I recently embarked on a journey to come up with a math vocabulary for Toki Pona, a lovely little artistic conlang which deserves better than what I'm doing to it. In Toki Pona, words are build up from simpler ones to describe a thing as it is. A friend is 'jan pona', a person who is good (to me, the speaker). So I've had to come up with names which describe math topics.
It's awful.
You know how many same-xs there are?! Eigenvalue, eigenvector, homomorphism, isomorphism, homeomorphism, homotopic. Which one gets to actually be "same shape"? Worse are when well meaning mathematicians use descriptive names anyway. Open and closed are not mutually exclusive, giving rise to the awful clopen (and don't pretend like ajar helps. an ajar door is an open door!). Groups, rings, and fields all sort of bring to mind the objects they describe, but only after you know the archetypal examples. Math is the study of giving the same name to different things, and that gives rise to more names than there are short descriptions.
So do you know what I did? Whenever I could, I used a real person's name. It freed up a limited vocabulary, and gave enough wiggle room to translate most undergrad math without too much loss. I suspect a similar thing is in play with math. Maybe the category theory people have abstractions to usefully describe "same-functions" without confusion. But in general, things are named poorly because it's genuinely a hard task.
It's awful.
You know how many same-xs there are?! Eigenvalue, eigenvector, homomorphism, isomorphism, homeomorphism, homotopic. Which one gets to actually be "same shape"? Worse are when well meaning mathematicians use descriptive names anyway. Open and closed are not mutually exclusive, giving rise to the awful clopen (and don't pretend like ajar helps. an ajar door is an open door!). Groups, rings, and fields all sort of bring to mind the objects they describe, but only after you know the archetypal examples. Math is the study of giving the same name to different things, and that gives rise to more names than there are short descriptions.
So do you know what I did? Whenever I could, I used a real person's name. It freed up a limited vocabulary, and gave enough wiggle room to translate most undergrad math without too much loss. I suspect a similar thing is in play with math. Maybe the category theory people have abstractions to usefully describe "same-functions" without confusion. But in general, things are named poorly because it's genuinely a hard task.