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field

Type of Math Object: 
Definition
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Mathematics Subject Classification

12E99 no label found03A05 no label found

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Why does English have to be cursed with this awful choice of
term "field" for this concept which happend to coincide with
a completely unrelated concept in differential geometry??!!!?
In other languages, the situation is much better --- for
instance, in Polish, one says "cialo" for the algebraic
concept and "pole" for the geometric concept; in Greek, one
says "soma" for the algebraic concept and "pedion" for the
geometric concept; in French, one says "corps" for the
algebraic concept and "champs" for the geometric concept....
It would be a lot saner if English followed the pattern
of other Indo-European languages and called this thing "body"
and reserved the term "field" for the geometric notion.

By the way, Pahio, how is the situation in the Finnish?

The situation in the Finnish and also in the other Finno-Ugric languages, I think, is quite good and clear.
In Finnish: kunta = 'corps' and kentt\"a = 'champs'
In Hungarian respectively: test and mez\H{o} (o with two acute accents).

The word "kunta" belongs to the oldest F-U words (has been at least 6000 years unchanged, but e.g. in Hungarian it has developed to the form "had"!). The present everyday senses of "kunta" are 'community', 'group of people with some structure', 'rural district'.

The everyday senses of "kentt\"a" are 'even area', 'room, space'.

You Rspuzio seem to be a bit worried about the situation of "field" in mathematics. What do you think to do? =o)

Jussi

I actually thought that algebraic fields actually had a connection to geometry that some people had deliberately sought to obscure, some way to visualize the algebraic concept geometrically that would actually make it easier to understand. But the very mixed parentage of English is just as plausible an explanation for this confusion.

In french, I think "champs" is now also used for an algebraic stack, so they're not in the clear either.

Cam

> But the very mixed parentage of English is
> just as plausible an explanation for this confusion.

The Russian is not so mixed language as the English, but the situation is similar: "pole" (i.e. \cyrp\cyro\cyrl\cyre) is used both for 'champs' and 'corps'.

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