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When we present a term for the first time with reference to another article, should we use definite or indefinite article? (without reference, we should use indefinite article)

Example (The Hilbert's or A Hilbert's):

A/The (the or a?) Hilbert's twenty-fourth problem is described in the article 2 of Higgins. The Hilbert's twenty-fourth problem impossible to resolve, because ..

https://en.wikipedia.org/wiki/Hilbert%27s_twenty-fourth_problem

Edit 1:

add "'s" to Hilbert -> Hilbert's

Edit 2:

My paper for high school students. Thus, they were totally unheard about Hilbert and for sure about his 24 problem. What is more proper for them?

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    Neither sequence above is valid. It's the twenty-fourth Hilbert problem (is described in article 2 of Higgins; no article before "article"! :). Where both twenty-fourth and Hilbert are being used "adjectivally" to modify the noun problem (they come in that order because we nearly always specify "number, sequence" adjectives before "type, class" adjectives).
    – FumbleFingers
    Commented Oct 3, 2021 at 17:13
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    @Ben, still; not quite correct, see my edited answer and comments below it.
    – David Siegel
    Commented Oct 3, 2021 at 17:40
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    We never include an article (definite or indefinite) with a noun phrase that also includes the Saxon genitive (Hilbert's, here). That's because the four highlighted elements in my problem, Hilbert's problem, that problem, and the problem are all "determiners" (which all single out one specific instance of whatever np they appear with), and we never attach more than one determiner to a noun phrase.
    – FumbleFingers
    Commented Oct 3, 2021 at 17:41
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    @FumbleFingers I think this is stated a bit too strongly. Consider "The President's twenty-fourth appointment", "the kings undoubted power", "the Congress's recent vote" "the mayor's famous speech", or "the company's benefit policy". when the noun phrase is a possessive of a title normally given with a definite article, both will appear. I wopuld add that I think the obscure but technically correct term "saxon genitive" may confuse some learners, and I would favor "possessive 's" instead
    – David Siegel
    Commented Oct 3, 2021 at 18:25
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    @DavidSiegel: Ooops! You're quite right (except I personally can't really endorse the Congress's recent vote, but since I'm not even American, I guess I shouldn't pontificate on how they should refer to that legislative body). I did include the example in brackerts immediately after the term Saxon genitive, so I reject that point. But if you know how to more accurately define those contexts where my crude "rule of thumb" doesn't apply, that might be useful. I'd still like to think that in most contexts, my rule is worth taking note of.
    – FumbleFingers
    Commented Oct 3, 2021 at 18:33

1 Answer 1

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In the case the referent is specific. and so if an article is used it should be definite. But

The Hilbert twenty-fourth problem incorrect, shown by red X

is incorrect. (as FumbleFingers says in a comment, this is because a "number" adjective should come before the noun in normal use.) It could be rephrased as

  • The twenty-fourth Hilbert problem correct, shown by green check
  • Hilbert's twenty-fourth problem correct, shown by green check

However, a definite article should not be used with the possessive form:

  • The Hilbert's twenty-fourth problem incorrect, shown by red X

That seems to apply the article to "Hilbert", as would be correct in a construction like:

The President's twenty-fourth appointment correct, shown by green check

But we do not speak of 'The Hilbert" so this form is incorrect and will sound very odd to a fluent speaker.

However, when a referenced term is not specific, an indefinite article should be used:

{X} is a famous proof by Galois

Here X is one of many famous proofs, so an indefinite article would be used. if it was a proof by a mathematician known for only one result, a definite article could be used:

{X} is the famous proof by Jones.

But an indefinite article could also be used, because although there is only one famous proof by Jones, there are many famous proofs by one person or another. This is a matter of emphasis, are we focusing on Jones, or on the proof as one of many famous proofs. However, in the case of:

{X} is a famous proof.

Only an indefinite article is appropriate, because ther are many famous proofs, and X is in no way specific among them (or if it is we have not said so).

In short it is not that there is reference to a thing defined elsewhere that determines what sort of article to use, it is the meaning and structure of the text itself, and particularly whether the thing is being discussed in a specific or general way.

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  • Thanks! please see my edit, I added "'s"->Hilbert's, as it exactly appears ( Hilbert's twenty-fourth problem) in wikipedia and science articles.
    – Ben
    Commented Oct 3, 2021 at 17:22
  • My paper for high school students. Thus, they were totally unheard about Hilbert and for sure about his 24 problem. What is more proper for them?
    – Ben
    Commented Oct 3, 2021 at 17:34
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    @Ben I am sorry, but that form is also incorrect, see my edited answer.
    – David Siegel
    Commented Oct 3, 2021 at 17:34
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    @Ben, one can always add explanation that the audience is likely to need. For example: "Hilbert's 24th problem (one of a set of famous problems first stated around 1900 by David Hilbert) is described in ..." possibly with a cite to the Wikipedia article about Hilbert, or another appropriate source.
    – David Siegel
    Commented Oct 3, 2021 at 17:39
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    I am afraid I can't recommend a good source, but perhaps others can. There are many pages on the web that discuss articles in grammar, searching for "articles grammar" should find several. Your question is phrased a bit oddly, by the way, more usual would be: "In what book or source can one study thoroughly the use of definite and indefinite articles for writing science papers".
    – David Siegel
    Commented Oct 3, 2021 at 19:21

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