Galois Theory — an implied genitive or not genitive at all?

Question

In the field of mathematics there are many concepts named after certain individuals: the Pythagoras's theorem, Galois theory, Hilbert space and so forth. In my native tongue of Finnish the person's name in the preceding examples would usually be seen in its genitive case: e.g. "Galois'n teoria", that is "the theory by Galois". One never encounters the non-genitive "Galois-teoria", meaning "the theory called Galois" or "...of type Galois".

Now, I've noticed that in English the names mentioned with these concepts aren't always explicitly genitive. True, "Pythagoras's theorem" has genitive but then you don't have "Galois's Theory" or "Hilbert's space". What I would like to know is that do native English speakers still think these being genitives or not. When one sees the name "Galois Theory", does she automatically think that the theory is of Mr Galois's doing or that the ownership is his? Or does she feel "Galois" is more like a name for the theory? That is, are the person's names in these examples somehow implicitly genitive or are they not genitive at all?

Answer 1

I don't believe there is any rule and that you will therefore see all sorts of usages depending on the personal preferences and maybe the ignorance of the writer. An additional complication is the fact that the rules about the use of apostrophes are strongly disputed, and even more disputed than usual if the name is foreign, like Pythagoras or, especially, Galois.

So you will see Pythagoras Theorem (named in honour of Mr P, like Victoria Station in London), Pythagoras' Theorem (for those who can't bear "'s" as a possessive of a word or name that ends in "s"), Pythagoras's Theorem (for those wise people who can't see why you would write a possessive in a different way to how you would say it). You will also see in scientific papers "Theorem 23 (Pythagoras)".

My conclusion is that some writers see these attributions as possessive but some see them as more commemorative than possessive.

Answer 2

Discoveries in science and in mathematics are often named after a person. This is an example of an Eponym.

Per the Wikipedia article, "English can use either genitive case or attributive position to indicate the adjectival nature of the eponymous part of the term. (In other words, that part may be either possessive or non-possessive.) Thus Parkinson's disease and Parkinson disease are both acceptable. ".

The two forms are often interchangeable. For example, in the Wikipedia article about Cauchy's convergence test, the title uses the genitive case (Cauchy's) while the first sentence refers to The Cauchy convergence test (implying "the convergence test named after Cauchy").

Interestingly, unlike theorems and laws which are often eponyms (see this long list), most theories that are associated with famous people have their own famous names (often used alone) and the person's name may be added in the genitive case: Darwin's theory of evolution, Einstein's theory of special relativity, Maxwell's theory of electromagnetism... and other theories are not associated with a name at all (Game theory, Number theory...)

Galois theory is an uncommon example of the opposite - the name itself is used as an attributive adjective without "the", rather than in the genitive case (it is not called "Galois's theory" in English, nor "the Galoisian theory"; although in French it is "La théorie de Galois"). I had a hard time coming up with another example of this naming scheme, and I found only one: Sturm-Liouville theory.