[dhash]

Iverson notation originated from APL, which was itself born out of the horror that Iverson saw when presented with "standard mathematical notation". Its use of strange, otherwise cryptic notation was influenced by two main themes: it was originally designed on a blackboard, so strange glyphs were normal, and a desire to become unmoored from "standard mathematical notation" in order to strengthen principle 1. of OP - Unambiguity. Casting off historic baggage and canonicalizing mathematical notation under the principles of OP was APL's prime goal, and it does a damn good job of it.

I wish they taught it to math majors.

APL's a wonderful rabbit hole to fall down, and J was my eso-lang of choice last year.