For the first sixty pages Nagel and Newman combine history — Euclid,
Hilbert and attempts to formalise mathematics, Russell and Whitehead's
*Principia Mathematica* — with an explanation of the necessary
preliminaries — the problem of consistency, absolute proofs of
consistency, the codification of formal logic, the difference between
mathematics and meta-mathematics (reasoning about mathematics), and
the key idea that "meta-mathematical statements *about* a formalized
arithmetical calculus can ... be represented by arithmetical formulas
*within* the calculus". In thirty pages they then present the proof
itself: Gödel numbering, arithmetizing meta-mathematics, and the actual
construction. This is a drastic simplification of the full proof,
obviously, but it is enough to, as they put it, "afford the reader
glimpses of the ascent and of the crowning structure". They close
with some brief comments on the broader philosophical implications of
Gödel's Theorem.

November 2001

**External links:**-
- buy from Amazon.com or Amazon.co.uk

**Related reviews:**-
- books about mathematics

- books about philosophy

- more popular science

- books published by Routledge