|Pulitzer Prize wining book whose chapters alternate between fictional
"dialogues" and more standard non-fiction format to present ideas from
philosophy, art, music and psychology as well as mathematical topics
such as computability, Zeno's paradox or symbolic logic. This book
does a fantastic job of conveying the beauty of mathematical logic,
and the mathematical logic of beauty. Where else can you see an
example of a logical paradox (a proof of Fermat's last theorem which
relies on the existence of a counter-example to the theorem) being
used by a tortoise to make a recording of Bach playing the
harpsichord? (Nowhere else that I know of anyway!)
I have received a lot of complaints from people about the inclusion of GEB on this list. Certainly, it is really a book of non-fiction and these fictional interludes are just there to be artistic examples of the points described elsewhere. However, both because of its celebrity and because its "interludes" have been reprinted in collections of mathematical fiction, I have decided to include it here anyway. It should be noted that in general I do not include works of non-fiction which illustrate some points through fictional examples.
While the book Contact makes me want to build or buy a supercomputer to analyze prime numbers, this book makes me want to run for public office in an attempt to burn mathematicians at the stake. What pompous tripe. This book does nothing to illustrate or expound on the inherent beauty of mathematics and mathematical relationships in nature. This book will serve only to alienate non-mathematicians and bore mathematicians. PS I did not finish the book. I tried twice and failed. Then it occurred to me; it's not my fault I couldn't read this book. I can read Eco like the Sunday comics. This book bored me to tears.
I found this monster of a book the work of a man who know a lot about a few things and a little about many, many things. Hofstadter, it seems to me, has an extraordinarily bloated ego. In trying to tie all the themes of human creation, he succeeds only in giving us pleasant "proverbs".
Most criticisms of GEB I encounter seem to me to stem from people's disappoinment that the book isn't quite what THEY would like it to be, rather than any particular flaw in the book itself.
It's entertaining, and for the most part accurate, and deals with interesting subjects. I'm sure Achilles and the Tortoise could have a lively debate concerning whether it's possible for there to be a PERFECT book covering broadly similar topics but at any rate there isn't currently a BETTER one.
At a personal level it's interesting to have read it once at 15 and once at 30, and assessing how ten intervening years at University studying music and philosophy changed my response to it: I think it's a compliment to Hoffstadter that I was able to enjoy it both times.
An extremely clever book, but certainly not a pleasure to read: the author has a rather juvenile sense of humour and isn't great at explaining his ideas - or motivating the reader.