[goku12]

> I'm actually planning on doing abstract algebra because I've enjoyed proof writing a ton!

That's interesting! I started with abstract algebra (on my own) because I don't know the proper sequence of learning it. I guess I will give proofs a try now.

> 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.

> I wish there was a way to have the rigour of set theory with the intuitiveness of visualization

Agreed! Intuition and rigour are equally important in Mathematics. The hardest part is making these two meet at some point.

One such moment in my life was when I created a visual model of 3D vector calculus (divergence, curl, gradient, etc) and developed it far enough to explain all its rigourous treatment that I learned in my engineering class. Things just flowed from there. I suddenly gained the superpower to imagine up the explanations for phenomena like the skin effect, and then effortlessly derive their mathematical models.