During a recent discussion it occurred to me that mathematical notation is a never-ending quest for symbolic density. We add superscripts, subscripts, overlines, underlines, special fonts, special characters, and if we’re desperate even images. But the world has recently moved on to using high-density symbols throughout written communication!
Emojis. We should use emojis in math. Yes, I’m serious.
The only problem I can see is that unlike mathematical symbols which are highly abstract, emojis have visceral, concrete meaning. But honestly that may be an advantage! Many symbols in math are meant to immediate “gut meaning” but it’s just difficult to convey to the reader in such a limited medium. I’ll think more about this and see if I can put together an exmaple of some kind. I think differential geometry or algebraic geometry both quickly run into the requisite symbol complexity.