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there was a similar question but sometimes you cite theorems just by of authors, e.g. you don't say by the Hopkins-Levitzky theorem we conclude but you just say it follows from Hopkins-Levitzky.

and in this situation, I am quite confused. My instinct tells me to omit the definite article, but my instincts are often wrong (in my native language we don't have articles). I am still citing the same theorem (just omitting to say theorem ) and it is a unique theorem.

Of course, I can avoid this issue by calling it always the full name but sometimes this does not feel natural.

EDIT: I am using Hopkins-Levitzky as an example because in this case, it is obvious that I am not meaning them as a person(s) but as a shorthand for their theorem. But this situation, I think, applies in other cases, when from context everyone knows I mean the theorem itself and not mathematician. For example, if you cite some Eklof's theorem in the text, name it as Eklof's and then you refer to it only as "Eklof".

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  • Well, in math series, we used L'Hôpital's rule, but that nomenclature begs the question for the "The" in the Frenchman's name.
    – Yosef Baskin
    Commented Mar 11, 2022 at 14:17

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In the Hopkins-Levitsky Theorem, the determiner the modifies Theorem. When you drop the word theorem, you no longer use it.

English is very inconsistent about whether to drop the when you drop the noun; it depends on what general category the noun belongs to.

For example, we say the Pacific Ocean and the Pacific, the Rocky Mountains and the Rockies. However, we would also say the Sundance Film Festival, the Woodstock Music and Art Fair, and the Burning Man Project, but these get abbreviated to Sundance, Woodstock, and Burning Man.

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  • Not to say that English isn't inconsistent, but there is a definite trend that "the <noun> <thing>" becomes "<noun>", whereas "the <adjective> <thing>" becomes "the <adjective>". In the examples in this answer the non-"the" examples are all nouns (we could, in principle if not idiomatically, say "the film festival of Sundance", "the rock festival of Woodstock", "the project of the burning man"), whereas we couldn't say "*the ocean of Pacific" or "*the mountains of Rocky".
    – psmears
    Commented Mar 11, 2022 at 13:54
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    @psmears: "by the incompleteness theorem" -> "by incompleteness", not "by the incompleteness".
    – Peter Shor
    Commented Mar 11, 2022 at 17:41
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    Right, that's consistent too :)
    – psmears
    Commented Mar 11, 2022 at 21:55
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  • A Google search for "from Pythagoras' theorem" shows 'about 15,100 results'. Whereas

  • A Google search for "from the Pythagorean theorem" shows 'about 929,000 results'.

  • A Google search for "from Pythagoras" -"from Pythagoras to" -"from Pythagoras's" shows '143,000 results'. But very few of the early tokens can be argued to be relevant. There remain few that are suitably scoped ('Plato may also have obtained the idea that mathematical and dynamic ideas are behind logic, science, and morality from Pythagoras', 'There is evidence that Plato possibly took from Pythagoras the idea that mathematics and, generally speaking, abstract thinking is a secure basis for', 'Six Famous Sayings From Pythagoras' and 'from Pythagoras' outright ban on beans' being interesting false positives).

The snag with '[It follows] from Pythagoras' in an academic sense (as opposed to everyday usages such as "I've just received a request from Pythagoras/Jim for a loan to help offset rising energy bills") is that it is ambiguous. From Pythagoras's famous theorem, from Pythagoras's theorem and related work (his work on a formula to generate Pythagorean triples, say) or from Pythagoras's complete academic legacy (maths. moral philosophy ...)? Not grammatically wrong, but potentially ambiguous (and therefore, if unresolved by context, unacceptable as violating the Gricean maxim of clarity).

You could choose 'from Pythagoras's theorem' (with perhaps a different apostrophe choice) or 'from the Pythagorean theorem' (which sounds overblown to my ears). Never 'from the Pythagoras'.

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  • Thanks for the effort to answer my problem. But I think that you missed my point a bit. I have tried to edit my question accordingly. I don't like the example with Pythagoras but I can put it in my setting too. Assume there is a whole class about the Pythagoras Theorem. Then later, they justify some geometric argument from it. Than when they say "it follows from Pythagoras" it is clear that they mean the theorem, not his moral philosophy.
    – dmk
    Commented Mar 11, 2022 at 13:13
  • In that precisely defined context, 'It follows from Pythagoras' is fine. I included the caveat 'unresolved by context [unacceptable]' to allow that specifying context could change things. Only with your new contextualisation does this become the preferred variant (though 'from Pythagoras's theorem' is also still acceptable).
    – Edwin Ashworth
    Commented Mar 12, 2022 at 16:50

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