KevinSorboFan

Somewhat related... Braess's Paradox.

Take the toy example illustrating that paradox ( https://en.wikipedia.org/wiki/Braess%27s_paradox#Mathematica... ) and an enlightened Google maps may do the altruistic thing of telling half of the drivers to stick on the upper route and half of the drivers to stick to the bottom route, but then some 3rd-party app will come along with the "shortcut" down the middle.

The thing that puts Tao in that upper echelon of mathematicians is his ability to solve unsolved problems and create new mathematics. Those aren't really the skills being tested on a qualifying exam, and you're right that it's just a matter of being more well-read.

You can flip this argument around for the person buying the house, though, so it doesn't really work. What if the house didn't sell for $1m less? Then those new buyers just lost an extra $1m that they otherwise could have invested elsewhere in the economy. Or conversely, when the house sells for $1m less, you're freeing them up from that additional burden and they can put their next $1m into investments besides the house.

Coxeter groups are fun. I took it as a graduate course, but honestly you can get pretty far (and we did) just using elementary proof techniques that a 1st or 2nd year undergrad could handle.

I would recommend the book by Michael Davis for an in-depth dive: https://people.math.osu.edu/davis.12/davisbook.pdf