> People have been practicing formal mathematics long before Godel Right, this was pretty much my original point. > This seems to indicate me that GP comment

> People have been practicing formal mathematics long before Godel Right, this was pretty much my original point. > This seems to indicate me that GP comment is right that the inciting incident was understanding the correspondence between mathematics and its encoding. Doesn't this sentence contradict the previously quoted one? Or, at the very least, the point is far more subtle than the GP's "...it's the conceptual leap to thinking about mathematical statements as mathematical objects..." I don't see anything in Hilbert's mathematics that indicates he did not "think about mathematical statements as mathematical objects". Very much the opposite, actually. I'll agree that the key insight was basically about mathematics and its encoding. And that this insight was extremely non-obvious. But Hilbert's program really was literally all about GP's "[thinking of] mathematical statements as mathematical objects". Or, to restate this contentious agreement we're having another away: things like the idea to do numbering in the first place are the details, and do not obviously follow from treating mathematical objects as objects of mathematics itself.