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The question I want to ask is about a concept for which there is a specific term in a foreign language. The problem is that this term doesn't have an accurate translation in english and since it covers a set of concepts rather than a concrete thing which means that trying to explain what that term means is also rather difficult.

To give a concrete example the question I want to ask about covers something which in German is called "Äquivalenzumformung". Both questions on German Stackexchange and Math Stackexchange agree that there is no accurate translation into English.

Since my question is rather about the subtleties of the term I doubt that me explaining that term can give English users who have never encountered that term an accurate concept.

Should I ask the question and just use the foreign word whenever needed or should I just post the entire question in German?

Also maybe someone does find an accurate translation for this case, but what about cases where there really are no accurate translations.

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    $\begingroup$ The idea that this doesn't have an "accurate translation in[to] English" is really just the Sapir-Whorf hypothesis(sciencedirect.com/topics/psychology/sapir-whorf-hypothesis ) in disguise, and that is not well thought of these days. The technique of using Äquivalenzumformung is described in English as "algebraic manipulations restricted to exact equivalences only"; if you want a single word feel free to coin "equivalencing", but remember to define it first. By an large, if an idea is expressible in one language, it's expressible in any (conlangs possibly excepted). $\endgroup$
    – postmortes
    Jul 29 at 12:14
  • $\begingroup$ "The technique of using Äquivalenzumformung is described in English as "algebraic manipulations restricted to exact equivalences only" Thanks for that translation. As for " is really just the Sapir-Whorf hypothesis" I beg to differ. As you have seen with your translation of "Äquivalenzumformung " into English we have to use a discription to do so. Even though in the case of "Äquivalenzumformung " the discription is rather simple and concise I don't think that it is always possible to do so while preserving the subtleties for every term. $\endgroup$ Jul 29 at 13:01
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    $\begingroup$ You're welcome to disagree, but you're actually still repeating the Sapir-Whorf hypothesis in your disagreement. The number of words required, or the circumlocutions required, to explain something to the same level of detail may change per language but there is nothing (to date) that has been found that can't be defined in a dictionary which means that everything, subtleties notwithstanding, can be translated (I suppose I should caveat hapax legomona but it's getting rather esoteric now :) ) $\endgroup$
    – postmortes
    Jul 29 at 13:06
  • $\begingroup$ I am not saying that it is impossible to explain a foreign term in English, but rather that to do so oftentimes lengthy and in depth explanations are necessary. But if one was able give such an explanation one probably wouldn't ask questions about the term in the first place. For example I wouldn't have been able to give such a clear translation as you did simply because I don't know every subtlety of what the term "Äquivalentumforung" exactly entails. Basically the problem is that if I want to ask a question about a foreign term, that I am unsure of, I need to first explain it. $\endgroup$ Jul 29 at 13:10
  • $\begingroup$ However I can't as otherwise I wouldn't want to ask a question about the term in the first place. @postmortes $\endgroup$ Jul 29 at 13:10
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    $\begingroup$ I really can't see how in the context of mathematics one has something that can only be understood in one language but not the other. For a mathematical concept, one just give a definition; if it is not mathematical, then likely it is also not crucial in understanding the question. $\endgroup$ Jul 29 at 13:26
  • $\begingroup$ @ArcticChar as you can see in the 2 links in my answer finding the definition of a foreign word isn't always that easy let alone translating it. But apart from that, yes I agree. $\endgroup$ Jul 29 at 13:28
  • $\begingroup$ What would also interest is especially for people who don't speak German when I ask "Is squaring an algebraic manipulation restricted to exact equivalences only?" is my question crystal clear or is further explanation necessary? $\endgroup$ Jul 29 at 13:57
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    $\begingroup$ If you're doing mathematics then being explicit about what you mean should be second nature ;-) Yes, if you want to explain a term unfamiliar to your audience, no matter what language it is from, you will need to take time and make effort. That's unavoidable. But that doesn't mean you can't convey the idea in another language, which is the impression you gave over in the original question :) $\endgroup$
    – postmortes
    Jul 29 at 14:11
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    $\begingroup$ Is squaring an algebraic manipulation restricted to exact equivalences only?" -- it is clear, but it could be clearer :) The problem is that the reader has to think about what "exact equivalence" means, and since it's a question you haven't prepared them for that thought and so some will miscomprehend it. Better might be, "if each line of an algebraic manipulation must be equivalent to every other (i.e. iff statements) then can I square a line and still preserve the equivalence?" (Sorry for the late post, the site appears to have gone down for a bit) $\endgroup$
    – postmortes
    Jul 29 at 16:04
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    $\begingroup$ Any mathematical notion that can't survive translation into a different language is a poor thing indeed. As to the particular question, you need to clarify what "exact equivalence" means. For example, sticking with real numbers, $a>b>0\implies a^2>b^2>0$ which I would regard as squaring an algebraic manipulation. $\endgroup$
    – lulu
    Jul 29 at 16:09
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    $\begingroup$ If your term can be rigorously defined, then it can be formalized in some formalization of math, and then the formalization can be translated into another natural language (e.g. English). $\endgroup$ Jul 29 at 16:31
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    $\begingroup$ Coming late to this discussion - just a question. Is it possible that "Äquivalenzumformung" is not even a mathematical term but is pertaining to mathematical education at some level in Germany? If so, the question for anyone else (including people fluent in German, but who are not math educators) would need to include full context. Which means either explain exactly what is meant by Äquivalenzumformung (which, if the OP knew, would mean they would know if squaring counts as Äquivalenzumformung or not), or use the untranslated word and hope someone familiar with it will answer. $\endgroup$ Jul 31 at 7:51
  • $\begingroup$ @StinkingBishop I am slowly getting that feeling as well. Especially as the definitions that I found where all verbal. But I can't say for sure. $\endgroup$ Jul 31 at 13:10

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It is not necessary in any circumstance I can conceive to have a word-for-word translation in order to pose a problem that can be resolved by mathematical reasoning.

Math.SE Questions should use the body of the post to completely formulate such problems, to set them up and delineate the goal of the problem. Of course customary definitions and conventional notation do not require special explanation, but any uncommon terminology (like your example) deserves that treatment. If a definition cannot be formalized, the problem may not fit the scope of Math.SE content well. If it truly interests you, then it should be worth making an effort at formalization (as in your example you found that previous post and its Answer, though reasonable Readers might disagree with your summary that "there is no accurate translation into English").

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