The thing is, APL was originally designed as programming notation. It was used by Kenneth E. Iverson to discuss programming problems on blackboards with his students for years before it had an actual implementation.

So it has much more in common with math notation as a result, which is why the focus is on expressing yourself tersely with symbols. Also: nobody has to worry about special keyboards with symbols when writing those symbols with chalk on a blackboard, right? So the medium shaped the mode of communication.

I wonder what it would be like to learn programming that way, without using a physical computer. Maybe it would actually be a lot more pleasant for working through programming problems together? Mathematicians seem to be doing just fine working out their problems together on the blackboard with their notation after all.

EDIT: Hah, just saw that elsewhere in the thread an actual mathematician laments the (ab)use of symbols in their field, so I guess I was wrong there. Well, in that case, maybe mathematicians and programmers (or at least language designers) should join forces and see if they can come up with a more ergonomic notation together. A new Bourbaki club, so to speak.