English is unusual among major languages in the number of technical words borrowed from other languages instead of being made up from native roots. We have some, listed under suggestive names. But how can you tell from looking at them what “parabola” or “homomorphism” mean?
The English word “carnivore” (from Latin roots) can be translated as “Fleischfresser” in German; to a German speaker, that word means literally “meat eater”. So a question such as “What does a carnivore eat” translates into something like, “What does a meat-eater eat?” (And do they do it in Grant’s tomb?) Similarly the word for “plane” (ebene) looks like “flat”.
Chinese is another language that forms words in that way: see the discussion of “diagonal” in Julia Lan Dai’s blog. (I stole the carnivore example from her blog, too.)
The result is that many technical words in English do not suggest their meaning at all to a reader not familiar with the subject. Of course, in the case of “carnivore” if you know Latin, French or Spanish you are likely to guess the meaning, but it is nevertheless true that English has a kind of elitist stratum of technical words that provide little or no clue to their meaning. German has a much smaller elitist stratum of words. I don’t know about Chinese.
This is a problem in all technical fields, not just in math.
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I’ve certainly noticed the difference between English and German that you allude to many times. It makes encountering unfamiliar words in German much easier for me to deal with than I imagine it to be for nonnative English speakers encountering long English words pulled together from sometimes disparate Latin and Greek roots.
However, the difference between mathematical English and mathematical German is much smaller. I’d guess this is because a lot of terminology was established back when Latin was the international language of scientific discourse, and some habits stuck. For example, the German word for “isomorphism” is “Isomorphismus”.
On a different but related note, learning mathematical terminology in another language can give you new appreciation for how arbitrary our use of standard English words as technical terms can be. In the first class of a topology course I took in Germany, a function was described as “stetig”, which a German-English dictionary will translate for you as “constant, consistent, steady, continuous”. I needed to wait for some more context to determine that the correct mathematical English translation is “continuous” and not “constant”.
Back in the 1960’s when you still had to read German to be a mathematician, I came across the word “lückenhafte” and in a German-English dictionary found the translation “lacunary”. I had never heard of lacunary and had to look it up in an English dictionary. If it had said “gappy” I probably would have understood. But modern web translators give “incomplete” instead of “lacunary”, which would have left me totally baffled.
“Lückenhaft” and “lacunary” are an excellent example of your original point. Some more dramatic ones include the famously half-translated-from-German-into-English “eigenvalue” and “eigenvector”, and the completely untranslated “schlicht” (which is sometimes used in complex analysis). Your German-English dictionary won’t even get you started on the latter – but a German speaker probably wouldn’t guess the technical meaning either. An even better example from physics is “Bremsstrahlung”, which I learned about under that name in the U.S., and whose literal meaning (“braking radiation”) is actually suggestive to German speakers of its technical meaning.
The reason I bring these examples up, however, is to point out that these days the language transfer mostly happens in the other direction, with English technical terms being imported into many other languages. At conferences I can frequently walk past two mathematicians speaking to each other in Hebrew, Russian, French, or Italian and guess which talk they are discussing, because they use English almost exclusively for technical terms of recent coinage. Of course, returning again to your original point, those English terms are likely to be formed from Latin and Greek roots.