True. Still, it seems archaic. I was never a fan of Axioms and
   Proofs generally speaking as it struck me as too legal a system.

   It works and it's useful and I wouldn't want it to go away, but
   I still like being able to backtrack at any point in time.

   In school, "Show your work" seemed a pointless exercise because
   all that _seemed_ to matter was the final answer, yet we'd get
   marked down for NOT showing work.

   Never made logical sense.

   But when I was learning BASIC on my little computer at home and
   had to use loops and such to do math, THEN I could _see_ the
   math working like a machine. I could see that squares were
   nested loops for example - and that's me at 11/12 yrs old, just
   before Pre Algebra - we were STILL at the end of basic
   arithmetic.

   By the time we started doing plug-and-play equations,, I hated
   eliminating x's and y's, a's and b's. Out of sight, out of mind.

   I wanted to trace back up the program to see what happened to
   them.

   So, in my mind, I had to do the work twice: translate the
   equation into a BASIC program, solve it, and THEN translate it
   BACK into the math language, and doing a "show my work" thing
   that would impress the teacher enough for my grade.

   So, I had a weird perspective on math. I learned programming
   before I learned proofs/axioms in Geometry in the 9th grade. By
   then, it was too late; my brain was fixed to thinking in
   programming loops rather than rules.