Index 279
Ribet, Ken 255
Ricci, Matteo 98
Richards, Joan 193, 207
Riemann, Bernhard 191
On the Hypotheses which lie at the basis of
Geometry 204
rings, Noether’s work 230–1
Ritter, James 20
Robson, Eleanor 19, 22, 26–7
Romans 57, 69–71
roots
ab ̄uK ̄amil’s work 115–16
al-K ̄ash ̄ı 122
al-Khw ̄arizm ̄ı’s work 110–11, 125–6
Tartaglia 145
Ruffini-Horner procedure 96–7
Russell, Bertrand 206–7, 240
definition of mathematics 213
Russell paradox, set theory 218
Sa’id Edward 95
Saccheri, Gerolamo
HOA 199–200
work on parallel postulate 190– 1
St Andrews archive 4
Sand-Reckoner(Archimedes) 194
scholastics 136–7
Oresme, Nicholas 139–40
scientific revolution 135–8
Schwarz, Laurent 253
scientific communities 42
scientific revolution 8–10
calculating tradition 141–3
Descartes 149–51
Galileo 133, 134, 153–4
influences 147
Oresme, Nicholas 139–40
scholastics 135–8
sources 134–5
Stevin 146, 149
Tartaglia, Niccolò 144–5
use of the infinite 151–3
Viète 146, 147–8
scribes, Babylonian 20–1, 26, 27
Fara period 27–8
second world war 238–40
secrecy 144, 165
self-fashioning in sixteenth century 147
series
divergent, Ramanujan’s work 228–9
Oresme, Nicholas 139–40
See also infinite Series
sets 215
definition of natural numbers 216
set theory
Axiom of Choice 218–19
inconsistency 218
rings and ideals 230–1
sexagesimal system, Babylonian 22–4
Shar ̄af al-D ̄ın al-T ̄us ̄ı 104
Shimura 255
Shushu Jiuzhang(Qin Jiushao) 91, 93
pointed field problem 95– 6
sic et nonmethod 137
Sign Rule, inNine Chapters 88
simplexes 226
sineseetrigonometric ratios
sine formula, in spherical and hyperbolic geometry 209
Siyuan yujian(Zhu Shijie) 91
slot machine, Heron 64
Smale, Steve 247, 262
horseshoe map 249– 50
Socrates, dialogue in Plato’sMeno34–5, 36
solvability of all problems axiom, Hilbert 217, 221, 231
Song dynasty 90–3
sources
Babylonian mathematics 17–20
calculus 163–4
Chinese mathematics 80
Islamic mathematics 103–5
modern mathematical history 237
non-Euclidean geometry 193
scientific revolution 134–5
twentieth century mathematics 214
space, nature of 207
Special Theory of Relativity (Einstein) 207
spherical geometry 195 , 199–201
failure of Euclid’s proposition I.16 207– 8
Helmholtz’s 1876 paper 209–10
spherical trigonometry 208– 9
square, doubling of, Plato’sMeno 34–5, 50, 51–2
‘square root of 2’ tablet 25
square roots√
246
al-Uql ̄ıdis ̄ı’s method 106–7
Archimedes’ approximations 62
in Babylonian mathematics 24
Heron’s approximation 73
squares, al-Khw ̄arizm ̄ı’s work 125–6
squaring, using counting rods 86, 87
squaring the circle, Albert of Saxony’s discussion 137–8
stages of history 6
stars
motion, Ptolemy’s ideas 67–8
parallax 205
statistics 249
Stevin 133, 146, 149
stone-weighing tablet 18
‘string worldsheet’ 251
strong program in the sociology of knowledge (SPSK) 1
structuralism 243
Struik, Dirk 2, 10
subtangent 171
Sui dynasty 82
Sumerians 15
sun, Ptolemy’s models of movements 68–9, 75–6
Sunzi suanjing 85
method for squaring 86, 87
surds
origin of term 114
see alsoroots
Synesius 71, 72