Agreed.

> Mathematical concepts need not necessarily have any practical or real-life applications (pure mathematics), but it's a worthy pursuit on its own.

I guess I always had a sense that this was true, but taking a formal proofs class has really opened my eyes to how true this is. I'm actually planning on doing abstract algebra because I've enjoyed proof writing a ton!

> It's that they don't know where to look for the mathematics they need. Here is the failure of math education.

This is a really interesting space imo, because I did try teaching myself calculus through 3blue1brown, who has super cool visualizations, but also isn't rigorous enough to apply it to complicated problems. On the other end, I also tried Khan Academy, but found it too abstract and hard to follow.

Perhaps that was just since I was 14 at the time, and now I'm better at symbolic reasoning. Yet, there's something so enticing about visualization, that I wish there was a way to have the rigour of set theory with the intuitiveness of visualization (that call is a big reason I love the work that dynamicland.org and folk.computer are doing right now).