Math is probably the subject least at risk. Every prospective engineer or scientist needs to learn a lot of math, and a significant fraction of those students will be unable to master the subject by simply watching videos. That means that there will always be a significant demand for real, live math teachers.
I'm not sure about that. Certainly the need to learn math will remain reasonably constant, but I think you underestimate the ability of technology. Once we get high quality explanations that remove most bugs before they form, and practice questions that expose problems quickly (it wouldn't be too difficult to design a program to choose which problems each student should be given), and some sort of weak siri-level AI that can watch the student working to discover what they understand ... when all that happens, the demand for maths teachers/tutors will be very low. I suspect that a single qualified teacher could service 400 students.
EDIT to add: the problem with human tutors is that they are inconvenient. It takes time to schedule a tutor, and you can only get help at certain times (that is, during the tutoring session). Human tutors have many advantages, but a program that is merely passable will nevertheless be immensely popular simply because it is convenient.
>Every prospective engineer or scientist needs to learn a lot of math, and a significant fraction of those students will be unable to master the subject by simply watching videos. //
One ordinarily learns the maths appropriate to ones course in that department which runs the course.
>$20/hr. math tutors fill the tables at my local public library. //
Do you mean your libraries have classrooms for private tuition? I'm not familiar with this sort of thing. In my country private tuition happens at the tutor or students house.
Nope, we have tables that fill the open spaces. These are first come, first served are available for tutors, project works or studying, or just general reading space.