BetterExplained: Clear, intuitive lessons about mathematics

Is there a way to save comments on HN? This is worthy of a save.

Second this. I’m working on a set of ideas about how best to enable arbitrary learning trajectories through a knowledge graph — partly in an effort to better capture my own learning in mathematical topics. I liked how Quantum Country integrated spaced repetition into its presentation of quantum computing, but I think you could go further and structure all knowledge you wish to communicate in a graph form. There are so many reasons to do this: it’s a graph in your head anyway, and if a machine can track and manage that graph it can better help you navigate it in a learning-optimal way. Just try reading some math on wikipedia and you’ll see where this could really shine. Currently it’s a frustrating experience because there are many slices of information that you might benefit from when you are looking up eg the article on distributive lattices, but the optimal slice to see depends on what examples you’ve encountered, what other topics are fresh in your mind, and what your short term goals are. Of course a textbook is a particular curated walk through this graph, but people are different, and there is no walk that is optimal for all people. A dedicated expert teacher can curate a path specifically for a learner, but almost no one can afford to employ such a teacher for them. If machines can handle the UX aspects of this graph-walking and graph-building for us (there are many simple ideas that fit into this), I believe we could have a real step change in learning efficiency with only modest investments in building such graphs. And the truth is, such graphs are actually fun to build because they are so interactive! It’s very similar to the semantic web, but catering specificity to humans and their idiosyncratic educational needs rather than to more nebulous things about machine reasoning or scripting.

Is there good material that covers advanced mathematics, ie, after multi variable calculus and algebra, but not primarily about proofs?

patrickJMT is really great. I remember frequenting his channel when I was taking some math courses in college.

So much good stuff in one post. I'm gonna go on a huge tangent bro!

I never loved Mathematics in high school, at least not the way we learn a bunch of things but never apply them or have any intuition about them, but I'm interested in it on personal level.

This is right up my alley.

Edit: forgot to say thank you!

You could buy his books on Amazon and gift them to curious people ?

Glad the site was helpful! Helping spread the word with people it could help (educators, students, curious autodidacts) is great. There are BetterExplained books/courses you can get as quick stocking stuffers, though helping support local businesses now may be even better :).

It is a good article, but actually it skipped the hard part.

Hey Chris, thanks for the support! =)

I got that same result from the book Visual Complex Analysis. In retrospect it seems stupid, but until then I actually believed, to the extent I considered it at all, that it was just a happy coincidence that e^x is its own first derivative.