> E.g. I'm sure we are generally less skilled in mental arithmetic since the advent of the calculator, but it has allowed us to solve vastly more complex problems in the end.

This is like saying we have been getting a lot worse at walking since the advent of the car but it has allowed us to practice global trade in the end.

Yes cars are a part of the solution but there are a lot more factors at play.

A calculator does not do math, a calculator (and computer) calculates or computes. The math is the study and understanding of the problem space (and the problem solving) that the human is doing behind the calculator.

"solve vastly more complex problems" the calculator has accelerated this but it is not really a cause effect relation. The advancements in the understanding of the complex problems could've also happened without calculators and the computation could have been done instead (for example) with 1000 people in a bunker.