If you want to be more pure, and consider the mathematical objects that are found rather than built, maybe the monster group? (As a layperson so I can’t appreciate the full extent of what’s going, on and like most people I only real know about it second-hand, but its existence seems like a crazy and beautiful fact about the world.)
Least favorite: I don’t know, maybe Chaitin’s constant?
Favorite: Irit Dinur’s PCP for constraint satisfaction. What a proof system.
If you want to be more pure, and consider the mathematical objects that are found rather than built, maybe the monster group? (As a layperson so I can’t appreciate the full extent of what’s going, on and like most people I only real know about it second-hand, but its existence seems like a crazy and beautiful fact about the world.)
Least favorite: I don’t know, maybe Chaitin’s constant?
I take it back, Chaitin’s constant is more cool than I thought.
I don’t like the cardinal ℵ1 very much, but I like 2ℵ0 just fine so it’s not really clear if it’s a problem with the object or the reference.
What changed your mind about Chaitin’s constant?
I hadn’t appreciated how hard and special it is to be algorithmically random.