Why are Japanese characters not used in equations?

Question

Why do Japanese texts/scientific articles not use kana/kanji in their equations? For example

f(x) = x + 1

instead of

f(あ) = あ + 1

I don't see the Cyrillic alphabet in equations either. Did someone once decide to only use latin letters or has this just happened and people are used to this convention?

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Example: Japanese Wikipedia entry for "function"

Answer 1

Here are some facts, and my speculations.

Actual Usuages

Japanese as Text

In non-technical context, we can use arbitrary text (just like in English) in equations:

長方形について， "面積 = 縦 × 横"

is a natural way of expressing the idea (so is "area = length × width").

Elaborating on this,

仕事 = ∫ 力・d(位置)

is very rarely seen but would be acceptable by most readers.

Japanese character as a symbol

Interestingly, I found a rare case where a Japanese character is used in the way you are looking for. On “The stack of higher internal categories and stacks of iterated spans”, page 13, they have this notation: "The Yoneda embedding よ : C → P(C)" (No \mathcal shown here)

The author seems to have decided that 「よ」 for 「米田」 is a good choice.

Other Alphabets

Latin and Greek alphabets are used everywhere. ℵ from Hebrew is a conventional notation in set theory, and ב is used in similar contexts. I believe what alphabets appear in equations mainly depends on conventions, rather than certain rules.

Why Not?

This is only my speculations on why Japanese characters aren't popular in equations.

• Conventions, across the world.
  • f for function. x for unknown. F for force, e for Euler, etc. g , being the successor of f, for another function. Certain conventions above are universal, and we don't really want to use different notations for discussions in Japanese and English. When you see x = a(f), you'll get slightly confused.
• No one can read it
  • There's no such thing as mathematics only for certain language community.
• Latin alphabets are more suitable for notating with a single letter.
  • 「か」 for 函数 really isn't appealing for me because it loses so much information. 函（変）= 正弦(変) + 2 looks interesting, but we can't have two variables (Kanji don't have natural succ/pred). 函(変₁, 変₂) = 変₁× 変₂² might be worth discussion. There's no practical benefits, though.
• I have never been told not to Japanese characters specifically. We just learn from what are widely used and stick with them, because that's the easiest for communication.

So I believe the answer is

• It's just because it isn't conventional to do so, and there aren't many reasons to do so, actually.
• If certain conventions are established (I'm hoping 「よ」 for 米田 to be among the first), that character for that usage will be seen everywhere.

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• Related question in Math.stackexchange.
• My finding on the 「よ」 is attributed to the following tweet:

数学記号として平仮名が使われる時代が既に訪れていたのか... pic.twitter.com/1MENyIDSwC

— ウニ (@unununum_1) 4 May 2017

Answer 2

According to this page(和算における連立代数方程式を解くアルゴリズム:数理解析研究所講究録), http://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/pdf/1787-04.pdf explains,

In Edo Period, Algebraic equations of three unknown variables were stated in the following expressions.

仮如、 勾股有り。 只云う、 勾再自乗数と弦再自乗数と相井せて共にー百五十二寸。 又云う、 股再自乗数と弦再自乗数と相併せて共にー百八十九寸。 勾股を問う。

There exists a right triangle(勾: x 股: y). Now, 勾再自乗数(x^3)と弦再自乗数(弦: hypotenuse z^3)と相井せて共にー百五十二寸(152) (x^3 + z^3 = 152)。股再自乗数(y^3)と弦再自乗数(z^3)と相併せて共にー百八十九寸(y^3 + z^3 = 189)。勾股を問う(What is x, y?)

As for the function, I saw some say one of the concept(ex: hit something into the black box and you get some outcome) was imported into Japan in Edo Period with the word(関数）.

Bonus

Yosh’s answer is very specific. I found japanese mathematician says an American mathematcian used 兄 for mathematical symbol.(https://mobile.twitter.com/FumiharuKato/status/860438562415628288)

N. KATZ. Nilpotent connections and the monodromy theorem : applications of a result of Turrittin. Publ. math. IHÉS, 39 (1970), p.175-232