[Reily]

All algebra is, is the manipulation of symbols to an end goal subject to a grammar (a body of logically consistent rules!). If you write computer programs you use an algebra. I argue also if you write grammatical sentences in a natural language you use an algebra. (Yes arithmetic is an "algebra"!)

You actually don't have to physically write anything down to do algebra, does Stephan Hawking write anything down? (Yes he uses algebra, the high school version as well as the other more abstract algebras.) I am sure he does some mental “algebra” to check his ideas before he communicates to his assistants.

[Chode]

i've been a programmer since 1981, but like i said, i guess i just don't know when i'm using algebra like i know when i'm using trig etc cause like you said, most of it's done in my head