I was talking to a group of 7th/8th grade students the other day. I forget what they were initially talking about but had veered into the topic of how much computers had changed. They had a hard time believing how much computers had changed. She called me in to kinda verify the point.
Your smartphone may not run circles around mainframes but they certainly run circles around the Apple I/II and similar models.
Fast forward a few years, I was in grad school taking a course titled "Sintering and Diffusion in Binary Metal Oxides".
The professor came into class one day wearing a huge grin; he had discovered an error in a colleague's published paper (no love lost between them I believe). He offered to replace one of the class's four exams if we could find the error and recalculate the data table.
Finding the error was a simple collaborative effort, but the formula for the table was HUGE. Doing hand calculations would have taken hours (more like days), so I was determined to use computing devices to ease my task.
1) I started on a line-printer terminal hooked to the IBM 360 running BASIC. No longer remember the problem, but gave up after a few hours and switched to the . . .
2) WANG calculator. This was a device midway between a microwave oven and washing machine in size with vertical columns of digits that could be illuminated growing out of the top. The WANG was overwhelmed before I had keyed in a fourth of the problem so . . .
3) TI 52 to the rescue. A friend had a brand spanking new Texas Instrument programmable calculator, which had an amazing 224 program steps available. An hour later, I had keyed in half the program, but had exhausted all 224 available steps. I was at the point of throwing in the towel and resigning myself to a week of hand crunching numbers when my brother offered his new toy . . .
4) HP 33 calculator. I scoffed at first because it boasted a measly 49 program steps and 8 memory registers, but my brother assured me the reverse Polish notation used by the HP made it far more step efficient.
He was right. By using all 49 steps and 8 memory registers and doing one step by hand, I was able to run the table in about an hour.
I have been sold on RPN calculators ever since.
Long story, and not sure how relevant it is, but your comment made me think of it.
EDIT: Thinking about it, I believe the problem with the BASIC terminal was the lack of pre-defined functions. I could have done better with FORTRAN but that would have required generating a (shudder) punch card stack.