Quite a bit more, you reply, especially since only 8% of you have actually read this amazing book. (Statistics gladly invented on the spot, of course.)
If you’ve heard of the book but haven’t read it, you may not realize that it’s far from Douglas Hofstadter’s only contribution to the popularization of mathematics and computer science. More below.
Although I don’t want to turn this post into a review of GEB (as the book is usually referred to), I clearly have to write a bit about it. But first about some of those other contributions that I mentioned in the previous paragraph.
Hofstadter was born in 1945, making him even older than I am, but apparently he has not yet retired. He has at least one clear connection with another popularizer who has inspired me: on August 30 I wrote about Martin Gardner, particularly his Mathematical Games column that ran for many years in Scientific American. When Gardner retired from this activity in 1981, Hofstadter took over for a short two-year stint, changing the title to Metamagical Themas. He collected these in a book of the same name, which also included some additional columns plus commentary on each, following Gardner’s tradition of doing the same. If you haven’t read Metamagical Themas, go do so! It’s a great collection with some overarching themes and themas but not a straight-through narrative. (I suppose that goes without saying, for a collection of magazine columns, but…) Of course you noticed that “Metamagical Themas” is an anagram of “Mathematical Games” (and vice versa, amazingly).
Hofstadter has also written many articles and several other books, though none of them stuck with me the way Metamagical Themas and Gödel, Escher, Bach did. So I will pass over the others in silence. Metamagical Themas and Gödel, Escher, Bach are more than sufficient to establish Hofstadter’s place as one of the five popularizers who have influenced me the most. With that in mind, let’s turn to the pièce de resistance, GEB.
Published 41 years ago, GEB seems somewhat out-of-date — but it isn’t really. The title invites you to think about math, philosophy, art, and music. A glance through the book invites you to think as well about Lewis Carroll and computer science and logic and linguistics. So yes, this incredible book is about all of these — and more. It’s no wonder that it has earned the #1 position in my Top Ten list. When I first read it in 1979, as a teacher at Lincoln-Sudbury, it captured me like no other book. Its interdisciplinary spirit overwhelmed me, in fact. I ended up incorporating large swaths of it into several courses I subsequently taught, including one called Advanced Math at the Massachusetts Advanced Studies Program and a precalculus course at Boston University Academy, each for several years. Before you decide to read (or re-read) GEB, you may want to check out this brief article about it, which not only summarizes some important points but also provides some great links to pursue before and while reading the book.
And don’t forget Hofstadter’s Law. which I have often reminded my students about over the past four decades: “Everything takes longer than you expect, even when you take Hofstadter’s Law into account.” How perfectly recursive!