LLM's, the internet, even physical books all tend to deal primarily with subjective matters that can be plagiarized. They're not fundamentally different from each other; the more advanced technologies like search engines or LLM's simply make it easier to find relevant content that can be copied. They actually remove the need for students to think for themselves in a way calculators never did. LLM's just make it so easy to commit plagiarism that the system is starting to break down. Plagiarism was always a problem, but it used to be rare enough that the education system could sort-of tolerate it.
It pains me (though that's my problem) to see people pull out a calculator (worse, a phone) to solve e.g., a multiplication of two single digit numbers.
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.
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
Fluency in arithmetic isn't something drilled into kids just to be obnoxious, it's foundational to almost all future math skills.
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.
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).
Copyright protects specific expression, which reproducing is specifically a non goal with LLMs
Once they're done, they submit a one-pager on 3 to 5 subtle / smaller / things they find the most interesting or counter intuitive. At the end of the semester, I intend to share all their one-pagers among all of their classmates and keep an open-book test on it. Let's see how that pans out.