I happen to think that novel facts and theorems and proofs are way overrated. If you find a new fact it just goes into the giant pile of facts that are sitting around uselessly. The useful progress in math is comes from "refactoring" efforts to make things simpler and more intuitive.

I don't mean that this is necessarily the case, but that it is where we are now: we have found ourself in a situation where we have way too many facts and not enough simple perspectives that make them useful and accessible.

Just my opinion, though.

I read this kind of essay as a certain part of the arc by which new thoughts are formed: an act of large-scale pattern matching, laying out a bunch of cases which resemble each other, searching for the essential basis of the resemblance.

To post such a pattern allows the thought process to become distributed. Perhaps someone else will see the insight.