Perhaps I Got Lucky Never Learning Math

This is an interesting post.

Teachers are often asked "why do I have to learn [this] when my calculator can do it?" or "why should I memorize [this] when I can just look it up online?" and now "why should I learn to reason through [this] if an LLM can just do it?". To respond to these questions some math teachers think quite hard about the purpose of learning mathematics (some just have a canned response). The consensus answer is something like: the topics themselves don't matter too much, but they serve as an instrument of becoming better at thinking logically, and becoming quantitatively savvy. Most students are not savvy. The author of this post appears to be an exception, probably becoming savvy as a child from all the unstructured activities they did while being home-schooled.

> What did I do with my time instead? … I took apart old computers and pieced them together to try and build something strong enough to emulate Super Smash Bros on the PC, and voraciously read vintage young adult fiction like Tom Swift or G.A. Henty novels.

> … if I ask my calculator the square root of 231, I also have no easy way to evaluate the output. I can sort of guess (10×10 is 100, 20×20 is 400, 15×15 is somewhere in the middle, so if the answer is 15-ish it's probably right), but I can also sort of guess at LLM outputs.

The standard mathematics education machine has no idea what to do with a student who is already savvy, capable of critically interpreting what the calculator/internet/LLM reports to them.

For the author, and for any other savvy folks, LLMs are a great new tool. I worry about everyone else who because they are not savvy, when they ask "why should I learn to reason through [this] if an LLM can just do it?" are quite happy to cognitively surrender to the tool, deferring their critical thought to the LLM, making it a crutch they now happily rely on.