[BlackFingolfin]

I am a research mathematician. In my field (abstract algebra, computational group theory), a sum or some such notation is like the most trivial of trivial things in terms of notation. There are a few things like sums that could in theory be made to "look more like what a computer programmer would expect", but that'd be just a tiny corner of it.

And if you think about how summation would look in Lisp or APL (which some smart people use to this day), I am not even convinced your argument for the "sum function" notation being superior holds in general.

[umvi]

yeah you'd have to make a "mathematical grammar" to cover all the cases. one problem with current mathematical notation is that it is optimized for writing by hand, not with keyboards. If you want to write mathematical notation with keyboards you have to use a complex typesetting tool like LaTeX to position all the super/sub-scripted, nested, etc. symbols.

And it all seems arbitrary anyway. Why are trigonometric functions written in english ("tan" being short for "tangent") but other stuff uses greek letters and other stuff still uses esoteric/abstract symbols? Why is the integral symbol shaped the way it is, and why use super/sub symbols for the bounds versus `integral [0,Inf] ...`?

In my ignorance, I'm assuming math is the way that it is because that's the way it's been for centuries, and messing with it harms its ubiquity. Math notation is not the way that it is because it's particularly well thought out. It's centuries of legacy tech debt that can't be changed. Kind of like how English is a crappy language in a lot of ways, but we can't change it now because too many people use it and you'd never get enough momentum to switch.