> They were right, though.

They were not. I'm not dead yet so I suppose there's still a chance, but so far in decades of living life I've always had calculators when I've needed them.

> For one, you still need to now what kind of equation to put into the calculator.

That's a very different construct. Math concepts don't care how the arithmetic is performed.

> If you don't know the concepts, what are you going to calculate.

If you don't know the concepts, then what kind of arithmetic are you going to perform with anything -- whether the mind's eye, pencil and paper, a sliderule, or a pocket supercomputer?