280 Index
table of powers, al-Samaw’al 118
tables, use in Islamic mathematics 118 ,
119 , 122, 129
table texts 20
tablets, Babylonian 15 , 16 , 18 –20,
21–2, 25 , 28
Tait, study of knots 225, 227
tangentseetrigonometric ratios
tangents to curves 169
Newton’s method 169–2, 183–5
Taniyama–Shimura–Weil conjecture 255
Tannéry, Paul 39–40
Tartaglia, Niccolò 144–5
Tartaglia’s rule, solution of
cubic 111, 144–5
Taylor, Richard 254
teaching 262
Bourbakists’ methods 240–3
technology, use of mathematics 236, 260
Teichmüller 239
tetrahedron 46
al-K ̄ash ̄ı’s work 128–9
Th ̄abit ibn Qurra 112–14, 127–8
ideas on velocity 152
parallel postulate 190, 196
Thales 40, 44, 177
Thales’ theorem, proof by reflection 55
Theatetus(Plato) 49
Theon 72
Theory of Parallels(Lambert,
Johann Heinrich) 200–1
theory of proportions, Eudoxus 47
tianyuan (polynomial notation) 92
Topcategory 250
topology 223–8, 249
Brouwer Fixed Point Theorem 219– 20
category theory 250–1
Torelli, Roberto 193
Torricelli 165
torus 224
transcendence ofeandπ 221
translation problems 7–8
Chinese texts 79
Islamic mathematics 136
OB tablets 18–19
in works on the calculus 164
transliteration, Chinese texts 79
triangles
angles of a triangle theorem,
proof 210 –11
area of, Heron’s formula 64–5, 73–4
Euclid, proposition I.16 207– 8
spherical 200
trigonometric functions
Bourbaki definitions 242
Keralan mathematics 167–9
trigonometry
Ptolemy’s use 68
spherical and hyperbolic 208– 9
true lover’s knot 225
tunnel of Eupalinus 70
Turing, Alan 244–5, 246
computable numbers 213, 220, 256–7
Turing machine 244, 257
twentieth century mathematics 213–14
‘Bourbaki’ 240–3
category theory 249–51
chaos theory 246–9
computers, invention of 243–6
crisis 217–21
drive for foundations 216–17
Fermat’s Last Theorem 254–5
Hilbert, David 221–3
Noether, Emmy 230–1
physics 251–4
Ramanujan, Srinivasa 228–9
real numbers, definition 215–16
sources 214
topology 223–8
Umar al- Khayy ̄ ̄ am ̄ı see Khayyam, Omar
units of measurement, Babylonian 20, 29
‘universal characteristic’, Leibniz 174
Unreasonable Effectiveness of
Mathematics in the Natural Sciences,
The(Wigner) 252
Ur III period 15, 28–30
‘uselessness’, Babylonian mathematics 26–7
velocity at an instant’ 152, 154, 170
Viète, François 133, 146, 147–8
influence on Descartes 150
Vitruvius 70
volume of cone, Archimedes 48–9
von Neumann, John 222, 245, 253
atom bomb project 239
water-clocks, Greek 64, 65
weather forecasting 249
Weil, André 240, 255
Weil, Simone 1–2
western Europe, attitudes towards
Islamic mathematics 102
Weyl, Hermann 219
definition of mathematics 213
‘honest’ real numbers 220
intuitionism 231
Whig history 1, 206
Wiener, Norbert 239
Wigner, Eugene 252–3
Wiles, Andrew 235–6, 237, 254–5
wine-barrels, Kepler’s measurement 157–8
Witten, Ed 254
Wittfogel, Karl, hydraulic project thesis 16
women in mathematics 231
Hypatia 71–3
Noether, Emmy 230–1
Yang Hui 90
year, length of 50
Yijing(I Ching,Book of Changes)78
Yuan dynasty 90, 95