Don't forget: SaveTheInternet actually TOLD people that they are sending emails to TRAI. Facebook did not even do that! Which is why the Advertising Standards Council is investigating FB's campaign.
> when most mathematicians look at a set of abstract symbols they don't "see" the symbols per se, they see what those symbols are meant to represent.
Might we benefit from a different set of symbols that actually convey the geometrical meaning behind them? If instead of π, we used a glyph that shows a circle over a diameter, instead of x for a variable, we show an empty rectangle that shows that it's a placeholder for a value?
> Students who said the answer was 44, how did the students who said 26 arrive at their answer?
I came across a great example of this approach in Chess: The Complete Self-Tutor by Edward Lasker. Instead of just showing the right answer for a chess puzzle, he tells you what you did right in your answer and what you missed in getting an even better answer. This was a printed book that was completely interactive.
The way I read the essay, it seems to me that math is compatible with [1]. You don't have to follow any given rules. Make up your own ideas and see what they lead to. What if square roots of negative numbers exist? What if the sum of angles of a triangle is not 180 degrees? What if a proposition can be both true and false at the same time?