I agree that mathematics should be taught in a 'larger context', but you have two problems - 1: even for a subset of math (take a fairly 'small' field that was

I agree that mathematics should be taught in a 'larger context', but you have two problems - 1: even for a subset of math (take a fairly 'small' field that was considered 'recreational' amongst mathematicians until recently - algebraic geometry) would end up filling up half all 4 walls of an elementary school room; b) a DAG is not the appropriate construct to capture entities (there is a lot of 'interop' both internally within a set of mathematics, and even more so as you go into the first rank poset containing that set; yet more as you go to rank 2)[1], c) most of those public school teachers wouldn't have the faintest what any of 80% of those nodes mean past "yeah, topology, I think I remember what a manifold is..." even if you kept the graph constrained to an 11x14 page of paper. I was fortunate enough to go to one of the those G20-esque schools[2] and by 10th grade I was asking questions that most of the instructors weren't capable of answering (and I'm not particularly bright - this a testament to those who tend to gravitate towards the profession). That being said, I was attending high school in the "we just got cable modems & youtube has 2 sets of lectures, one being Sussman teaching SICP" days. Those who are interested can easily find dozens of lectures from any conference/symposium/some-random-bright-grad-student-talking-to-a-room-of-8-people and then directly e-mail him/her. Knowledge is accessible really accessible these days, and those who are motivated to read further on a topic have high quality textbooks, pre-prints of papers, and open discussion amongst the communities (i.e., lurking on a Terry Tao project, or watching in real time as the classification of finite groups is underwent by a group of post-docs and grad students). For those who are motivated and learn by conversation/immersion like I do (did?). Perhaps this[3] explains my point a little clearer. (Note that Fermat has more than one proof, and I could easily at least the intuition behind the proof to a 2nd year undergraduate with no background in higher mathematics, given perhaps two semesters.) Conceptually, something like Poincare would be way more challenging just because at that phase everyone's used to Newtonian physics and Euclidian geometry; unteaching those 'intuitions' would take a semester alone. It could, however, be 'intuitively' (i.e., without rigor) taught fairly easily to someone with a background in higher level physics (i.e., most of the foundational maths of Riemannian geometry, etc, have been both taught and intuitively absorbed by students at that point). [1] https://www.youtube.com/watch?v=6oWLIVNI6VA https://www.youtube.com/watch?v=6oWLIVNI6VA Here's a lecture from a Princeton professor emeritus (IIRC) that demonstrates what I'm sure I poorly explained here. Introduction ends around ~6 minutes. [2] https://en.wikipedia.org/wiki/G20_Schools https://en.wikipedia.org/wiki/G20_Schools [3] https://jeremykun.com/2013/02/08/why-there-is-no-hitchhikers-guide-to-mathematics-for-programmers/ https://jeremykun.com/2013/02/08/why-there-is-no-hitchhikers... and in refutation - actually there is, sort of[4]. [4] https://en.wikipedia.org/wiki/Lists_of_mathematics_topics#Pure_mathematics https://en.wikipedia.org/wiki/Lists_of_mathematics_topics#Pu...