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Is ZF set theory a hack?
Raph links to some discussion whether ZF set theory is a hack. The up shot is that all the different proposed formulations for the foundations of mathematics are several times as large as you would expect.
I've long thought that the one true criterion for acceptability of a basis of mathematics was its intuitive acceptability to a human. Unfortunately there is a long history of humans, including professional logicians, forming bases which later turned out to be inconsistent. Now we know that our intuitions about what is simple are also completely wrong.
Perhaps instead of judging based on untuitive acceptability, a fundamentally subjective and poorly defined criterion, we should instead judge based on number of symbols in representation. That at least is a well-defined and measurable concept. Maybe its possible to make a basis which is based on much more abstract concepts even than set, which requires some work to build even our most basic intuitive concepts, but is much simpler at core.
Formulating a better foundation of mathematics may also help with computer proving. Perhaps we are crippling our theorem provers by forcing them to view mathematics through the lens of human intuition due to our selection of an extremely cumbersome set of base axioms.
clickmazes.com is cool.
I came up with some interesting twisty puzzle ideas.
Smith numbers raise some interesting philosophical questions.
Jumping champions are neat.