If you all can forgive the plug, here is another difficulty facing self-taught recreational mathematicians
In short, math as a field is (a) not a (one) field, (b) extremely non-linear, and © deriving most of its power from its incestuousness. If you learn math in school my understanding is that you’re just expected to slog through most of the major fields with a, or many, bottles of whisky and helpful tutors until you get basic competency. If you’re doing it on you’re own you, essentially, still have to do this and will suffer a bit of “missing the inside jokes” until you get your head around a sufficient basis set of skills.
In a real sense programming is nice because you spend some time learning different applications and languages and ideas and it all feels like it’s growing this core skill of programming which is highly translational. Math is kind of the same except that it’s presented much more like taking an intensive course in graphics programming and then another one in real-time robotics control and stepping back and saying that the core skill you’re growing is just basic programming sanity. This is right, and the saner you get the more you start to realize that the both of these might as well just be an application of linear algebra, but it can take a bit more patience than what meets the eye.
Math is big. Really big. You just won’t believe how vastly, hugely, mind-bogglingly big it is.
Fortunately, the part of it we’ve discovered so far is quite small; you could learn it all in probably less than 1024 lifetimes.
I had a bizarre idea a while ago. When I try to self-teach myself mathematical subjects using Wikipedia and other online resources, it’s a serious problem that the page about the concept I’m interested in has dozens of transitive dependencies on other mathematical concepts. Many of the other concepts are already familiar to me, and many are not, and it’s overwhelming to sort through things. Of course, textbooks and planned curricula work around this, but that’s really not an ideal learning style for me…
If someone feels like making this work, go for it. I think it’s a relatively silly idea, but personally I’d probably use it.
Scrape the relevant portion of the Wikipedia link graph to figure out conceptual dependencies among areas of mathematics. It probably makes sense to ignore links outside the first couple paragraphs, and to have a manual cleanup process to resolve cycles.
It definitely makes more sense to use the Mathematics Subject Classification as the backbone for what nodes to include, using the Wiki data only for the edges, but that does involve building a mapping between the two.
With the data collected, build a UI that will let you pick what you want to learn about and present either the concept DAG, or a topologically sorted list based on it. For bonus points, let the reader click to assert they already know something, to simplify their view.
As a freebie, make each item in the to-learn list go to a Google search identifying reading material about it.
Could you (or anyone else) point me to resources to getting toddlers started with math concepts? I’ve been trying youtube, but have not found anything satisfactory.
I’d recommend a Montessori school. Done properly, it has manipulatives (ie physical toys) that have proven to be very good at that.