The article strikes at the right general idea: that a startup that grows large quickly must have executed an idea that was not widely known (e.g. being exploited well, or in the natural adjacent competency of a current large company).

Peter Thiel's analogy of this is "what's true but few people agree with you on" and pg's version is "the best ideas look like jokes / bad on first glance". There's a popular venn diagram that's almost analogous to the one in the article: the best startups are at the intersection of true and not obvious.

This article maps "obvious good ideas" to "provable in a formal system", which makes the Godel analogy work, but the Godel analogy seems like a worse analogy.

Analogies are supposed to put a new concept (startup ideas) in terms of more accessible concept (Godel statements?). The analogy target (Godel statements) was so obtuse that the author needed to spend pages explaining it.

Also, the Godel analogy is misleading. The canonical Godel sentence is self referential and also refers to the formal logic system -- a good startup doesn't need to be self referential or refer to the formal system. Besides generating Godel's incompleteness theorem, I don't think Godel statements are "interesting", unlike the most recent successful startups. (In fact, what's interesting are simple yet difficult theorems that were totally provable within Peano arithmetic to begin with, like Fermat's Last Theorem.)