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I would like to extend a previous question on the capitalization of theorem names . This time, it's not about numbered theorems like "Lemma 1.1", but about theorems that carry a name.

Question: Which of the following variants is to be preferred?

  1. "By Zorn's lemma, we can conclude..."
  2. "By Zorn's Lemma, we can conclude..."

Additionally, I would like to know how to deal with the corner case where the name of the person after which the theorem is named starts with a lowercase letter

Question: Which of the following variants is to be preferred?

  1. "The proof of van der Waerden's theorem can be extended to ..."
  2. "The proof of Van der Waerden's theorem can be extended to ..."
  3. "The proof of van der Waerden's Theorem can be extended to ..."
  4. "The proof of Van der Waerden's Theorem can be extended to ..."
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Greg Graviton
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    This is a question about Dutch spelling practice. Note that Dutch-speaking Belgians have different rules, and then there's the French... – Chris Godsil May 23 '12 at 12:31
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    Downcasing ("Zorn's lemma", "van der Waerden's theorem") is increasingly popular. "Zorn's Lemma" is still acceptable if you prefer it, though. But really, this is a question about English rather than math. – Charles May 23 '12 at 13:20
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    In Dutch, the proper way of writing the name would be "Van der Waerden", and to sort the name under the "W". This does not mean that you should do that when communicating with non-Dutch people though. I don't know how this should be done in Flemish, French or German (von Dyck or Von Dyck?). – Jan Jitse Venselaar May 23 '12 at 14:33
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    To summarize, this is a question about multicultural adaptation of orthographical practices of transliteration of proper names from one germanic (Germanic?) language to another. So yeah, not about math. – Lee Mosher May 23 '12 at 15:58
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    If this question is inappropriate, I apologize, but I do not believe that consulting, say, a generic style manual will help me adhere to the conventions that are actually practiced by the mathematical community. It won't be much of a problem if I refer to "Van Der Waerden's Theorem" in my thesis, but I would like to dot all i's and cross all t's. – Greg Graviton May 23 '12 at 19:11
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    @Greg Graviton: first, personally I like this type of question, but in principle agree it is not on topic. You say you will not be able to know the conventions of the math community by consulting standard style guides. But look, either there is a set convention then it will be ease to figure it out by just emulating what is done in the majority of (high quality) source you use, or there is none. Actually I think the later will be the case. Eg with the right crowd you can have a good discussion whether it is Abelian or abelian. –  May 23 '12 at 20:24
  • To put it differently. If you just want to avoid doing something strange: immitate. If you want to know what is/could be the rational behind different ways of doing things, it is more a standard style question –  May 23 '12 at 20:28
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    @quid: Indeed, but that still leaves the question of which specific sources to imitate. It just occurred to me that the Princeton Companion to Mathematics is probably perfect for that, though, as it was written by many high profile authors yet has consistent copyediting. A quick look at the index ( http://books.google.de/books?id=ZOfUsvemJDMC&pg=PA1015 ) shows that the variant "van der Waerden's theorem" is used. Thanks! – Greg Graviton May 24 '12 at 08:45

2 Answers2

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If you are writing for a journal or book series, follow their style guide. Both versions

Zorn's Lemma

Zorn's lemma

can be found recommended in different places. Sometimes you could imagine more than two possibilities:

Chinese Remainder Theorem

Chinese Remainder theorem

Chinese remainder theorem

And also

Triangle Inequality

Triangle inequality

triangle inequality

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Gerald Edgar
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  • I can imagine either lowercasing result names, leading to "Chinese remainder theorem", or uppercasing them, resulting in "Chinese Remainder Theorem", but I can think of no consistent principle that would lead to "Chinese Remainder theorem". What do you have in mind? – LSpice Oct 30 '21 at 23:11
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I'd say that in general, such questions about standardization in mathematics (not only in mathematics, of course) are quite important today, because they make easier the use of search engines. So, it is relevant that we all agree to call "Zorn's lemma" a certain result, instead of e.g. "Chain's Upper Bound Theorem", much more relevant than in the past.

In particular, spelling of names is an important issue, of course, and creates a problem, for several different transliterations from other alphabets are used: e.g., Чебышёв is romanized as Chebyshev (English), Tchebychev (French), Tschebyschow (German), Chebyshov (Spanish), Tsjebysjev (Dutch), Čebyšëv (ISO 9),...&c. Here, we should at least care to write correctly the names in their original form, which is also a point of respect (yet we meet wrong forms like Lebesque or Holder or Erdös even here at MO).

On the contrary, the issue of upper vs. lower case does not seem that relevant, as search engines are usually case-insensitive. Also, Google does not care so much about the Saxon genitive, even for queries into commas.

In conclusion, as to your questions, for your thesis I would mainy care to respect an internal coherence, and of course, the correct spelling of personal names.

KConrad
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Pietro Majer
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    The only "Lebesque" on MO at the time I write this comment is in your post, which understandably I should not edit given the context. I have corrected all the other ones, so at least for now this annoying misprint has been removed from all of its unintentional appearances on MO. – KConrad Oct 30 '21 at 22:39