I love that "system 1" and "system 2" are tossed out as fundamental concepts of mind when they're basically labels for some semi-random ideas based on bullshit studies in a pop sci fluff book. Is there any actual science that ties these ideas to mathematical reasoning?
Then we have:
>> By analogy, we can now state the main hypothesis proposed in this paper: a crucial component of the usefulness of a new proven theorem t (in the context of previous theorems T(S)) is how efficiently T(S)∪{t} compresses the set of all provable mathematical statements M. That is, T (S) ∪ {t} is a good compression of M if many provable statements, beyond those in S, can be derived from T (S) ∪ {t}, say using at most k derivation steps.
which says "Occam's Razor, that's good isn't it?" in more words.
Then we have:
>> By analogy, we can now state the main hypothesis proposed in this paper: a crucial component of the usefulness of a new proven theorem t (in the context of previous theorems T(S)) is how efficiently T(S)∪{t} compresses the set of all provable mathematical statements M. That is, T (S) ∪ {t} is a good compression of M if many provable statements, beyond those in S, can be derived from T (S) ∪ {t}, say using at most k derivation steps.
which says "Occam's Razor, that's good isn't it?" in more words.