“If you encounter a mathematician at a conference, and ask them how their proof works, then they will almost always give you a clearer insight than what’s in the paper”

Adding to this, the valuable insight – the thing you can actually use in thinking – is the compressed form of the knowledge. You’re more likely to get that in a short in-person conversation. The author’s hand is almost forced. “Ah, yes, I basically just realized I could transform the problem using X, and then theorem Y would apply, and I could convert back and conclude Z” or whatever the case may be. The essence of an insight must end up being short like that, because we can’t “think” on the scale of 20 dense pages of equations. The elaboration is an expansion of the insight, rather than the other way around.

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