So it was originally designed by a Harvard Math professor (Kenneth Iverson) as just that. A new mathematical notation to write down. He didn't get tenure (although later got the Turing award for some of that work) so he went to IBM and they actually implemented it. Aaron Hsu has done some blog posts on how he sometimes code using a nice calligraphic pen and paper with APL.

https://www.sacrideo.us/paper-is-dead-long-live-paper-progra...