I asked this question on Mathematics Stack Exchange (here) but I haven’t had any luck so far. Allow me to copy the question:
If I wanted to be scrupulous about correct spelling, is there any reason that I should prefer either:
- non-abelian or nonabelian?
- nondegenerate or non-degenerate?
- hyperkähler or hyper-Kähler?
NB: For some reason, hyperkähler is more common than hyper-Kähler, however quasi-Fuchsian is more common than quasifuchsian, and I don’t think anyone writes “pseudoriemannian”.
While I’m at it, allow me to ask a second spelling question: should I write PDEs or PDE’s? It seems to me that there is no reason to use an apostrophe but a lot of people do.
PS: Wikipedia says something about the use of lowercase “a” in “abelian”: here.
Three specific answers:
- nonabelian and non-abelian are roughly the same frequency over the past few decades but noncommutative is by far the standard nowadays
- nondegenerate is somewhat favored over non-degenerate
- hyperkähler and hyper-Kähler both seem to be used in mathematical literature with no clear higher frequency.
That is what is, but you’re probably asking for what should be. In general though, the orthographic trend is at first for ‘non’ followed by a name-adjective, just like any noun-noun pair, is to go through successive states of neologism:
– ‘non’ followed by a hypen then followed by the capitalized name, eg ‘non-Abelian’
– ‘non’ followed by a hyphen then followed by the uncapitalized name, eg ‘non-abelian’.
– ‘non’ followed directly by the uncapitalized name, eg ‘nonabelian’.
This is because the name part of the word is, at first, very distinctive and meaningful as a name, but slowly becomes opaque, and eventually a regular word, similar genericization, how a trademarked company name, like Kleenex or Google, becomes a corresponding generic, kleenex (for any kind of facial tissue) or google (to search the internet using any search engine).