Earlier quoted context omitted.
> and I just derive the thing instead of remembering or looking it up. Most people can't do this or have a very hard time learning much easier things. I find that the crowd that talks about "pointless learning/testing/education" are often either ones that struggled mightily and were never really that smart, or they are so smart that they are above it.
I guess then the point becomes - in the age of computers, what's the value in memorising the quadratic formula without understanding where it comes from? It's much more important to know that there is a quadratic formula, or more fundamentally that every quadratic equation has 0-2 roots (exactly 2 if dealing with complex numbers) and what the different cases loom like (does the parabola touch or intersect the x-axis?…
The importance has always been "how its applied." Tons of people failed classes despite knowing the formula. It has always been about the basic application.
I don't think many math tests consisted of "write down the quadratic formula" and that's it.