I found a lot of Google results for both "Mathewettbewerb" and "Mathe-Wettbewerb". Is there a guideline that recommends one over the other? More generally, is there a guideline for when to use a hyphen for compound nouns and when to simply join them as one long noun?
(Note: Even though the Google search contains some false results, it does have a significant number of accurate ones.)
To regard Mathe-Wettbewerb as a proper spelling at all, you already have to have a special situation or make some rather liberal exegesis of the official spelling rules. In those, not using the hyphen is the default, and using it is allowed only in certain exceptions. Though these are plentiful, most of them do not apply to Mathewettbewerb, except:
§ 45 Man kann einen Bindestrich setzen zur Hervorhebung einzelner Be- standteile, zur Gliederung unübersichtlicher Zusammensetzungen, zur Vermeidung von Missverständnissen oder […].
Dies betrifft
(1) Hervorhebung einzelner Bestandteile, zum Beispiel: der dass-Satz, die Ich-Erzählung, das Ist-Aufkommen, die Kann-Bestimmung, die Soll-Stärke; die Hoch-Zeit, das Nach-Denken, Vor-Sätze, be-greifen
(2) unübersichtliche Zusammensetzungen, zum Beispiel:
Arbeiter-Unfallversicherungsgesetz, Haushalt-Mehrzweckküchenmaschine, Lotto-Annahmestelle, Mosel-Winzergenossenschaft, Software-Angebotsmesse, Ultraschall-Messgerät(3) Vermeidung von Missverständnissen, zum Beispiel:
Drucker-Zeugnis und Druck-Erzeugnis, Musiker-Leben und Musik-Erleben; re-integrieren
Case (1) only would apply, if you put special emphasis on Mathe for some reason, e.g.:
Es ist ein Mathe-Wettbewerb, kein Physik-Wettbewerb.
However, it can be doubted that this is what the authors had in mind as in none of their examples features a noun as the first part.
The examples for case (2) only include multiple compounds (which Mathewettbewerb isn’t), but if you take the rule literally, every compound can be regarded as unübersichtliche Zusammensetzung by somebody and thus spelt with a hyphen.
Case (3) is quite similar to case (2): In all examples you can take a subsequence of the letters to form a word that is not a part of the original compound. This does not apply to Mathewettbewerb, but interpreting the rules literally, you could argue that every compound may cause misunderstandings.
Wettbewerb is compound of wetten and bewerben, although a rather old one.
To give you a rough idea, hyphens are necessary when
proper nouns are involved
Ein guter Wikipedia-Artikel über die deutsche Grammatik.
more than two word classes are combined
Das Hin-und-her-Rennen der Kinder macht mich traurig.
to avoid ambiguity
Abc-De ≠ Ab-Cde
the composition includes numbers or letters:
52-Jährige sind viermal so alt wie 13-Jährige.
U-Form.
This list is far from complete, but the thing is that no matter how long it got, Mathematik and Wettbewerb wouldn't fall under the exceptions. They are "normal" nouns (not proper names etc.), and in German, one may adjoin those hyphenless – even if it's more than two. Prominent examples are Donaudampfschifffahrtsgesellschaftskapitän and Rindfleischetikettierungsgesetz.
Thus:
Mathematikwettbewerb → Mathewettbewerb
(You can use hyphens if the design of some T-shirt demands it, for instance, but that's not very "German".)
There is no reason to use a hyphen in Mathewettbewerb. Hence, why use one? Recommendation: Don't.
