>>13951427Whenever I say we need to reform maths education, I always get a lot of people complaining about how introducing too many symbols and proofs will put kids off or whatever.
But I'm not arguing that. The issue is that we talk to kids about topics that are just a bit too high level for them to make relevant intuitive leaps of reasoning. Thus a lot of kids are left without a decent reasoning muscle.
That would be the only reason I would introduce say, set theory, group theory, logic or topology to kids. These come in with axioms, and encourage one to make those leaps of reasoning.
We can, of course avoid those altogether by working their reasoning muscles a lot earlier while they learn basic arithmetic and such.
That said: no I don't think there is too much reason to. There will always be people in those fields with mathematical interest who will drag that into their work. Theory driven people need to be counterbalanced by those who understand practice, and we put a lot of practical people off by forcing them to sit though too much theory.
Machine learning is going through the revolution from a practical field to a theoretical one. I sat through part of a lecture course by Jared Tanner this term, and honestly it just seemed impenetrable (even though I do practical ML in my spare time and am a logician/set theorist/topologist by day.) I can see why people get turned off by over theoretic courses in complex areas.
