> There are so many _symbols_ used in mathematics. It's all as if they're spells written by wizened greybeard wizards and passed down to apprentices throughout the centuries.
Think of it as jumping into a new codebase you have never worked with before. It is full of strange functions calling each other for unknown reasons. It takes a while to get a good intuition for why.
M/L could be written Field-extension(M, L). That might make it easier to Google what's going on, rather than having to pick up a group theory book. And indeed in this case it would be extra helpful, because M/L could also mean "quotient group" or even "division" depending on the type of the objects M and L. I personally prefer M:L for field extensions.
But Googling individual concepts is hardly a good way to learn group theory. So I don't think it matters too much. For anyone that spends enough time working in the given field, the notation is by far the easiest thing to figure out.
In general it is nice that mathematics - still being largely a handwritten endeavor - has the freedom to introduce new notation where it makes sense.
See https://mathoverflow.net/questions/42929/suggestions-for-goo... for cool examples of new notation improving the lives of everyone.
Think of it as jumping into a new codebase you have never worked with before. It is full of strange functions calling each other for unknown reasons. It takes a while to get a good intuition for why.
M/L could be written Field-extension(M, L). That might make it easier to Google what's going on, rather than having to pick up a group theory book. And indeed in this case it would be extra helpful, because M/L could also mean "quotient group" or even "division" depending on the type of the objects M and L. I personally prefer M:L for field extensions.
But Googling individual concepts is hardly a good way to learn group theory. So I don't think it matters too much. For anyone that spends enough time working in the given field, the notation is by far the easiest thing to figure out.
In general it is nice that mathematics - still being largely a handwritten endeavor - has the freedom to introduce new notation where it makes sense. See https://mathoverflow.net/questions/42929/suggestions-for-goo... for cool examples of new notation improving the lives of everyone.