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Comment by bloppe | Hacker News Reader

Sure, calculators made people worse at mental arithmetic, but arithmetic is mechanical. It's helpful sometimes, but it's not intellectually stimulating and it doesn't require much intelligence. Mathematicians don't give a shit about arithmetic. They're busy thinking about much more important things.

Synthesizing an original thesis, like what people are supposed to do in writing essays, is totally different. It's a fundamental life skill people will need in all sorts of contexts, and using an LLM to do it for you takes away your intellectual agency in a way that using a calculator doesn't.

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Engineers care about arithmetic. Carpenters do too. Any number of other creative endeavors require (or, at least, are dramatically improved) by the ability to make basic calculations (even if approximate) quickly in your head.

Arithmetic is the "write one sentence" of composition. The ability to think through a series of calculations with real-world context and consequences is the 5-paragraph essay. If you're not competent with the basics, you won't be able to accomplish the more advanced skill. Being tied to a calculator (not merely using, but being unable to not use) takes away intellectual agency in the same way as an LLM-generated essay (though, I'll agree, to a lesser degree).

> Mathematicians don't give a shit about arithmetic

Sure, once you know how to multiply you don't care about it. But try learning first year CS math without being able to multiply without perfect command of the multiplication table

Exactly. My wife tutors kids at the high school who never mastered arithmetic and are trying to learn algebra. It's hopeless.

That was true before calculators too. Correlation, causation.

I'm not sure what you mean. These kids can't do arithmetic without a calculator. While it was possible to simply not learn arithmetic before calculators, it wasn't possible to hobble onward using the calculator as a crutch.

If those kids were truly applying themselves to the algebra, I think they'd quickly internalize arithmetic too as they used it. But whatever reason led those kids to not do arithmetic without a calculator could well be a reason they don't do well at more advanced math.

My point is failing to learn the basics is a huge hurdle to learning more advanced things. You posit that one could learn the basics and the advanced math at the same time. Maybe, but that would clearly be harder than doing them in order.

Fluency in arithmetic isn't something drilled into kids just to be obnoxious, it's foundational to almost all future math skills.

> They're busy thinking about much more important things.

Generally I agree (because the content of modern mathematics is largely abstract), but to nitpick a bit, number theory is part of mathematics too!

Ramanujan and Euler, for example, certainly cared a lot about 'arithmetic', and historically, many parts of mathematics have been just as 'empirical' in terms of calculating things as they've been based on abstract proof.

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