# The origin of Japanese translation of sheaf, 層

A sheaf (French faisceau) is called 層 in Japanese. Literal meaning of 層 would be a layer, a stratum, or a story (as in a building,) so the terminology is a bit different from what sheaf or faisceau might suggest. Korean and Chinese translations are the same, but Japaneses are likely the first to use the translation, per the early contribution of Japanese mathematicians like Oka Kiyoshi.

Who was the first to introduce the translation 層, and why?

Akizuki Yasuo seems to be the one who first used the term. According to his book 輓近代数学の展望 (quoted from here):

--秋月康夫「輓近代数学の展望」p.176 (1970年)。ダイヤモンド社。東京

So he chose to use 層 because:

• it sounds like the last syllable of faisceau, (which complies with Zhen Lin's answer,)
• and if you change your perspective, layers are a horizontal bundle.

It's worth noting that English-speaking mathematicians also tried to introduce the term stack for faisceau for similar reasons, as seen in Hodge & Atiyah (1955):

The French word "faisceau" has been translated into English as "sheaf" or "stack". In this paper we use the word "stack", since "sheaf" has been used before in mathematics.

According to Masaki Kashiwara:

It has been said that, when they translated this term into Japanese, they decided to translate it as “sō (sheaf)” because the pronunciation is similar to the sound of “faisceau.” However, I haven’t been able to confirm if this is true or not.

There is a similar hypothesis for 函数 (= function) in Mandarin Chinese: the first character, hán, is pronounced like the first syllable of “function”. (There are other hypotheses.)

• Then I'll call functions 方神 from now on (wtf lol Commented Sep 28, 2020 at 6:32
• As a native Cantonese speaker, I learnt Mandarin at elementary schools. I don't see the similarity in those pronunciations : 函 [han] and "fun" [fʌn] have distinct vowels. Commented Oct 8, 2020 at 9:17
• The English vowel conventionally denoted by [ʌ] has shifted over the last 50 years to something more like [ɐ], so it’s not that far. Of course it would sound different from [a] to a Cantonese speaker – the two are contrastive in Cantonese. But not in Mandarin. Commented Oct 8, 2020 at 9:49
• The term 函數 as a translation of "function" was coined by Li Shanlan (李善蘭) in his translation of "Elements of Analytical Geometry and of the Differential and Integral Calculus" by Elias Loomis. The definition 凡此變數中函彼變數者，則此爲彼之函數 seems to be a translation of "One variable is said to be a function of another variable, when the first is equal to a certain algebraic expression containing the second." Commented Mar 2, 2021 at 16:04
• Thus the choice of the character 函 seems to be primarily based on its meaning of "containing". As a native speaker of Mandarin Chinese, I find the phonetic connection between /han/ and /fʌn/ tenuous at best, at least certainly much weaker than the similarity between "faisceau" and "ソー". Commented Mar 2, 2021 at 16:05