This book is not for everyone. Another review describes this book's topic as thinking and thinking about thinking. That is accurate. If you are interested in the mechanics of logic, the limitations of formal logical systems, parallels of formal logical systems in music and art and Zen koans, and the applicability of such systems to AI, then this might be the book for you.

This book is dense. It is 740 pages, but takes three times as long to read as any fiction that length. Most paragraphs require stopping and pondering.

This is my second time attempting to read this book. The first time, I was 19 and had barely started college. Now, having finished a college education in Computer Science and Math, it was more approachable. I'm curious how approachable (or not) this book is to people who've never had much experience with formal logic or computation theory. Hofstadter certainly tries to write it for a general audience, but my education precludes me from commenting on how well he succeeds.

The dialogues between Achilles and the Tortoise are humorous (and at some times downright ridiculous) but (usually) do a good job of illustrating his topics more simply/lightly before diving into them, though they won't really help understanding the more difficult concepts. If you're in a programming mood, you might try reading The Little Schemer (it's short!) to get the best explanation of the Halting problem, then read this book with the understanding that Godel's Incompleteness Theorem is, more or less, the mathematical analogue.

He invents his own system of formal mathematical logic and his own procedural programming language to explain concepts, without going into what would be considered a more "standard" formal logic system or even the Turing machine itself. He does a good job piecing them together but at certain times I feel like it'd be more meaningful to read the original works on several of the subjects he touches on.

While formal logic certainly predates this book, a lot of the AI and neuroscience research that he describes were (and are) very much active. The book was published in 1979, and its references to AI reflect the time period. Hofstadter surmises that computers won't pass humans in chess-playing ability in the foreseeable future, but while it might be fun to read and go "oh yeah Deep Blue happened" a more interesting development has been in the use of statistical methods to approximate intelligence that have been more recently developed. For example, Hofstadter discusses translation of text between human languages as having been attempted through trying to parse the sentence and put it back together in another language and expects that computers will only get better at this when they have a fuller model of the world, complete with cultural context; instead, we've made advancements mostly through statistical predictions based on known existing corpuses of translated works, despite complaints about the validity of this approach (see also: Chomsky, Noam). While it might be interesting to see an updated version of the book taking these things into account, he does discuss why he doesn't (in the introduction to the 25th-anniversary-edition) and I agree.

Any complaints? Sure. The book is hard to read, especially for prolonged periods of time. It's dense and the concepts are not the easiest to begin with. Read a chapter every day or two and don't expect to finish this in a week. In fact, read three or four other books while you plow through this one. He gets a little too excited about some of the contrived analogies he comes up with (and sometimes he spends more time explaining an absurd analogy than the concept it is supposed to help) and reaches borderline smugness about certain cute coincidences he has arranged, but on the whole it's only a slight distraction from his main point.

Worth reading? Maybe. Will it expand your thinking? Probably, though maybe not as much as you might expect; due to the broad spectrum of topics covered, it's not as deep as I would like in some areas and spends too much time smoothing over difficult topics in certain fields in order to make "clever" maps between concepts in the fields (though in this aspect he's just being a computer scientist---we like simple representations that map cleanly across everything! Sadly, the world is not that way). Very good? Absolutely.
informative mysterious slow-paced

I think hofstader is a little too full of himself and into his own cleverness, but also I found this book to be both informative and thought-provoking and it was quite an enjoyable read with my bookclub even if we did sometimes struggles and had multiple dropouts. 
informative reflective slow-paced
challenging informative reflective slow-paced

Some really interesting things. I like the dialogs between chapters a lot--especially the "crab canon" dialog. The writing is accessible with lots of good examples, and tons of puns and references. I learned some good ideas about meta-states, reduction, levels of complexity, epiphenomena, etc.

However, I did get tired of this book by the end. It went on a bit too long, or spent too much time on things that ultimately didn't seem to be greatly pertinent.
challenging informative reflective slow-paced

5.0

The most thought-provoking book about artificial intelligence I've ever read, especially because it was written before Kasparov's defeat. Hofstadter's predictions that came true are almost as interesting as the ones that did not.

Read GEB slowly, as later chapters depend on a complete understanding of earlier chapters; I had to read entire chapters multiple times before I could move on.

In the running for best book I’ve ever read. Not at all easy though.
challenging funny informative inspiring lighthearted slow-paced

Recommended by HJPEV, indirectly, and by Eliezer Yudkowsky, through mention. Honestly, though, a much much better book than HPMOR could ever be.
Extremely insightful and intelligent, and exactly the type of thing that makes me love maths (even if I'm choosing to let go of it for now).
Will definitely reread it eventually.