It's wild to me that, of all the things to call LLMs out for, this piece has chosen to include math tutoring. I've been doing Math Academy for a bit over 6 months now, going from (essentially) Algebra II through Calc II (integration by parts, arc lengths, Taylor expansions) and LLMs have been a huge part of what has made that effective:

* Clear explanation of concepts that respond to questions and reformulate when things bounce

* Step-by-step verification of solutions, spotting exactly where calculations have gone

* Instantaneously generating new problem sets to reinforce concepts

LLMs are probably not going to live up to all sorts of claims their proponents make. But I don't think you can ever have tried to use an LLM in a math course and reach the conclusion that it's "demoware" for that application. At what point, over 6 months of continuous work, does it stop being a "demo"?

It's nice that you think it's clear and responsive, but I think it [1] needs to be validated by an expert in both the material and education. Or we need some way to show that people have actually learned the topic. People sometimes prefer explanations that are intuitive and familiar but not accurate.

Meanwhile, there are math education resources like iXL that maybe cost a little money but the lessons and practice problems are fully curated by human experts (AFAICT). I'm not saying these resources are perfect either, but as a mathematician who has experimented a lot with LLMs, including in supposed tutoring modes, they make a lot of mistakes and take a lot of shortcuts that should materially decrease their effectiveness as tutors.

[1] LLM-based tutoring (edit: footnote added to clarify)