Math student Ken Iverson being annoyed at the inconsistency of math notation and its precedence rules decided to come up with a better one. "Iverson notation" or "the notation", he went through Harvard and became Dr Iverson, got picked up by Adin Falkoff at IBM when they were designing the IBM/360 processor and adapted the notation for the blueprints of how the thing would work, and then got rid of superscripts and subscripts and cut it down a little so it could become a line-based executable thing to run on an IBM/360 as a kind of matrix-aware desktop calculator / "A Programming Language" (APL). IBM made custom Selectric/golf-ball printer heads and keyboard overlays for it.
An APL keyboard typically wasn't exactly a custom keyboard, but a standard keyboard with APL characters accessible through modifier keys. Often there were adhesive labels on the front of each key showing the special characters or you could get custom keycaps that had the special characters printed on the front. And of course many of the special characters were created through overstrike rather than separate keys. Way back, I programmed in APL on a DECWriter that had support for APL characters.
I have a keycaps set imitating the classic Space Cadet keyboard (from Symbolics Lisp workstations). The Space Cadet had APL tops and fronts [1], but these caps only have the tops presumably because the cost to get keycaps printed on the fronts would be way too high. Frustrating though. I've thought about getting the rest printed on clear plastic adhesive.