> Check out William Bricken's "Iconic Math" http://iconicmath.com/ http://iconicmath.com/ or "Proofs without Words" https://en.wikipedia.org/wiki/Proof_without_

> Check out William Bricken's "Iconic Math" http://iconicmath.com/ http://iconicmath.com/ or "Proofs without Words" https://en.wikipedia.org/wiki/Proof_without_words https://en.wikipedia.org/wiki/Proof_without_words or the other 3Blue1Brown videos for that matter. Yes, those references demonstrate that some mathematical facts can be demonstrated easily, given the right presentation. I agree that there is large gap between current mathematical presentations and the optimal presentation. I am curious how effective the optimal presentation is. How easy can we make math? We have to be careful of the trap that the 3b1b video warns us against - when we understand something it is very difficult to put yourself in the shoes of a beginner. Something that looks like an elegant and clear presentation may seem like gibberish to the beginner (look at the YouTube comments on the 3b1b video). I tried to google "Alan kay teaching calculus smalltalk" and didn't find anything. I am curious to see how much he actually taught the kids. It's clear that the typical college student, after taking a typical calculus class, doesn't really get the point of calculus. They may be able to follow some algorithms for differentiating and integrating but I don't think they understand when they can apply calculus.