CZ:Formatting mathematics/Theorem capitalization

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Statement of proposed policy

Proposed policy: Do not capitalize names of theorems for that reason alone, either when referring to them in prose or when creating new CZ articles. Normally capitalized words within theorem names should still be capitalized.

Proposed good example: The fundamental theorem of covering spaces should never be called Martin's theorem, because Martin isn't a topologist.

Proposed bad example: The Fundamental Theorem of Covering Spaces should never be called Martin's Theorem, because Martin isn't a topologist.

Editors' opinions

  • Greg Martin 16:20, 10 May 2007 (CDT) supports this proposed policy.

Arguments in favor

  • In current usage, not capitalizing is much more common than capitalizing. Quoting Fredrik Johansson from the forums: 'From a quick arXiv search, "prime number theorem" outnumbers "Prime Number Theorem" by 3 to 1. I saw a few hits for things that were apparently not *the* prime number theorem; but they were called "XX prime number theorem" or "prime number theorem for XX", not "the prime number theorem". A couple were inconsistent; I even saw an article that called the (classical) prime number theorem the "prime number theorem" and a different prime number theorem a "Prime Number Theorem" (due to the latter being mentioned in a title). In the case of "fundamental theorem of algebra", there's no competition: lowercase outnumbers uppercase 10 to 1.'
Rebuttal: This data is limited. And capitalizing theorem names is the traditional way to do it.
  • Chicago Manual of Style, 15th Ed., rule 8.157: "names of laws, theories, and the like are lowercased, except for proper names attached to them." Examples: The big bang theory; the general theory of relativity (or Einstein's general theory of relativity); Boyle's law.
Rebuttal: Let's do what's smartest, not what some book tells us to do. Maybe this very article will be "the book" someday!
  • Using a Bunch of Capital Letters in the middle of a sentence looks funny.
Rebuttal: What looks funny is a function of what we're used to.
Mischievous rebuttal: You look funny!

Arguments against

  • Theorem names are proper nouns and thus should be capitalized, like the Empire State Building. You can tell it's a proper noun because we say the Prime Number Theorem rather than a prime number theorem.
Rebuttal: Proper names aren't always capitalized - see the quote from the Chicago Manual of Style above. And the the serves as enough of an indication that the prime number theorem is a unique entity; capitalization isn't needed to signify that.
  • It is traditional to capitalize the name of the theorem, and insisting on not doing so would seem to be self-consciously iconoclastic.
Rebuttal: Although it is traditional, common usage has shifted: now not capitalizing is more usual, and capitalizing looks old-fashioned.