Is there an etymological connection between 奇数 in Japanese and "odd number" in English?

Question

I couldn't find any etymological information about 奇数{きすう} online. I found it interesting that it has the characters for "strange/odd" and "number", and wondered if it was influenced by English, or if the same meanings arose independently.

Answer 1

奇数 is an ancient Chinese word, and it is unlikely to be a calque (translation) of the English word odd number. A 2nd century dictionary 説文解字 already has an entry:

奇：異也。一曰不耦。
奇: 1. strange. 2. not paired.

奇 "odd" and 偶 (耦) "even" are historically mainly technical terms in Chinese cleromancy 易占, but it has a long history of use. But beware that this 奇 sometimes means "lower" numbers (like odd in "30-odd" or "odd pricing") in certain divination procedures.

陽卦奇，陰卦偶。（易經）
the Yang lines are odd (or made by one stroke), and the Yin lines are even (or made by two strokes)

乾至九而止，奇數也；坤數偶，無奇數也。（朱子語類）
乾 "Force" never exceeds 9 and called 奇; 坤 "Field" is a 偶 number, that is not 奇.

日本国語大辞典 dates the first attestation of 奇数 in a Japanese literature in 1477.

史記抄〔１４７７〕一八・日者列伝「前の一変が奇数で五なれば、見の策は四十四なり」

But it is, strictly speaking, the "small number" sense in this context, because you can see in the original book...

前ノ一変カ奇數テ五ナレハ。見ノ策ハ四十四ナリ。偶數テ九ナレハ。四十策ナリ。

The next appearance is in 1508, of the right sense.

六物図抄〔１５０８〕「隻は為_㆓奇数_㆒陽之数也」
"隻 is for odd numbers, or Yang numbers"

As it is still before the first contact of Westerners and Japanese, the possibility of being an English (or European) translation is next to zero (I'm saying this because many modern coined Japanese words are seemingly Chinese but are actually calque from Western languages).

As an aside, 奇 has two readings (i.e. stands for two words) in Chinese, although they are etymologically related and indistinguishable in Japanese on'yomi. The "strange" one is qí (< MC *ɡˠiᴇ < OC *N-k(r)aj) and the "unpaired" one is jī (< MC *kˠiᴇ < OC *[k](r)aj). So it is technically not true that 奇数 literally means "strange number".