In mathematics, it often occurs that the last names of famous mathematicians are used as adjectives with mathematical meaning. Most of these adjectives are written with a capital letter. Then, prefixes may be added to these adjectives to denote derived mathematical properties.

How do capitalization and hyphenation appear in these adjectives. For example, we could derive from "Boolean" the adjective


Other examples (not necessarily in use yet) could be


I am aware of "pre-Hilbert" as an adjective that is actually established, but as a general rule this spelling looks peculiar to me.

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    tchrist's answer below gives the general rule, but mathematical usage does seem to know some exceptions. Poking about the Mathematical Reviews database, it does seem that the spelling "nonhamiltonian" does appear in titles in the literature (if rather less frequently than "non-Hamiltonian"), whilst "nonabelian" appears about as frequently as "non-Abelian." There is also a standard term "anabelian," though this seems to be the straightforward adaptation into English of Grothendieck's coinage in French of "anabelien." – Branimir Ćaćić Mar 2 '13 at 21:04
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    Both abelian and boolean are frequently lowercase in math papers, thus allowing nonabelian and semiboolean. If you capitalize Abelian, you should use non-Abelian; tchrist's answer is correct. – Peter Shor Mar 2 '13 at 22:15
  • @PeterShor Yes, you're absolutely right, the folks who write nonhamiltonian are precisely the folks who write hamiltonian instead of Hamiltonian. So, there's a real usage question here about mathematicians opting to write certain very common adjectives formed from proper nouns, like Hamiltonian or Boolean or Abelian, without the capitalisation generally required in such cases. I'd hazard to guess that such a usage is more common in branches of mathematics where much of the literature is still in French (e.g., number theory, algebraic geometry?), though I'm likely totally wrong. – Branimir Ćaćić Mar 2 '13 at 23:41
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    @BranimirĆaćić My UK maths lecturer told us that it was a great honour for a mathematician to have their name used in lower-case. I recall he was talking about "abelian". – donothingsuccessfully Mar 3 '13 at 6:20
  • "Other examples (not necessarily in use yet) could be coriemannian". I used this term in 2008 in arxiv.org/abs/0809.3108 where I used your second option: "co-Riemannian". – Loop Space Mar 25 '14 at 11:25

NOTE: All examples below gleaned by creatively grepping the OED.

Whenever you create a brand new word by applying a productive prefix to a proper noun, which therefore begins with a capital letter, the hyphen is obligatory.

  • miso-Hellene
  • pre-Einstein
  • pre-Freudian
  • pre-Socratic
  • post-Cantor
  • post-AIDS
  • post-Newtonian
  • post-Nicene
  • post-Pliocene
  • anti-American
  • ante-Justinianian
  • de-Stalinize
  • intra-European
  • trans-Siberian
  • pan-European
  • proto-Hittite
  • un-American
  • pseudo-Gothic

This general rule is especially useful for nonce words, coinages you create on the fly, which might not otherwise be recognized by the reader. When you create a new derived term where each part is normally capitalized, then with time, the hyphen and the second capital tend to become lost.

For example, we oppose the Arctic not with the *ant-Arctic, but with the Antarctic. And while terms like Tibeto-Himalayan or Proto-Indo-European seems resilient to this process, many others are not, including:

  • Amerasian
  • Amerenglish
  • Amerindian
  • Eurafrican
  • Eurasian
  • Mesoamericanist

(There are also a few false positives to be wary of, like Bildungsroman and Künstlerroman, which do not, in fact, involve any Roman elements. :)

Counterexamples, where neither capitals nor hyphens remain, include:

  • acatholic — a word the OED equates to non-Catholic
  • misogallic
  • paganochristian
  • rechristianize
  • subatlantic
  • subarctic
  • transatlantic
  • uncatholic
  • unchristian
  • unfrenchify

Some terms enjoy more than one attested spelling. The fully hyphenated and capitalized version tends to occur first historically, as the term is first coined and then popularized, while the smoothed-down version follows once the term has been around a while. So the Pre-Cambrian period of geologic time is now often spelt Precambrian, and the “European climatic period that followed the Arctic and preceded, or marked the transition to, the Boreal period, and was characterized by the spread of birch and pine forests is variously spelt Preboreal, pre-Boreal, and preboreal.

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