[Math] Why aren’t fields called “bodies” instead

fieldsho.history-overviewterminology

The discrepancy regarding the names of commutative division algebras in German and English has always startled me. In English they are called fields, whereas their original German name is Körper (hence the $K$), a word which usually means "body" in everyday language. Nearly all other English names of algebraic objects are direct translations of the corresponding German terms (or maybe also the other way round), so I'm wondering which historic development lead to this divergence in naming conventions.

By looking up the Wikipedia article on fields in the respective languages, I found out that most languages seem to have adopted the German name. For example a field is called corps commutatif in French, cuerpo in Spanish, Σώμα in Greek, corpus in Latin, Ciało in Polish, kropp in Swedish and Norwegian.

However there also seem to be some languages where the name for fields translates to "field", such as Russian (Поле) and Italian (campo). Dutch seems to assume a special role, since the term used in the Netherlands seems to be lichaam, whereas the Belgians call it veld.

Does anyone know how this strange division in naming conventions did evolve?

Best Answer

It might be worth noting that the word "Feld" is also (sometimes) used in German, at least in the compound "Galoisfeld" (for "Galois field"). And, this is not some modern-day re-translation from English but classical usage (of Witt for example), see the discussion in comments of https://mathoverflow.net/a/18638/9072 for references.

In my opinion this provides additional support for anon's answer that quite at the start there were two different names and just in the one language the one 'won' whereas in the other one the other 'won' the 'competition'.

Regarding other theories and in general, it might be worth noting that "Körper" does not only mean body, like in human-body, but is also used to designate certain structures/organizations/groups, like "Justizkörper" (comprising judges, attorneys, and so on). And, in that meaning "Körper" fits a lot better with "Gruppe" (group) and also with "Ring" (also used as name for organizations, like in English) and also "Verband" (again used to designate organizations, the math meaning being lattice, in the order sense, providing another example where it is not a translation). See https://mathoverflow.net/a/117354/9072 for some discussion. So that "Körper" is really not all that sensual in that context but quite corporate (which ultimately derives from the same source, I think).