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by IngoBlechschmid 1896 days ago
Working mathematician here. Generally I concede.

However I'd like to add that often in mathematics, we are discussing very generic situations. For instance, we are not talking about the radius of some specific circle, which perhaps should be named `wheelRadius`, but about the radius of an arbitrary circle or even an arbitrary number.

I wouldn't really know a better name for an arbitrary number than `x`. The alternative `arbitraryNumber` gets old soon, especially as soon as a second number needs to be considered -- should it be called `arbitraryNumber2`? I'll take `y` over that any day :-)

Also there are contextually dependent but generally adhered to naming conventions which help to quickly gauge the types of the involved objects. For instance, `x` is usually a real number, `z` is a complex number, `C` is a constant, `n` and `m` are natural numbers, `i` is a natural number used as an array index, `f` and `g` are functions, and so on.

My favorite symbol is by the way `よ` which denotes the Yoneda embedding and is slowly catching on. All the other commonly symbols for the Yoneda embedding clashed with other common names. This has been a real nuisance when studying category theory.

2 comments

We use i, x, y, etc. all the time as variable names as professional programmers.

So you're sort of arguing against a straw man there, almost no programmer would expect you to name such a concept 'arbitraryNumber2', we would also name it x or y if it made sense in the code.

Sorry, I didn't want to argue against a straw man. You are right. I just wanted to indicate that in mathematics, we are much more often in such generic situations than in programming. Accordingly, I wanted to argue that the increased brevity in mathematics is to some extent to be expected.
For the curious:

"My favorite symbol is by the way `よ` which denotes the Yoneda embedding" which was named after its mathematician inventor/discoverer Yoneda [1]

The character is the syllable "Yo" in Japanese katakana, and although not everyone knows katakana, still it is mnemonic for "Yoneda" rather than being wholly arbitrary. [2]

[1] https://en.wikipedia.org/wiki/Yoneda_lemma

[2] https://en.wikipedia.org/wiki/Yo_(kana)