Mathematics, poetry, and beauty

Introduction: magic

Mathematics and poetry

Displacement

Part I: Order. The curious case of the ants on the pole

Hidden order

To discover or to invent

Order and beauty

Mathematical harmonies

Why [square root] 2 is not a rational number

The real numbers

The miracle of order

Simple conjectures, complex proofs

Independent events

Part II: How mathematicians and poets think. Poetic image, mathematical image

The power of the oblique

Compression

Mathematical ping-pong

The book in heaven

Poetical ping-pong

Laws of conservation

An idea from somewhere else

Three types of mathematics

Topology

Matchmaking

Imagination

A magic number

Reality or imagination

Unexpected combinations

What is mathematics?

Deep tautologies

Symmetry

Impossibility

Infinitely large

Cantor's story

The most beautiful proof?

Paradoxes and oxymorons

Self-reference and Gödel's Theorem

Halfway to infinity: large numbers

Infinitely small

Infinitely many numbers having a finite sum

Twists

Part III: Two levels of perception. Knowing without knowing

Content and husk

Change

Estrangement

An endless encounter

Appendix A: Mathematical fields

Appendix B: Sets of numbers

Appendix C: Poetical mechanisms mentioned in the book.