I don't know if I'd want Linear Algebra proofs - they tend to veer into results over vector fields rather than the more useful "solve Ax=b" and "here is how AI

I don't know if I'd want Linear Algebra proofs - they tend to veer into results over vector fields rather than the more useful "solve Ax=b" and "here is how AI works" parts (i.e we should teach real-world computational linear algebra rather than the pure parts of field). That said, I think proofs are an important thing we should teach in high school - its more a flavor of "real math", and logical thinking involved is a better transferrable skill than the symbol manipulation and bag-of-tricks-you-never-really-use-in-the-real-world you get from high school calculus courses. I'd just focus it on something easier to grasp, like basic number system construction.