1979 was a long time ago, and it’s possible that not every reader may know of—much less have read—this book. My editor proposed that I summarize or quote from it to make things clearer for such readers.

Considering that Gödel, Escher,
and Bach are all known for their intri-
cate multilayered works and that Hof-
stadter’s book is a well-mixed stew
not only of their works, but also of the
works of Cantor, Church, Gantõr, Tur-
ing, and pretty much any other math-
ematician or philosopher you care to
mention, I will not attempt a sum-
mary beyond: “It’s a book about how
we think.”
The relevant aspect of the book
here is Gödel’s incompleteness theo-
rem, which, broadly speaking, says
that no finite mathematical system
can resolve, definitively, the truth
value of all possible mathematical
conjectures expressible in that same