To be on this list the book must satisfy the following conditions:
- It doesn’t require an enormous amount of background material to understand.
- It must be a fun book, either in recreational math (or something close to) or in philosophy of math.
Here are my two contributions to the list:
- What is Mathematics? Courant and Robbins.
- Proofs that Really Count. Benjamin and Quinn.
Gödel, Escher, Bach: An Eternal Golden Braid, by Douglas Hofstadter. Very interesting read – details Gödel’s Incompleteness Theorem, and manages to touch on a wide variety of topics, including genetics, reductionism/holism, programming, art, music, brains, zen, language, etc. The central idea is that a special kind of self-reference (which Hofstadter calls a strange loop) seems to pop up everywhere, and is perhaps at the heart of intelligence and the appearance of meaning in a structure made up of meaningless parts.