Sure, but if the only math you're into is pop math then you're not a mathematician.

It might be that, in GP's experience, people who straightaway reply "I love Mozart" are less likely to actually have heard a substantial amount of his work, perhaps to have sat with them for some time, and (for lack of a better word) pondered over them, than someone who says they like something else but replies in a manner that sounds more sophisticated, e.g. "I enjoy the structure inherent in Bach's music" or what-have-you. (I might just be putting words in their mouth, though. Apologies if that's the case.) Answers of the latter kind can indicate that one has actually spent some time thinking about whatever it is one has learned, however elementary it might be. And that's always great!

It's probably the equivalent of someone saying "omg fractals" or "the incompleteness theorems, man, math is broken, I find that so beautiful" in response to "So you like math/CS?" After a while, that becomes a red flag that you learn to small-talk your way out of, albeit with some shame: while I agree with GP, to some extent, I do understand how this can be exclusionary, though. Almost by construction, someone who isn't in really deep is far more likely to have met the parts of a field that have been popularized than other things, and putting them down for this can be counterproductive if you're looking to attract more people or, well, just evangelize. I don't know of a good way out of this.

I do seem to have noticed that this isn't the case if you replace "fractals" by, say, "differential equations" or even "trisection". Maybe what one really needs to avoid in introductory literature is powerful ideas that are easy to lossily summarize for a lay audience in the form of really general, unexpected-sounding incorrect-when-unqualified statements that seem to say profound things about life, the universe, and everything. Leaving off the last condition shouldn't make an appreciable difference in hype/excitement-generating power: you could very well do, say, some topological/geometric staple like the hairy ball theorem, or some knot theory, and so on. That way, you retain the visual appeal that $REALLY_BIG_NUMBER-x zooms of Mandelbrot give you, while significantly decreasing the tendency for the target to go into (partial or full) "woah, dude, everything is connected and I am pure energy" mode in the way that Gödel often does.[0]

As an aside, GEB can be a good (rigorous, even) introduction to a few very powerful ideas. For me, what I call "interpreter-y thinking" was a good example, as was a healthy respect for how complex emergent behavior can arise from simple rules. This is something that's unfortunately hampered by the "bag of really cool ideas" nature that the book seemed to have when I read it four or five years ago.

[0]: I've actually heard the "everything is connected" bit from a good friend who loves watching videos like in TFV, so it isn't entirely a strawman. :)

Yeah, who needs nuance anyway? Just communicate using pure logic next time.

He he, good one. That reminds me of a joke I once made, in some relevant context, referencing Heisenberg and Pauli, but I'm uncertain what it was now, so I'll exclude it from here.

https://en.wikipedia.org/wiki/Wolfgang_Pauli

https://en.wikipedia.org/wiki/Werner_Heisenberg