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When we are referring more than one proper noun, then do we need to capitalize the first alphabet of it. For example: which one of the following is correct?

1) By Theorems 4.2 and 4.3, we can prove the following.

2) By theorems 4.2 and 4.3, we can prove the following.

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  • Most people write "Presidents Roosevelt and Truman" rather than "presidents Roosevelt and Truman". See Ngram. I think this answers your question. (I was actually quite surprised by how large the minority who lowercase "presidents" here is, when almost nobody lowercases "president Truman".) Dec 1, 2014 at 11:42

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"theorem" is not a proper noun. Capitalization is not needed.

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    But "Theorem 4.2" is a proper noun, as is "Theorem 4.3". See the comments under this related question, for example.
    – Dan Bron
    Dec 1, 2014 at 8:49
  • According to you. "theorem 4.2" and "theorem 4.3" happen to be capitalized, probably because they were capitalized when used as a section heading in a textbook. That does not make "theorem" a proper noun. It should not have been capitalized in this or the "related" question or answers. One could refer to, say, the second chapter of a book as Chapter Two, but that does not make "chapter" a proper noun. You are correct that it does not need "the", but that is because it already carries its own qualifier, namely the number. Dec 1, 2014 at 11:19
  • @Brian: by your reasoning, since "president" is not a proper noun, we should write "presidents Roosevelt and Truman" and not "Presidents Roosevelt and Truman". And since "ocean" is not a proper noun, we should write "Pacific ocean"? Do I correctly understand what you're saying? Dec 1, 2014 at 11:33
  • You are correct; honorifics are typically capitalized. Dec 1, 2014 at 11:44
  • ... And in math textbooks, references like "Theorem 4.2" are typically capitalized, even in constructions like "by Theorem 4.2, there is a ...". Dec 1, 2014 at 11:45

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