Still, that training is not unavailable outside an academic environment to translators. I’m not saying a freshly-minted translator is going to be able to do this, but there’s nothing precluding a translator gaining experience through work and independent research in order to gain that level of proficiency. Conversely, a trained mathematician who kept up practice in a language outside the field of mathematics would probably be able to achieve the same results. There’s nothing inherent in mathematics that makes it totally inaccessible to a translator, and I still argue that the more-developed language skills would give the translator an edge.
I can’t disagree more.
A mathematician with weak language skills could determine the mathematical content of a paper in his or her area and join that content together with English sentences resulting in a fairly good translation.
A translator without nearly PhD level training in the specific area of the paper would have no idea what the mathematical content was intended to be and as such would have no way to tell if his or her translation was faithful.
The fact every translated work I can think of was done in the manner that I am describing suggests that it is the best way to achieve a faithful translation.
When I was in grad school ('89-91), the University of Illinois required a reading knowledge of two of the languages mentioned in the OP for a math PhD.
I know we have a few working mathematicians here on the Dope. I’d be interested to hear how often they need to refer to something, old or recent, that was published in another language.
No, but it is inaccessible to a non-mathematician. There’s no reason a single person can’t be both a competent translator and a competent mathematician, but such folks are much rarer than translators in general.
What I find interesting is that it’s mathematicians specifically who are expected to know other languages. There are plenty of physics papers published in languages other than English, too, and I’d expect those would have a higher proportion of human-language content than math papers would have, and yet I’ve never heard of an advanced physics program that required knowledge of other languages.
No indeed. The point applies to all highly technical subjects. That is why, for instance, chemists often find it much to their advantage to know some German, and specialists in ancient philosophy need to be able to read Greek (and Latin will help too). Indeed, although English translations of almost all the significant texts of ancient philosophy are available (often in multiple and significantly varying versions) they have almost invariably been made by people who were philosophers first and foremost, and scholars of the Greek language very much second. A translator with an excellent knowledge of Ancient Greek, but only a superficial knowledge of ancient philosophy, would be almost certain to make serious errors (and a translator with excellent German but only superficial chemical knowledge would almost certainly screw up the chemical texts too).
And now that you’ve vented, may I point out that I made absolutely no statement about how to translate the phrase “prime number” to or from Ruissian, but rather gave what I called a “two-word definition” – which itself has faults, including the obvious one of “except itself and 1” being omitted. In my experience, a phrase like “two-word definition” generally implies “this gives the essential concept in general terms.”
My point, though, was not to say something about prime numbers per se, but to exemplify the significance of нет plus the genitive (singular, please note) as being something that comes easily even to Russian preschoolers but which defies quick-and-easy precise rendition into English – it may mean, essentially, “it has no factors” or “there are no factors” but that is not what it literally says. And for that, you almost have to go to Pres. Clinton’s famous appeal to epistemology.
Oddly enough, in my current research, I frequently need to reference Lie Groups and Lie Algebras: Chapters 4-6 by none other than Nicolas Bourbaki (who has posted to this thread*). The English version of this book is almost always checked out of the Math library, but the French version is reliably present and my advisor has the same book in Russian. Usually one of these two copies suffices despite my never having taken either French or Russian.
- Most mathematicians will know why the SDMB poster Nicolas Bourbaki could not possibly the “real” Nicolas Bourbaki.
When I was in graduate school in Biology in the 1970s, a Ph.D. had a foreign language requirement. (Since I intended to work in Latin America, I chose to take Spanish, although I had mostly taken French in high school and German as an undergraduate.) Looking at the requirements for my department today, there no longer seems to be any foreign language requirement.
For what it’s worth, in my university, the Math department retains a nominal foreign language requirement (I believe the test is, as a poster noted above, to translate a paper with the aid of a dictionary), while the closely related but technically distinct Logic group, which used to have the same requirement, decided years ago to waive it when a student (now a rather prominent set theorist) completed all the other requirements of the program and moved on to a professorship elsewhere without bothering to ever actually take the language exam. I can only wonder why his colleagues in the Math department haven’t tried the same tactic…
(To clarify: the requirement wasn’t just waived for this one student, but, as a result, was dropped from the program entirely, which, in my own laziness, I find both amusing and inspiring)
Bourbaki would fear his proofs would be skewered by Ellery Queen’s insight? 
It’s my understanding that in fact Francis Bacon wrote almost all of the works attributed to Bourbaki (as was discovered by Georg Cantor in the last period of his life, and which he was murdered to cover up).
Regarding the russian sentence “factora nyet” and parallel constructions, I doubt there’s anything ineluctable about it. It looks to me as though it has a perfectly straightforward translation into English. I’d love to say the translation is “No factors,” but I know people will dislike the way this appears to be an incomplete sentence (it’s not really; it’s only “incomplete” in formal, written English) but even barring that, it appears the translation is pretty straightforwardly, “it doesn’t have any factors.”
It appears the “ineluctibility” Polycarp refers to comes from a fact that there’s no single, uniform way to translate all instances of the grammatical construction into English. Perhaps in one case it should be translated as “it has no…” and in others “there are no…” and perhaps in other ways in other contexts. But this doesn’t mean the construction says something you can’t say in English. Rather, it means the construction says something that in English is said in several different ways depending on the context.
In Japanese, I think there’s a construction very similar to the one you’re talking about. (A bit of a WAG here). “X ga arimasen” sometimes means “There is no X,” sometimes “It doesn’t have an X,” and indeed, sometimes, “We have no X” or “there are no X’es” and the list could be added to.
But “X ga arimasen” doesn’t say something special that it’s very hard to put into words in English. In each case there’s a single clear way to communicate in English what the Japanese is trying to communicate. It’s just that you have to look at the context in order to determine what the correct translation is. You can’t just look at the text. And this is pretty normal when doing translation. Languages don’t map directly onto each other from construction to construction. Rather, they map somewhat more indirectly (but still completely) from construction and context to construction.
Idealistically, the Ph.d is supposed to demonstrate that one is capable of taking a place in an on-going international conversation stretching across generations. Having a reading knowledge of at least English + something is part of that ideal. Now, in practice one may take a Ph.d and go do something else with one’s life, something that doesn’t require a foreign language, but that’s not what the program is designed for.
In a research journal about electronic imaging, I found a recent article co-authored by a certain Nikolaos G. Bourbakis. It cracked me up.
Even though this is what I’m currently working on, I don’t know if my university has language requirements for mathematics Ph.D. students, but just as a matter of course we have to know French (as it is a French-language university, and classes are in French) and English (as most research papers are in English and most conferences have English as their main language). I’m not really fluent in any other language, but I probably could read math papers in a few others if required. (I already find it hard enough to read and understand research papers in English.) I have books in English and French, and pretty much all articles I’ve read were in English, but I know (having just asked a few fellow students) that one of our professors has written articles and/or books in Spanish.
That said, it can be more useful to think in one language or another for some concepts. For instance, Latin uses the same word (“ubi”) for “when” and “where”, a way of thinking that can come in very handy in relativity.
I thought that English “when” and “where” mapped pretty much exactly to “quando” and “ubi” in Latin.
I’m a mathematician in real life, and there are certainly untranslated works out there that I’ve had to read (a lot of work in algebraic geometry is in French, for example, and some of the massive works like GAGA have never (to my knowledge) been translated into English). It’s not absolutely imperative to know a foreign language; I don’t know any German or Russian, but I managed with just English and French. Knowledge of one foreign language (from a short list, I think) was required at my undergrad school for its grad students, but my grad school didn’t have such a requirement.
As for why there aren’t translations available, my guess would be that there just aren’t enough competent editors available. Translating math is very different than translating ordinary prose, or even technical documents from areas outside of math. With the use of TeX and its packages widespread now, most mathematicians write up their own texts themselves or run it past another mathematicians, rather than relying on a general editor. For that matter, many of the translations I’ve seen have been done by students of the original author. In short, translation is hard and time-consuming, and there’s not a huge market for the products or much prestige in making them.
I should also mention that, while knowledge of foreign languages isn’t required in physics, it’s still not uncommon (though I think it’s mostly for communicating directly with collaborators, not for reading papers). I remember one amusing time when one of my (American) professors gave a talk in French, because he had just gotten back from a conference in France and hadn’t had a chance to translate all of the slides he’d presented there.
FWIW, the university where I got my Master’s degree (not in Math) would not allow you to enter the program unless you either had some basic level of proficiency in a foreign language or agreed to take a foreign language class. However, we were never, ever called upon to demonstrate that we actually possessed the foreign language skills we’d claimed on our applications.
Since the department had my undergraduate transcript they might have verified that the language I claimed to speak was the same one I’d actually taken, but there wasn’t even the most casual of tests to see if I remembered any of it. This subject came up in conversation once with some classmates and everyone said that they’d never been questioned about their foreign language skills. So at least some schools (and this was a Big Ten school, not Sticksville U) are pretty lax about their foreign language requirements.