Let’s make language exams useful

Every year, many hundreds of mathematics graduate students take language exams. In most departments, this means that they must demonstrate the ability to translates 2-3 pages of technical writing from French, German or Russian into English, with the use of a dictionary. In my experience, the usual texts are old text books, and the translations are discarded after they are graded.

I think a number of mathematicians have had the idea that all of this effort could be put to better use. Most recently, Kevin Lin just proposed this at mathoverflow.

The idea would be to take an important mathematical work that had never been translated and divide it up into 3 page chunks, across the math departments of the English speaking world. Each chunk would be assigned to 3-5 students. For each chunk, the grader would select the best translation. These would then be stitched together into a single document, producing a terrible rough draft of a translation, that could be a starting point for future editing.

Moreover, we don’t necessarily have to bring in a skilled editor immediately. Put the texts online and parcel out the first pass to volunteers. I am thinking here of a system like Distributed Proofreaders, who has done a superb job taking scans of public domain works and converting them to digital text. In my experience, web 2.0 projects work best when they rely on small inputs from many procrastinating people. And no one procrastinates like a grad student!

The point of this post is to generate discussion of this idea. A few specific questions are below the fold.

UPDATE: For those who are interested in the idea of distributed translation of mathematical texts more generally, Anton Fonarev has volunteered to create a software infrastructure for this purpose. Join the discussion at his weblog.

  • Does anyone have better numbers on how many language exams are taken? There are roughly 1000 Ph. D’s granted in mathematics in America every year. At Berkeley, almost all of those students took the French and German exams. And, of course, not every student who takes the exams gets a degree. Is it a good assumption that we are dealing with about 1000 French exams taken per year, or is there a factor I am missing?
  • At some point, we are going to have to have skilled translators finish up the text. My assumption is that a skilled translator would find it much less work to fix a rough draft then to start from scratch. But I’m not a translator! Is this naive of me?
  • The text most frequently proposed is EGA. This is good, in that EGA is written in very simple French. But it is bad, in that EGA spends a lot of time clarifying technical distinctions; omitting a single adjective could radically change a paragraph. Could we find a text which was more robust against minor translation errors?
  • Seven years ago, Bas Edixhoven proposed a similar project to convert SGA into LaTeX. What happened to it? UPDATE: It is still on going and completed the first two volumes.

31 thoughts on “Let’s make language exams useful

  1. Maybe this is jumping too far ahead, but the biggest difficulty for actually setting up such a thing that I can think of is that it would probably require the participation of at least a couple dozen schools. I don’t have any idea of how amenable such an idea would be to math departments.

  2. Language requirements are going away as more mathematics is written in English. For example, Penn reduced its language requirement from two of French, German, and Russian to zero (that is, got rid of it) last year.

    It seems like most PhD programs have this sort of information online, so it would be a tedious but not difficult task to determine what proportion of those getting a PhD in mathematics actually have to pass a language requirement.

    It would be a bit harder to determine what proportion of those students use any given language at institutions where there is a choice, though.

  3. It seems to me that most students pass their language exams without really knowing too much of the language, merely enough to get the gist of some reading. Would we really want a translation of SGA done by numerous first-year grad students, many of whom have no real knowledge of either algebraic geometry or French?

  4. Regarding your last point of retyping SGA in LaTeX (still in French), it has been happening. SGA 1 and 2 at least are on the arxiv, and the Wikipedia page for SGA links to retypeset versions of SGA 3 and 4.

  5. > My assumption is that a skilled translator would find it much less work to fix a rough draft then to start from scratch. But I’m not a translator! Is this naive of me?

    It is naive of you I am afraid. Having a translator proofread a translation is normally paid somewhere between 50% and 100% of what the translator would be paid to do the translation from scratch. This is so because it is an extremely time consuming task, and it is very different from simple proofreading the translated text without comparing with the original. (I have a few years experience as a translator, that was before becoming a mathematician)

    Secondly, a “distributed” translation would not really produce acceptable results without clear agreements on the style of the translation. This amounts for most translations to a great amount of preliminary work, so big that it is not really a sensible thing to do. It might be that it is easier for extremely technical texts, I would however agree with comment #3 that the result would not be of great quality. Probably not much better than an automated translation.

  6. Nice idea, but: having graded some German language exams, I can attest that if I wanted to translate a particular document, I would just do it from scratch; the student papers would be of little use to anyone who actually knows the language.

    Incidentally, one of the best arguments I have heard for abolishing the language requirement is that Google’s translation tools produce just as good (ie crappy) results.

    There do exist online projects to divide up the work of translating things (among skilled translators) which might be worth looking at if you actually want to translate something big.

  7. My school (UCSB) does not have language requirements, but I am learning Mandarin anyway. It seems like people who speak a common language tend to cite each other which leads “small worlds” within the literature. This would be especially true of Russian or Japanese where the orthographies are different.

  8. This issue came up repeatedly during my decades at
    UMass (especially when I was graduate program director).
    Initially some reading knowledge of two languages
    (chosen from French, German, Russian) was required for
    the Ph.D. The program being small and drawing at first
    mostly students whose first language was English, one
    or two people administered such exams. Supposedly the
    student got advice from a thesis committee and built the
    language study around a thesis area. In reality the
    committee is often just a formality, while most students
    delayed the language exam as long as humanly possible
    while struggling with the thesis. Thus failing a student
    just for one language exam was almost unthinkable.
    Besides, most of our Ph.D. students never read anything
    outside English for their thesis work (or later in life).
    At some point two languages shrank to one, I guess.

    It got worse when almost half of our students had
    English as a second language. A few from Germany
    found the German exam tempting, etc. But more came
    from Spanish or Chinese or other backgrounds. I recall
    one Asian student struggling with the French expression
    “il y a” (finally translated as “the y has” or such with “y”
    read as a variable).

    Then the statisticians in our department wanted to
    substitute a computer “language” for their few Ph.D.
    students. Eventually we gave up on the whole thing,
    leaving just a loose recommendation to advisors on
    the books. (This past year a similar controversy was
    raging about language study requirements for all
    arts and sciences undergrads at UMass.)

    In my own case, I managed to learn on my own some
    basic reading knowledge of those three languages.
    For me it’s been useful, but as most math papers now
    get written in English (sort of), the requirement is
    certain to fade further. I suspect it’s already pro forma
    in many places where it is kept on the books.

  9. I think it’s too much to expect to get anything resembling professional quality from a project like this for the reasons in 5. In particular, from a usefulness to mathematicians perspective something like having a consistent style isn’t a deal-breaker.

    What 6 says about machine translation strikes me as implausible in the context of technical math writing. The fact that the math is logically correct makes it easier to sort out what the sentence must be saying and thus complements the machine. On the other hand, it’s a good point brought up in 3 that this requires having students who are capable of understanding the mathematics involved. So it might not be practical to set up a situation where people can leverage their mathematical competence into improving a bare machine translation.

  10. Does it have to be restricted to these language exams. I think a better idea would be to have an “open source” type project or a “wiki” type project, whatever you want to call it, where everybody can make modifications, and discussions are had on what is the best translation. This could function similarly to the Stacks Project. I believe this would be a better solution, if the aim is to get a good translation of say EGA. All these small errors that could radically change the meaning of a paragraph should be caught by the community, and the language should be better.

    Here is a link to the stacks project

  11. I’ve been thinking of the same thing as Grétar for a while. Distributed translation with a wiki-type face. Actually, the engine should be slight different.
    I’ll try to modify some wiki engine and present a prototype in january.

  12. @11: The reason for attaching this to department requirements is that then you can guarantee a certain amount of free work. It’s going to be hard to recruit people for a project like this when everyone has so many other things they would like to be working on.

  13. Maybe most students won’t need anything but English, but I’ve had plenty of call to read (and sometimes even speak) French. I even had to brush off my Latin to read something of Euler’s nobody else seemed to have reworked or translated.

  14. The idea to add at least a rudimentary programming requirement in place of a rudimentary foreign language is a good one, though. If a student should find himself with a Ph.D. outside the academy, programming skills seem to be essential for any job that would be at all interested in their academic background.

  15. @Noah (14): Some of that free work will be from people who resent having to do the free work, namely people who are in a topic that’s far from algebraic geometry. And English-speaking people who aren’t familiar with the vocabulary of algebraic geometry in English hardly have any reason to be familiar with the same vocabulary in French. Perhaps there are similar texts in other subfields of mathematics that need translation, although I’m having trouble thinking of them off the top of my head.

  16. Call me a snob and a francophile, but I like the fact that
    (a) math grad students have to pass language exams, and
    (b) that after they do their exams, they sometime encounter French (and occasionally German) untranslated math papers/books.

    It makes me feel like a proper academic to think that we all read in French if necessary.

  17. I should emphasize that I also prefer Ph.D. students to
    have some reading knowledge of the traditional
    mathematical languages (even Latin, my favorite course
    in junior high school). But there are problems in writing
    and enforcing a meaningful requirement for all students,
    including those who will go through life needing only
    English. Computer programming languages are usually
    required at UMass in some courses and are acquired
    voluntarily by most of our students anyway. In the case
    of international students, we’re happy if students really
    master English and ecstatic if they go beyond that.

    Translation of mathematics will always be tricky in any
    case. Before so many Russian mathematicians emigrated,
    I used to read quite a few articles in Russian: usually the
    commercial journals did a very poor job with translation,
    in one memorable case just omitting a line of math that
    the translator couldn’t handle. But it’s a fact that less
    and less serious mathematics gets written in other
    languages, while few students actually need the older stuff.
    Graduate study already places heavy demands on them.

  18. Joel’s comment reminds me of one of my favorite bits of prose:

    “Theirs is a translation for the few, rather than the many. That is a little odd. Can’t the few read French for themselves anymore?”
    –Caleb Crain’s review of Mansfield and Winthrop’s translation of “Democracy in America”

  19. My language exam consisted in translating to English an excerpt from Serre’s “Corps locaux”, if I remember right (there was no requirement at Rutgers to take a language other than one own’s native language)… This was quite amusing.

    More seriously, I would think that a Wiki-style translation system could work, but it may be necessary to be careful with copyright law: I think most contracts typically give the original publisher all rights to arrange for any translation. If the work being translated in still copyrighted, one might have to be careful (I have done some translation from French to English, including a math textbook for physicist; I think the — very small — publishing company of the original French version would rightly have been very upset if some students had decided to produce a “distributed” translation, since that would probably have stopped any chance of getting a US publisher to do an official translation).

  20. IMHO, such translations are best done by fluent dedicated individuals rather than students learning the language. A good example is the nice bilingual edition of the Grothendieck-Serre correspondance, a wordy text by its very nature, accurately translated by an algebraic geometer fluent in french.

    I have to disagree with Joel, perhaps reading french or german is not that hard for an english-speaking person, but arguably much more so for, say, a korean-speaking person.

    So probably all recent big papers in french, like those of L.Lafforgue or Ngô B.C., do require a translation. These could make easier projects for online collaborative translation than EGA, but that definitely involves settling nontrivial author and publisher agreement issues first. I’ve just had a look at the highly regarded Journal of the AMS: for the period 1996-2009 it published about 336 papers (56 issues, about 6 papers per issue) of which 7 were not in english (namely, all 7 in french).

  21. Perhaps the effort might be better spent collaborating with Google to help the current technology do a better job translating technical documents.

  22. the statisticians in our department wanted to
    substitute a computer “language” for their few Ph.D.

    Off-topic: I think this is completely sensible, under the following justification for language exams in general. (BTW I am not a

    If one doesn’t know French and one is presented with one French paper to read, a reasonable response is to not read the paper. But presented with ten such papers, the reasonable response is to learn French. Usually, one gets presented with the papers one by one, so one makes what turns out to be the wrong choice over and over. The language exam is a bit of paternalism to save people from this mistake.

    Now repeat with “If one doesn’t know how to program and is presented with a problem best solved by computer, …”

  23. I’ve worked in translation professionally (Japanese to English). It’s a major pain. I don’t know how much the “rough draft” idea would help- I think it’s approximately as difficult to correct somebody else’s rough draft as it is to start from scratch.
    What could work is to have a finished text, and just have it proofwritten. So, give “reputation points” or something, and only assign to people who actually can translate.
    Of course, translating mathematical papers from French to English is orders of magnitude easier and less painful than translating novels or films or computer games from Japanes to English, where you care about things like tone of the character, language that character would use, etc…

  24. Another idea is to cooperate between students from different countries who want to study math and English (and English-math writing).

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