Teach category theory, and if you can't, then don't bother teaching math at all.
Because you'll be teaching the awful wasteful rote math that everyone hates and can't use, instead of the nice universal stuff that lets you transfer intuition and see how ideas communicate between different knowledge domains far beyond what was traditionally seen as math.
The 20th century gave us real new ideas in math. But our primary math education is still 200 years out of date. Until that changes, math education will remain a deadening cargo cult that throws away far more human potential than it develops.
The rote stuff’s about all I’ve ever actually managed to find a use for, as an adult.
It’s useful daily. Pre-algebra is useful fairly often (even if I weren’t a programmer, plugging numbers into a formulas and basic graphing are very handy, quite often). Trig I think I managed to use once, but only because I didn’t know the right way (if you find yourself using trig on a minor home project you’re probably missing some trick or standard or something that lets you not do that—I suspect it was the case then)
That’s… about it. Stats, kinda, but mostly looking up the formula for the thing I want and plugging in the numbers, which barely counts.
Out of curiosity as an adult how much category theory have you learned? Why aren't you doing more to find applications for the complex and abstract math? Don't you feel a duty and skill to advanced the state of play? Don't you feel an inherent gift and ability to do so? Why or why not?
My feeling is that we're producing graduates who don't understand abstract math or how to turn it into value in the real world. Category theory would only provide the abstraction part. I think we'd still have to work hard to instill the duty to translate abstract math into real human values. That's why we got to teach both the abstraction and the translation to people at a very early age. Otherwise they will simply never do it for themselves.
> Out of curiosity as an adult how much category theory have you learned? Why aren't you doing more to find applications for the complex and abstract math? Don't you feel a duty and skill to advanced the state of play? Don't you feel an inherent gift and ability to do so? Why or why not?
I don’t enjoy math as a hobby (recreational math puzzles can be fun, but may as well just be Sudoku—I don’t like doing real math as a hobby). I feel dyslexic reading proofs and formulas—algorithms feel natural, I have to translate everything into those to make any sense of it and that’s painfully tedious.
The jobs I’ve had have never really needed it. I’ve seen people who go casting about for reasons to MATH mostly be frustrated and make things worse. Maybe like once every five years I’ve seen something come along that benefits from some not very advanced college level math and everyone in the team gets a little thrill that we have an excuse to use any of that even a very little bit for a day or two, and that’s that.
I’ve been measured in the top 1% of spatial reasoning ability which you’d think would make me suited to math, but I kinda hate it and don’t actually seem to have a knack for it, so instead I use that ability to skate by doing pretty damn OK for myself but without seeking out reasons to use math more—and, for something allegedly so ultra-useful, such reasons rarely manifest on their own. I dunno, show me the job and a big raise first and I might brush back up, but I’m not gonna do something I find about as fun as pulling floor staples simply out of some sense of duty (duty to… do what? Do more math? Why? I want the motivation first, I’m not interested in forcing it)
True that! LA is probably the most "powerful" math tooling available to UGRAD students. Speaking from my own experience, I survived a degree in ENG, PHYS, and CS
coasting just on my knowledge of linear algebra. It's like the rosetta stone of math concepts...
Is this comment still taking into account all the ~8 yr old common core changes to math curricula around the country? Even that's 200 years out of date? What're we supposed to be doing with five year olds that's so much better?
Common core has a lot of potentially useful stuff for learning basic math in an intuitive and fun way. But the math it teaches to a 8 year old is never under 2000 years old.
We could be teaching 8 year olds how to use crayon drawings to solve differential equations, graphically analyze back propagation, analyze electronic circuits, and validate quantum teleportation protocols. This stuff is fun and relevant to understanding the technological world all around us.
It would be about as easy and fun as common core. We have a lot of new math from just the last 15 years that shows us how to present these really complicated subjects in a simple way by doodling diagrams that are so simple that even a kid could learn it.
For an example, look up "Kindergarten Quantum Mechanics" by Abramsky and Coecke. They only joke about teaching it to kids. But I think that kind of stuff is definitely how we'll teach our kids 100 years from now, when quantum computers might be important for even kids to understand.
Because you'll be teaching the awful wasteful rote math that everyone hates and can't use, instead of the nice universal stuff that lets you transfer intuition and see how ideas communicate between different knowledge domains far beyond what was traditionally seen as math.
The 20th century gave us real new ideas in math. But our primary math education is still 200 years out of date. Until that changes, math education will remain a deadening cargo cult that throws away far more human potential than it develops.