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In Denes and Keedwell's book the word "latin" is not capitalized, and there seems to be some precedent in the literature for this usage. However, the vast majority of work on the subject capitalizes the term "Latin square."

Indeed, most English dictionaries and computer spell checkers treat the word Latin as a proper noun. To me, this doesn't seem a particularly compelling argument for its usage in mathematics as, for example, neither Merriam Webster nor Dictionary.com contain an entry for the word "quasigroup."

Perhaps this is a pedantic question, but I have encountered it in personal correspondence several times in the past couple of months. Nonetheless, it may also be worth asking if there is any value to having a consistent convention within the mathematical community.

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    $\begingroup$ Whatever you choose, do it consistently. $\endgroup$
    – Theo Johnson-Freyd
    Commented Jan 8, 2020 at 1:08

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English adjectives that derive from proper nouns are usually capitalised. However, over time, such an adjective can lose its capitalisation provided that it sufficiently departs from its origins in the speaker's mind.

The word 'latin' derives from the central western Italian region of Latium, but its mathematical meaning has little to do with Latium, so it seems sensible to de-capitalise it, much like the term 'roman' in 'roman numerals'.

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  • $\begingroup$ Wow, I didn't even know that "roman numerals" and "hindu-arabic numerals" are written without capitals. Is it the "chinese remainder theorem" too? $\endgroup$
    – bof
    Commented Jan 8, 2020 at 7:27
  • $\begingroup$ isn't it the Chinese Remainder Theorem? :) $\endgroup$
    – Eevee
    Commented Jan 8, 2020 at 10:48
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    $\begingroup$ The "Quadratic Reciprocity Theorem" tells you about quadratic reciprocities. By analogy, I believe that the "Chinese Remainder Theorem" tells you about chinese remainders. Definition: A chinese remainder is the unique remainder mod $mn$, where $m$ and $n$ are coprime, which has remainders $a$ and $b$ respectively upon division by $m$ and $n$. $\endgroup$
    – Theo Johnson-Freyd
    Commented Jan 8, 2020 at 16:12
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A close mathematician friend of mine used to try to stick to the rule of capitalizing any word that derives from a person's name: Noetherian (not "noetherian") ring, Abelian (not "abelian") group, etc. My response: Narcissism?

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    $\begingroup$ What a Dunce . . . $\endgroup$
    – Will Brian
    Commented Jan 8, 2020 at 1:24
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    $\begingroup$ Hah! Dunce comes from John Duns Scotus, who was seen as a hairsplitting scholastic (for those, like me, who had to look it up). $\endgroup$
    – Nik Weaver
    Commented Jan 8, 2020 at 3:57

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