Reading Messy Proofs

In fall of 1985 when I started graduate school, my advisor Michael Sipser asked me to read an early handwritten manuscript by Johan Håstad of his switching lemma. I spent many hours decoding the notation and working through the messy conditional probabilities until I felt I had checked every step of the proof. When I started presenting this to Sipser, he stopped me and said he didn't want the details but instead the intuition of the proof. I had nothing. I'm reminded of this story as I hear the complaints of how badly OpenAI wrote the 712 papers released on October 6th, as though humans wrote crystal-clear proofs beforehand, definitely not the case in general, especially in the early versions. Noam Nisan once told me that reading a badly written proof leads to better understanding since you really need to figure out the details instead of having them neatly spelled out. Perhaps, but do not use this as an excuse for not taking the time to write the details properly. I approach reading…