Non-mathematician here (psychologist now doing work in data science & machine learning). I was told this book had interesting insights about AI, consciousness, and the like. But I read it last year and found it the most tedious, absolutely unfocused book I've ever read.
Hofstadter is clearly a brilliant person, a polymath. He clearly loves wordplay and classical music. But his ramblings are so often tangential and self-indulgent that probably half the book could be trimmed out without cutting anything insightful. Gödel is important to the book. Escher...makes pictures that, if you squint real hard, could be construed as kind of relevant. Bach...well, the author just likes Bach and decided that he needed to be present. The latter two figures are essentially just used for some examples that could probably have been explained more clearly without using music as the context, given that it then requires him to delve into all the details about how fugues are different from canons, etc. etc.
Let's just say, reading the author's introduction to the 20th anniversary edition of the book states his main premises much more succinctly, to the point where you can skip the rest of the 700+ pages of the book.