Should names of "named theorems" such as the following be capitalized (a) when being mentioned? (b) when being enunciated (of course the first letter would normally be capitalized in the latter case)?
- Fundamental Theorem of Calculus
- Urysohn's Lemma
- Axiom of Choice
- Intermediate Value Property
It seems to me that such phrases are noun phrases constituting "proper names" and hence should be capitalized, as shown, both when enunciated and when referred to in text.
On the other hand, the house style of the Mathematical Association of America is:
"Do not capitalize ... the names of theorems, e.g., fundamental theorem of calculus, mean-value theorem, Picard’s theorem, etc., in most situations." [https://www.maa.org/sites/default/files/pdf/pubs/General_Editorial_Guidelines.pdf]
Moreover, in at least some books published by the American Mathematical Society, such a name is capitalized, as shown, when enunciated but not capitalized when referred to in text (where, e.g., it would be 'fundamental theorem of calculus').
