Part I: Order. The curious case of the ants on the pole
Why [square root] 2 is not a rational number
Simple conjectures, complex proofs
Part II: How mathematicians and poets think. Poetic image, mathematical image
An idea from somewhere else
Three types of mathematics
The most beautiful proof?
Self-reference and Gödel's Theorem
Halfway to infinity: large numbers
Infinitely many numbers having a finite sum
Part III: Two levels of perception. Knowing without knowing
Appendix A: Mathematical fields
Appendix B: Sets of numbers
Appendix C: Poetical mechanisms mentioned in the book.
