Agree that math on its own isn’t the truly compelling thing for everyone. I do believe that, since it fundamentally links and describes all sorts of observable

Agree that math on its own isn’t the truly compelling thing for everyone. I do believe that, since it fundamentally links and describes all sorts of observable phenomena, math is a gateway to a general understanding of the universe. And so might lead someone to their true passion. I also hear you on the “binary tree” front - focusing exclusively on particular algorithms like that is a hiring antipattern, imo. Where I differ is that I treat math as one level lower and more fundamental - the ability to understand why the algorithm works at all and to prove it to yourself if you wanted to. And correspondingly the toolset to construct algorithms of your own. I don’t think people need to readily recall partial differential equations on a daily basis, or be able to spot recall how to factor a complex polynomial. I do think taking practice at those things builds mental strength that is useful for detecting patterns, chasing theories, describing and testing facts, and solving puzzles, and that that’s the true value of math education.