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In my mother language, Spanish, when we refer to a famous equation, say those for electromagnetism, we say "Ecuaciones de Maxwell". This translates, literally, as "Equations of Maxwell", as a reference to the person who formulated them. The same occurs for famous laws in mathematics and physics, such as with the Theory of Relativity of Einstein or the Integral Theorems of Gauss.

So far, so good. My question refers to when we write these terms in a contracted way. For example, for the equations of electromagnetism, if we take the literal translation from Spanish, they would be "Maxwell's equations"; or, in the other cases, "Einstein's Theory of Relativity" or "Gauss's Integral Theorems". Nevertheless, in many books and articles, both from English native-speakers and non-native-speakers, electromagnetism equations are simply referred as "Maxwell equations", which, up to my knowledge, does not show possession. However, theories or theorems, as the ones mentioned, do show the possessive contraction.

My question is how should I write down these equations in my thesis, as "Maxwell's equations" or as "Maxwell equations," and why.

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    It can work either way, though in my experience with these topics, the possessive seems more likely with named equations, theorems, lemmas, axioms, or hypotheses. I always call them Maxwell's equations, just like Cantor's diagonal proof or Gödel's proof. Jan 30, 2023 at 21:29
  • Best practice is not to reinvent the wheel. Many books use Maxwell equations? Why not use that? And Einstein's Theory of Relativity is not known as the Theory of Relativity of Einstein. Jan 30, 2023 at 21:57
  • Have you asked your advisor or other professors to see what your school's preference is? That would probably provide better guidance than anything anyone here could yell you. Jan 30, 2023 at 22:31
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    Note that for titles and section titles, punctuation, including the possessive apostrophe, is deprecated. This leads to a lack of consistency if possessive forms are used in the body. Also note that multiple names are not done in possessives, so Maxwell-Heaviside equations, Laplace-Runge-Lenze vector. This suggests that it's just easier to do without the apostrophe in longer, busier, more structured works.
    – Phil Sweet
    Jan 30, 2023 at 22:59

2 Answers 2

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"Maxwell equations", which, up to my knowledge, does not show possession.

Neither the genitive "s" nor "of" refer directly to possession. The genitive "s" usually shows some sort of contextual control (The tenant's house), and "of" usually points to an origin (a ring of gold / Robin of Loxley.)

Maxwell's equations and the equations of Maxwell are accurately understood as the equations associated with Maxwell - the nature of the association is contextual.

(As a matter of law, I don't think that you can "own" equations.")

Maxwell equations = noun1 + noun2. These forms, in which the first noun is attributive are very common. (It does not particularly matter that Maxwell is a proper noun.)

We have such phrases as "Information technology" - technology associated with information - and language department - the department associated with language.

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  • Yes! This is exactly what I was looking for. I now see that the confusion comes from the difference between English and Spanish. On the latter, Maxwell equations refer not to the tittle the equations have, but the fact that they are Maxwell's, since he derived them. Your last example even answers a subsequent question I had on the topic. Thanks! Jan 31, 2023 at 2:14
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The following ngram, or rather the pages of examples that result from it show that there is no real principle; one should be careful not to go by the ngram itself as there is an obvious and horrifying error in it.

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ngram

Checking Maxwell, you can see that the possessive case is use most of the time (Maxwell's equation). However, in the case of Schödinger, out of thirteen cases only one is written in the possessive. This means that any one of the two forms is as good as the other.

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