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Comment by MperorM | Hacker News Reader

During the first year of my undergrad someone introduced me to Gödel, Escher, Bach. I thought it was mind blowing at the time and still find it to be an incredible introduction to formal systems, thinking mathematically and understanding the concept of proofs.

All these concepts are central to higher level mathematics, and are not covered in high school (at least not the Danish one).

I'm was very thankful for that introduction, hopefully they would be as well :)

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I have to disagree with you here, and strongly. I don't think Gödel, Escher, Bach is a good book. Hofstaeder is clearly very smart, curious, and open-minded, and I love all those things, but the book itself is just so pretentious and sort of pointless. It's precisely the wrong kind of book you want to give a bright teenager, because it will only encourage them to get a head-start inserting their head up their own arsehole, metaphorically speaking.

> I don't think Gödel, Escher, Bach is a good book. Hofstaeder is clearly very smart, curious, and open-minded, and I love all those things, but the book itself is just so pretentious and sort of pointless.

I'm curious: Do you feel this way because it isn't a math textbook?

Not at all. My own recommendation, God created the Integers, isn't a math textbook. I doubt Hofstadter himself would claim GEB had a point - it was more of an intellectual fugue put to paper. If GEB was a novel it would be more along the lines of Finnegan's Wake than Les Misérables, and I would never ever give the former to a teenager.

I read it when I was 16 and it was just wonderful. I can also recommend it.

Here's an interesting review:

https://journal.infinitenegativeutility.com/why-i-dont-love-...

It's a negative review, and I agree with all its points. In addition, I don't like Hofstadter's proof of Gödel's theorem - it's so LONG that it's hard to keep track of the parts. (The best proof of Gödel's theorem I've come across was given verbally by John Conway, and he had the opposite strategy - make the proof as brief as possible so that you can easily see an overview of it.)

But despite these criticisms, I think it's a wonderful book, and I agree with the idea of giving it to a teenager as an introduction to mathematics.

I first read it when I was 14 and went on to do a lot of mathematics and philosophy of mathematics.

Do you have a link to Conways proof?

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