I think there is also an argument for general numeracy as a life skill. Lots of people I run into just have no intuitive sense of how numbers work and how to calculate roughly.

The number of people that cannot calculate a tip in their head, or have a basic grasp of how interest works is constantly shocking to me. Yeah, we all carry calculators around, but you should be able to reason about numbers enough to know when an entry error has been made on a calculator

(Shrug) Every time a higher level of abstraction becomes available, a lower one loses importance. That's how it's worked for humanity since the dawn of recorded history. As others have pointed out, the ancient Greek scholars had the same baseless fears.

I don't think I've ever had to do polynomial division by hand. It comes up in control theory and a few other subfields, obviously including mathematics itself, but for me it's always been handled by software. It's safe to say that any given clanker will have better odds of doing it right than I will.

People love to cite the Phaedrus (although usually they just cite Plato) as a reason for why we should discard the warnings or fears about the cognitive effects of new technology as baseless.

But I think that this is foolish. Firstly, the fears weren't baseless! There's no question that the replacement of an oral culture by a literate culture meant the loss of certain cognitive skills for some people.

But more importantly, even if those fears were baseless, a fear in the past being baseless does not mean a similar one in the present is baseless. From our vantage point we can see the benefits of a literate society, but are we confident that what comes next will be as beneficial? Maybe it will be far more beneficial than literacy was, or maybe it will heighten inequalities to feudal levels. Either way, it's moving at a much more rapid pace than the spread of literacy, so we have much less time to reflect. It pays to be prudent here.

The point I tried to make wasn't that we still need to be able to do everything by hand. My point is more that we need to develop our brains. And for that we need training excercises. Similar to excercises in the gym. I doubt anybody encountered a barbell in real life outside the gym. Yet it is good tool to develop muscles. Math is an excellent tool to develop certain aspects of the brain.