272 Index
arithmetic
consistency of axioms 217
Kit ̄ab al Fus ̄ul f ̄ı al-His ̄ab al-Hind ̄ı
(al-Uql ̄ıdis ̄ı) 106–7
Arithmetic(Diophantus) 111
Arithmétique(Stevin) 149
Array (Fangcheng) Rule 89
‘asamm’ numbers 114
astrology 66
Astronomia Nova(Kepler) 151, 152– 3
astronomy
in Greek mathematics 66–9
planetary motion 152
Newton’s ideas 176
and ratios 50
role of Islam 124
Atiyah, Michael 250
atom bomb project 239
Auden, W. H. 260
Axiom of Choice, set theory 218–19
Axiom of Comprehension 218, 231–2
axiomatization of geometry 206–7
axioms 222
for arithmetic, consistency 217–18
axiom systems, Bourbakists ideas 241Babbage, Charles 244
Analytical Engine 243
Babylonian mathematics
abstraction 18–19, 20–1, 24–6
Fara period 27–8
interpretation 7
number system 22–4
sources 17–20, 21–2
units of measurement 20, 29
Ur III period 28–30
‘uselessness’ 26–7
Barrow, Isaac 49, 170
beginning of mathematics 14
Bieberbach 238
Beltrami 192
Berggren, J. L. 3, 103–4
ab ̄u-l-Waf ̄a 107
al-K ̄ash ̄ı 122
Greek historiography 35
Berkeley, George 162, 163
The Analyst179–80
Bernal, Martin 43
Bernoulli, Jakob and Johann 166, 178–9
literature 163
representation of curves 181
biography, St Andrews archive 4
Bishop BerkeleyseeBerkeley, George
Black Athena(Bernal, Martin) 43
Bolyai, Janos 189, 191, 192, 193
construction of geometry 202
isolation 203
Bolzano 218
on application of geometry 199
Bombelli 146
Bonola, Roberto 193Book of Changes(Yijing,I Ching,) 78
Bos, Henk 3, 163–4
construction of curves 180–1
independent variable 176
‘Bourbaki’ 240–3
Algebra 256
Bradwardine, Thomas 135, 136
ideas on infinity 197
Brouwer, L. E. J. 219–20
intuitionism 231–2
Bruno, Giordano 197
bureaucracy as trigger for mathematics 16
‘Burning of the Books’, China 81
‘butterfly effect’ 246, 247calculating tradition, role in scientific revolution 141–3
Calculator’s Key, (al-K ̄ash ̄ı) 104, 117, 120–3, 128– 9
calculus 161–3
Archimedes, possible use of 61
Berkeley, George,The Analyst179–80
Bernoulli brothers’ adaptation 178–9
de l’Hôpital’s contribution 179
Keralan mathematics 167–9
Leibniz, 1684 paper 185 –6, 172–6
limits 215
practical use 180–2
Principia(Newton) 176–8
priority dispute 165–6
sources 163–4
tangents, Newton’s method 169–72, 183–5
use of infinitesimals 182–3
calendar construction 50
cooperation between Chinese and Near East 95
Matteo Ricci, China 98
Cantor, Georg 215
continuum hypothesis 217
Cantor, Moritz 1
Capra, Fritjof 252, 254
Cardano, Hieronimo 144, 145
cardioid, area of 182– 3
Carr, E. H. 3
Cartan, Henri 240
Cartier, Pierre 241
category theory 249–51
catenary 180– 1
cell decomposition, topology 223–4
Ceyuan Haijing(Li Zhi) 90, 91 ,92
Ch’in Chiu-shaoseeQin Jiushao
chaos theory 246–9
Chasles, Michel, descriptive geometry 198
Chemla, Karine, on Liu Hui 84
Ruffini-Horner Procedure 97
Chevalley, Claude 240
China, early history 80–2
Chinese mathematics 78–80
counting rods 85–8
matrices 88–90
Ming dynasty 98
Nine Chapters on the Mathematical Art82–4
Qin Jiushao 90, 91
Song dynasty 90–3