From the Book - Regular Print - First paperback edition.
1 From mystery to history 1 --
A mystery within an enigma 1 --
Illusions of certainty 2 --
Analogy that never breaks down? 21 --
Thinking about thinking 24 --
By the pricking of my thumbs 26 --
Bare bones of history 28 --
Creation or evolution 33 --
Ordinals versus the cardinals 36 --
Counting without counting 41 --
Counting with base 2 51 --
Neo-2 system of counting 56 --
What's so special about sixty? 64 --
Spread of the decimal system 68 --
Dance of the seven veils 72 --
Place-value system and the invention of zero 81 --
A final accounting 101 --
3 With form but void 106 --
Thinking by numbers 127 --
Bourbachique mathematique 129 --
Arithmetic in chaos 134 --
Mathematicians off form 140 --
4 Mothers of inventionism 147 --
Trap-door functions 150 --
Mathematical creation 154 --
Marxist mathematics 156 --
Complexity and simplicity 159 --
Maths as psychology 165 --
Pre-established mental harmony? 171 --
5 Intuitionism: the immaculate construction 178 --
Mathematicians from outer space 178 --
Intuitionism and three-valued logic 185 --
A very peculiar practice 188 --
A closer look at Brouwer 192 --
What is 'intuition'? 196 --
Tragedy of Cantor and Kronecker 198 --
Cantor and infinity 205 --
Comedy of Hilbert and Brouwer 216 --
Four-Colour Conjecture 227 --
Transhuman mathematics 234 --
New-age mathematics 236 --
Computability, compressibility, and utility 245 --
6 Platonic heavens above and within 249 --
Growth of abstraction 249 --
Footsteps through Plato's footnotes 251 --
Platonic world of mathematics 258 --
Far away and long ago 265 --
Presence of the past 268 --
Unreasonable effectiveness of mathematics 270 --
Difficulties with platonic relationships 272 --
Seance or science? 273 --
Revel without a cause 276 --
A computer ontological argument 280 --
A speculative anthropic interpretation of mathematics 284 --
Maths and mysticism 292 --
Supernatural numbers? 294.