Pi in the Sky

Part 1 From mystery to history: a mystery within an enigma; illusions of certainty; the secret society; non-euclideanism; logics - to be or not to be; the Rashomon effect; the analogy that never breaks down?; tinkling symbols; thinking about thinking. Part 2 The counter culture: by the pricking of my thumbs; the bare bones of history; creation or evolution; the ordinals versus the cardinals; counting without counting; fingers and toes; baser methods; counting with base 2; the neo-2 system of counting; counting in fives; what's so special about sixty?; the spread of the decimal system; the dance of the seven veils; ritual geometry; the place-value system and the invention of zero; a final accounting. Part 3 With form but void: numerology; the very opposite; Hilbert's scheme; Kurt Godel; more surprises; thinking by numbers; Bourbachique mathematique; arithmetic in chaos; science friction; mathematicians off form. Part 4 The mothers of inventionism: mind from matter; shadowlands; trap-door functions; mathematical creation; Marxist mathematics; complexity and simplicity; maths as psychology; pre-established mental harmony?; self-discovery. Part 5 Intuitionism: the immaculate construction: mathematicians from outer space; Ramanujan; intuitionism and three-valued logic; a very peculiar practice; a closer look at Brouwer; what is "intuition"?; the tragedy of Cantor and Kronecker; Cantor and infinity; the comedy of Hilbert and Brouwer; the four-colour conjecture; transhuman mathematics; new-age mathematics; paradigms; computability, compressibility, and utility. Part 6 Platonic heavens above and within: the growth of abstraction; footsteps through Plato's footnotes; the platonic world of mathematics; far away and long ago; the presence of the past; the unreasonable effectiveness of mathematics; difficulties with platonic relationships; seance or science?; revel without a cause; a computer ontological argument; a speculative anthropic interpretation of mathematics; maths and mysticism; supernatural numbers?.