book shelf, a translation of Dedekind's "Was sind und was sollen die Zahlen?" The English title was "What are numbers and what should they be?" (Better, in my opinion, would be "What are numbers and what are they for?"; probably the Germans here can come up with even better translations.)

In general, I'm not happy to rely on translations. Sometimes, the translators know exactly what they're doing and they do a magnificent job (example: Gödel's collected works), but too often they don't really understand the material and/or the languages, and things get garbled. Given a choice, I'd rather read originals --- except that I've heard that translations into Russian often contain useful annotations and even additional chapters. (Unfortunately, I don't read Russian.)

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Not knowing the book probably the best translation would be "What are numbers and what is their meaning? –  sisn Sep 10 '11 at 13:16
If it were up to me, I'd go with "the is and ought of 1s and noughts". –  Yoav Kallus Feb 19 '13 at 17:13

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