[stefco_]

> Progress in math often (or usually) isn’t driven by physical problems

This is true at the largest scale, but the math classes that most people take are directly applicable to (and often were developed partly to solve) physical problems. I, too, found the high school presentation of math dry and boring until I took a good physics class, and I was amazed by how much of the math I learned was directly useful for that subject.

Unfortunately, the dry treatment math gets in high schools also usually fails to highlight the beauty and subtlety of pure math. I didn't realize how much I loved pure math until I took my first proof-based analysis class after junior year of college.

I think we're seriously failing both the applied and pure camps of students with the way we currently present math. The fact that it took me till nearly the end of college to really like it, despite my proclivity towards the abstract and technical, really drove this point home for me.

[Retric]

Practical does not mean interesting. A lot of math is based around accounting and taxes.

How big is this field and how do I split it evenly into N pieces. That’s more or less why Geometry was considered foundational for so long. Carpenters are often used as examples, but they generally avoid anything mathematically complicated instead using simple rules.

[hyperpallium]

> failing both the applied and pure camps

Yes. Neither its use nor truth. Just a bunch of stuff to learn.

Much less could be covered if driven by applications/problems or from axioms, and the rest of the math ecosystem is built around it. So, hard to change.