Index 277
Ma Yize 95
machine construction, Heron 63–4, 65
machines, curve-drawing 150, 156
MacLane 250–1
Madhava 168
Mandelbrot (complex) quadratic maps 248–9
manifolds 223
Mao Zedong 11
Martzloff, Jean-Claude 7, 80
Chinese and Western equations 95
Mei Wending 98
‘Pascal’s triangle’ 97
rod numbers 85–6
Marxism 10–11, 125
Mathematical Cuneiform Texts(Neugebauer
& Sachs, 1946) 19
Mathematics for the Million(Hogben, Lancelot) 235
mathematics, Hilbert’s definition 222
Russell and Weyl’s definitions 214
matrices, in Chinese mathematics 88–90
mean-taker (mesolabe) 59
Measurement of a Circle(Archimedes) 61–2, 137, 138
Menaechmus, doubling of cube 58
Meno(Plato) 33–5, 36, 50, 51–2
mesolabe 59
metamathematics 222
Method, The(Archimedes) 61
method of double false position 83–4
Method of Fluxions and Infinite Series(Newton) 171–2,
183–5
Metrics(Heron) 64, 73–4
Mift ̄ah al-his ̄ab(al-K ̄ash ̄ı) 104
‘Millennium Problems’ 261
military applications of mathematics 59, 60, 260, 262
Ming dynasty 98
Möbius 223
modernism and anxiety 218
Moerbeke, mathematical translations 136
Monge, Gaspard 236
descriptive geometry 198
months, length of 50
Montucla, Jean Étienne 1, 7, 254
mosques, alignment of 124–5, 131 , 195
motion, relationship to curves 169–70
Muhammad ibn M ̄usaseeal-Khw ̄arizm ̄ı
multiplication, relationship to ratios 50
multiplication tables, Babylonian 23
Nash, John 237
Nasir al-D ̄ın al-T ̄us ̄ı 190
natural numbers, definition 216
Nazi Germany 238–9
negative numbers
as roots of quadratics 111
use in Chinese mathematics 88
neoplatonism 72
Netz, Reviel 7, 36
Greek mathematics, community 41
origins 45
Newton, Isaac 161–2
ideas on infinity 197
literature 163, 164
method for finding tangents 169–72, 183–5
nature of space 207
Principia176–8, 186
priority dispute 165–6
Nicholas of Cusa 153, 174
Nicomachus of Gerasa 57
Nine Chapters on the Mathematical Art78–9,
80, 82–4
matrices 88–90
Noether, Emmy 230–1
expulsion from Nazi Germany 238
non-Euclidean geometries 189
consequences 206–7
construction of 201–3
delays in development 203–5
Escher, Moritz,Circle Limit III 192
failure of Euclid’s proposition I.16 207– 8
Helmholtz’s 1876 paper 209–10
Lobachevsky and Bolyai 191, 192, 193
proof of consistency 191–2
source material 193
spherical geometry 199–201
spherical and hyperbolic trigonometry 208– 9
normal science 8, 9
notation, Leibniz’s 173
Nova stereometria doliorum(Kepler) 157–8
number rings 230
numbers
Babylonian 22–4
Chinese 85
Islamic 116, 120–1
representation by counting rods 85, 86
Stevin’s views 149
number theory, Ramanujan’s work 228–9objects in mathematics 216
octahedron 46
Old Babylonian (OB) period 15, 17–19
On computable Numbers(Turing) 244
On the Hypotheses which lie at the basis of Geometry
(Riemann, Bernhard) 204
one, status as number 149
operational research 239
Oresme, Nicholas 136, 139–40
influence on Descartes 150
Quaestiones super Euclidem155–6Pappus 40
on Heron 63–4
papyri, mathematical 17
paradigm 8
paradoxes of Zeno 139, 140
parallax of stars 205
parallel angle ( (p)) 202–3
parallel lines, Lobachevsky’s definition 202
parallelograms, equal (Euclid) 37 –8
parallel postulate 194–6
attempts at proof 190–1, 196
partition number, Ramanujan’s formula 228–9