Capitalize question after colon or not?

Question

I am wondering whether I should capitalize the first word after the colon in the following sentence:

I wondered: how can I utilize knowledge of algebra to reach my goals?

All resources on the internet I found dealt with different cases, such as enumerating after a colon. However, I am almost putting a different sentence after the colon.

I am aware I could rephrase the sentence not to include a colon, but I need to include it.

The Oxford Manual of Style says that it is only necessary when introducing direct or paraphrased speech, or quoted material. — Mick, Dec 05 '16 at 18:30
You can capitalize, or not, a sentence after a colon: it's up to you. — Alan Carmack, Dec 05 '16 at 18:33

score 1 · Accepted Answer · answered Dec 05 '16 at 23:10

Definitely not: when do you capitalise? When you end a sentence.

In my mind, this is simple: you have not ended a sentence, so you do not need to capitalise the initial letter.

On the other hand, if you are quoting (even if you are quoting yourself), it is optional.

I wondered: "How can I utilise knowledge of algebra to reach my goals?".

Note the full stop after the quotation; if you have capitalised the initial letter, then you are treating it as a separate sub-sentence, as such, you end the sub-sentence and then you end the super-sentence, much like algebraic brackets.

Another case where it is common to capitalise after a colon is in titles, as in all these many examples where the initial word after the colon is frequently of a type (article, preposition) that would not have been capitalised if it hadn’t been preceded by a colon. — Janus Bahs Jacquet, Dec 13 '16 at 21:26

Capitalize question after colon or not?

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