Strongly agree with the second point, that visualization is used not as a tool for understanding but for confirming, whereas it should be vice versa. It remind

Strongly agree with the second point, that visualization is used not as a tool for understanding but for confirming, whereas it should be vice versa. It reminds me of a thread on MathOverflow (the StackExchange for professional mathematicians) asking for proofs without words (which tends to fall in the category of "visual" proofs: the second most-voted answer is "because I think proof by picture is potentially dangerous, I'll present a link to the standard proof that 32.5 = 31.5". Link: https://mathoverflow.net/a/17347 https://mathoverflow.net/a/17347