I went through EE using an HP 49G+ and continue to this day using RPN in Emacs calc-mode.
>> I find it nearly impossible to parse this without actually maintaining the stack in my mind.
> You compute the problem going from smaller units to larger units getting intermediate results as you go and combining them
That's totally it. I've tried doing infix/standard algebraic notation on a calculator and unless the screen is big enough to see all of your brackets you're almost certainly going to screw up one of the big terms in a fraction or something like that. I think a good different way of stating the "intermediate results" part is that instead of computing the solution from left to right you're computing the solution from the inside-out.
By far the most satisfying part of doing computation in RPN is that moment at the end when you've got a big stack full of intermediate results and you just do that "+ + + + +" to add them all up and bam! Answer!
Edit: I had two thoughts back-to-back after writing that.
First thought: I do actually struggle sometimes with doing math in Lisp because prefix notation isn't a way that I'm used to doing math. Which led to "Hmmm... what if you did Lisp but with postfix notation instead of prefix notation"
Second though: "Ohhh... that's Forth. And you don't need brackets at all..."