Linear algebra, probability, and symbolic logic require significant prior work with math that high school students usually don't have exposure to. Getting them through arithmetic and algebra apparently presents enough problems.
40+ years ago in Australia I took the Year 11|12 (upper high school) stream that included calculus, probability, basic linear algebra and a wee bit of abstract algebra (groups, fields, rings).
The middle stream covered math for technical trades; serious electricians, woodworkers, metal workers, locomotive and heavy equipment engineers.
The basic stream was math for balancing budgets.
> math that high school students usually don't have exposure to.
My response is that myself and significant numbers of other high school students took math at levels sufficient to talk about LLM's + AI.
It's not for all high school students, which is why sensible high school curriculums aren't monolithic.
FWiW I didn't attend a fancy private school, just a regular public high school in a semi remote (at the time) part of Australia.
The OP asked about motivating students in high school math (country not specified) by teaching the math underlying LLMs. That assumes LLMs or "AI" look more interesting or relevant to high school students than the math they learn now. But they would still need a good grounding in algebra at minimum, and the average high school student in America barely gets through that, and with little motivation to continue studying math. So I don't think dangling LLMs in front of them will spark more interest.
Eg: at least one fellow high school student I studied calculus with now teaches machine learning and other math as a professor in a Canadian university.
My high school (in the US) offered programming classes that counted as math credits. Very few students took those classes, and quite a few students lost interest in the first few weeks. A handful of us had sufficient motivation to learn how to program, back when that was the next big thing (1970s).
The strategy in my state was to have a standard curriculum, on top of that all manner of things were tossed out to high school as bait to catch students with an aptitude or interest in languages, law, physics, chemistry, biology, applied trade skills, etc.
Can you motivate all high school students studying { X } with Y? - No.
Will that motivate some? Possibly - it's worth a shot.
I currently work part time as a teachers aid at an Australian rural school, I have a background in exploration geophysics (field work and coding aquisition, processing, interpretation suites for mag, grav, radiometrics), in computational symbolic algebra ( CAYLEY|MAGMA, being used to today to crack quantum encrypt candidates ), and general engineering (the nuts and bolts mech|civil type).
I talk to farm kids about drones, programming, multi spectral signal processing, ANOVA & sample crops, linear programming constraint optimisation and farm budgets.
And a slew of other things, I prep a few weeks in advance and CC my notes to others in ed chat groups. There's a strict regular curricula, I'm outside that in the "and also" after school activities.
Not all of them are into everything, a few of them at most will get into the nitty gritty, all of them can grasp how these things apply to modern agriculture.
Othe part time teachers aids include semi retired trades people that can and have fixed everything from locomotives, boom cranes, combine harvesters, screens, crushers, light aircraft, helicopters, etc.
It's been that way in this state for 50 odd years, my son went to a high school with an aviation program, they built and flew a plane over two years.
We also have sensible health care and a minimum wage that people can get by on without tips.
Now do all that at distances between several and dozens of AU [not that AU], and you get to call it Planetary Science...
It 'twas by pure chance I caught this reply; it was several pages back in a collapsed thread that I by chance caught an comment increment on
HN was never built for conversation over days and I have no addons to track replies (nor do I see myself using any.
Please forgive my hackers' instinct to use things despite (or maybe even in contradiction to) their final causes!
Derivatives are already motivated by geometry, physics, and optimization. Aren’t neural nets just another form of optimization?