I don’t think this is a fair comparison because arithmetic is a very small and almost inconsequential skill to develop within the framework of mathematics. Any human that doesn’t have severe learning disabilities will be able to develop a sufficient baseline of arithmetic skills.

The really useful aspects of math are things like how to think quantitatively. How to formulate a problem mathematically. How to manipulate mathematical expressions in order to reach a solution. For the most part these are not things that calculators do for you. In some cases reaching for a calculator may actually be a distraction from making real progress on the problem. In other cases calculators can be a useful tool for learning and building your intuition - graphing calculators are especially useful for this.

The difference with LLMs is that we are being led to believe that LLMs are sufficient to solve your problems for you, from start to finish. In the past students who develop a reflex to reach for a calculator when they don’t know how to solve a problem were thwarted by the fact that the calculator won’t actually solve it for them. Nowadays students develop that reflex and reach for an LLM instead, and now they can walk away with the belief that the LLM is really solving their problems, which creates both a dependency and a misunderstanding of what LLMs are really suited to do for them.

I’d be a lot less bothered if LLMs were made to provide guidance to students, a la the Socratic method: posing leading questions to the students and helping them to think along the right tracks. That might also help mitigate the fact that LLMs don’t reliably know the answers: if the user is presented with a leading question instead of an answer then they’re still left with the responsibility of investigating and validating.

But that doesn’t leave users with a sense of immediate gratification which makes it less marketable and therefore less opportunity to profit…