I think what I appreciate most are the smaller notes, that probably don't represent a publishable result in any way.

There was one where he describes a problem that he had seen in an elementary school -- find a fraction between a/b and c/d. Everyone he talked to had the same basic answer; find a common denominator, find the midpoint, and if necessary, double the denominator. So 2/3 and 3/4 -> 8/12 and 9/12 -> 16/24 & 18/24 -> 17/24. And to him it was immediately obvious that a better answer is just (a+c)/(b+d), which he immediately intuited but then set out to make a better proof for.