On another note, I was shocked to find that some members of my family have aphantasia which is a complete inability to visually imagine geometric figures or pictures, and yet, they were good at math. So, there are faculties beyond visual imagination which are invoked, and even within visual imagination, there is a spectrum among people as to its strength, and quality.

[1] https://www.amazon.com/Mathematica-Secret-World-Intuition-Cu...

For the more geometry-based ones where you have move triangles around and so, it's often not obvious to me that two angles that look the same really always are the same, and that things that add up to rectangle do so reliably, independently of the actual angles used in the examples.

I guess in these cases, a more parameterized, interactive version would work better, where you can use sliders to adjust some of the angles and lengths used. That should make it much more obvious that it's not just an artifact of particular angles used in an example.

On the linked page, a lot of the proofs are essentially proofs by induction that stop at some (pretty small) n. Maybe there’s a way to make it rigorous by visually showing the induction step that proves n+1 given n, but if there is, it’s not shown.

This can be great for building intuition for a statement known to be true by other means, but I wouldn’t consider them to be proofs.

- The game of life

- The fractran language (a Turing-complete programming language consisting only of fractions)

- Surreal numbers

- The “Conway base 13 function” (a brain-scramblingly hideous function that is everywhere discontinuous and yet somehow takes on every real number on every interval - invented as an analysis counterexample to prove that a function can satisfy the intermediate value property and yet not be continuous).

- A lot of work on sporadic simple groups. The three groups Co1, Co2 and Co3 are named after John H. Conway, and he was co-author of the “Monstrous Moonshine” paper and conjecture that Richard Borcherds won the Fields medal for proving.

… and a bunch of other whacky stuff, such as inventing an algorithm to figure out what day of the week any given date in history was (he used to do this in his head)

Sadly he died of complications from Covid. https://en.wikipedia.org/wiki/John_Horton_Conway