In truth, middle-mathematics (undergrad university courses, henceforth lumped into the "calculus" umbrella) is a proxy for symbolic reasoning. The grungy part is looking at an arbitrary problem from your area of expertise, realizing that it's fundamentally a calculus problem, and then rephrasing it as a calculus problem and reinterpeting the solution back to your area of expertise. People have a hard time doing that if they aren't familiar with the actual nuts and bolts of calculus -- in my experience, every student that comes out of a "black box" course is entirely dependent on the specific tooling they were exposed to and typically has zero curiosity about what lies beneath -- those students tend to not get very far.

Likewise, we still teach bubble sort because it's an easy thing to teach rudimentary proof skills with. Similarly, we start students off with Newtonian physics.

Given GPT-3, should people spend less time learning to write?

> If a program can now solve these problems better than most people can, even after studying the relevant subjects, does that mean people should spend less time learning how to solve these problems?

This is a classic local-maximum situation. If you don't train people to solve problems as well as a low- or middle-competence program, then no-one is ever going to develop the expertise that will allow them to outperform the program.

I would say that people will be able to focus more on understanding fundamental concepts clearly and intuitively, rather than simply learning how to apply textbook math in a narrow and mechanical way. I believe AI will help people absorb new ideas, solidify their understanding, discover their own misconceptions, and help them solve their problems without getting bogged down in the details or derailed by small errors.