An easily understood proof of Cantor’s Theorem: http://www.mathacademy.com/pr/prime/articles/cantor_theorem/...

"Take a minute to ponder what this means. Cantor’s Theorem shows that given any set, there is another set which is 'larger' in the special sense of being a bigger kind of infinity. Hence, there can be no 'largest infinity' either! The kinds of infinity are therefore 'infinite!"

Infinity is thus far the most violent idea humanity has come up with.

I really like the first paragraph of this article, but at this point:

"Art starts to happen when we project these personal maps back out on the world. Each of us has an impulse to express his or her experience of reality."

He lost me. This is the kind of formulaic definition of art you hear all too often. The reason art isn't math is that there is no such formula. Art is contradicts itself. It's messy and evades attempts to pin it down.

Self-expression, pursuit of aesthetic ideal and refinement of craft are three distinct though frequently overlapping pursuits all called 'art'. The problem with definitions of art is that they usually fail to address the polysemy of the word.

This is kinda cool but the pictures are the standard interpretations of what mathematicians imagine. I would have liked to see some non-standard approach with a bit more abstraction.

I don't know about the "standard interpretation"... the first picture is usually expressed with all of the "squares" of equal size (it's a matrix), and an "x" through each digit at (x_n, y_n), n being positive integers.

Some of them are pretty standard but, IMHO, for most of them he struck a nice balance between the standard and artistic interpretation.