points (dice game) 43
polynomials 237
Portraits from Memory (Russell) 160
prime numbers 70–71
almost primes 308
and Fermat’s Last Theorem 99–100
Germain primes 116
infinity of 100–101, 102–3
irregular primes 126–7, 177
practical applications 103–7
333,333,331 not prime 178
twin primes 308
Principia Mathematica (Russell and Whitehead) 156–7
probability 43–7
counter-intuitive 44–5
Problèmes plaisants et delectables (Bachet) 61
puzzles, compendiums of 138
Pythagoras
abhors irrational numbers 50, 54–5
at Croton 9–10, 27–8
death 28
and mathematical proof 26
and musical harmony 14–17
and perfect numbers 12–13
and study of numbers 7
travels 7–8
Pythagoras’ equation 28
‘cubed’ version 30–32
and Fermat’s Last Theorem 32, 65–6
whole number solutions 28–30
Pythagoras’ theorem 6–7, 19–20, 26, 333–4
Pythagorean Brotherhood 9–11, 13, 27–8, 49, 50, 108
Pythagorean triples 28–30, 65, 338
quadratic equations 236–7
quantum physics 162
quartic equations 237
quintic equations 237–8, 239–40, 245, 248–9
Ramanujan, Srinivasa 3
Raspail, François 242–3
rational numbers 11
rearrangement of equations 216
recipes, mathematical 8, 237
reductio ad absurdum 49–50, 53–4
reflectional symmetry 196
Reidemeister, Kurt 142
religion, and probability 46
Reynolds 323
Ribenboim, Paulo 144
Ribet, Ken 220, 229, 267, 270–71, 272, 276, 288–9, 304
Fermat Information Service 282
and significance of Taniyama–Shimura conjecture 221–3
Riemann hypothesis 73
Rivest, Ronald 104
Rosetta stone 212
Rossi, Hugo 46–7
rotational symmetry 195–6
Rubin, Professor Karl 268–9, 300
Russell, Bertrand, 22, 44, 147, 153, 160
Russell’s paradox 152, 154–7
St Augustine (of Hippo) 12
Sam Loyd and his Puzzles: An Autobiographical Review 138
Samos, Greece 8–9
Sarnak, Peter 285–6, 291
Schlichting, Dr F. 144–6
scientific proof 21–2
scientific theories 22–3
scrambling and unscrambling messages 103–5, 168, 170–75
Segre 314
Selmer groups 287
Shamir, Adi 104
Shimura, Goro 193, 191–5, 202, 203, 206
relationship with Taniyama 205, 207, 209
and Taniyama–Shimura conjecture 209–10, 272, 274
Shimura-Taniyama conjecture see
Taniyama–Shimura conjecture Silverman, Bob 284
Sir Isaac Newton Institute, Cambridge 4–5, 266
Sir Isaac Newton’s Philosophy Explain’d for the Use of Ladies (Algarotti) 112
6, perfection of 11–12
Skewes, S. 179–80
Skewes’s number 180
sociable numbers 63–4
Socrates 109
Somerville, Mary 113
square, symmetries of 195–6
square-cube sandwiches 64, 184
square root of one 93
square root of two 53–4, 91–2, 312–4
strings
and particles 23
vibrating 15–17, 16
Suzuki, Misako 207, 208
symmetry 195–202
Taniyama, Yutaka 190, 191–5, 202, 203
death 205, 207–8
influence of 209
and Taniyama–Shimura conjecture 202, 204–5
Taniyama–Shimura conjecture 205, 209–15
and Fermat’s Last Theorem 216–19, 221–3
Wiles and 215, 223, 225–31, 232, 258–61, 263–5, 274, 304
Taniyama-Weil conjecture see
Taniyama–Shimura conjecture
Tartaglia, Niccolò 40–41
Taylor, Richard 285, 292, 293, 296, 297, 299–300
Thales 26
Theano 9–10, 107–8
theorems 21, 71–2
Theory of Games and Economic Behaviour, The (von Neumann) 167
13 Lectures on Fermat’s Last Theorem (Ribenboim) 144
Thomson, J. J. 22
three-body problem 81
threeness 152
tiled surfaces, symmetry of 196–9
Titchmarsh, E. C. 166
Tokyo, international symposium (1955) 203
translational symmetry 196–7
trichotomy, law of 148
truels 167, 343
Turing, Alan Mathison 167–176
uncertainty principle 161–2
undecidability theorems 159–63
von Neumann, John 159, 167
Wagstaff, Samuel S. 176
Wallis, John 38, 42, 64
weighing problem 61, 337–8
Weil, André 160, 210
Weil conjecture see Taniyama–Shimura conjecture Weyl, Hermann 149
Whitehead, Alfred North 156
whole numbers 11
Wiener Kreis (Viennese Circle) 157
Wiles, Andrew xviii, 181, 224, 276, 302
adolescence and Fermat’s Last Theorem 5–6, 33, 77–8
graduate student days 180–81, 183
tackles elliptic equations 183, 184–5, 188, 189
and Taniyama–Shimura conjecture 215, 223, 225–31, 232, 258–61, 263–5, 274
uses Galois’s groups 251–3, 258, 296
announces proof of Fermat’s Last
Theorem 1–2, 5, 33–5, 34, 266–72
reaction of media 272–4
mathematical celebrity 274, 290–91
submits proof for verification 277–9
proof flawed 279–91, 293, 296
proof revised 296–300
proof published 304–5
wins Wolf Prize 308
collects Wolfskehl Prize 308
and the future 309
Wiles, Nada 230, 265, 281, 298–9
Wolf Prize 306
Wolfskehl, Paul 132, 133–5
Wolfskehl Prize 135–7, 143–6, 268
Zagier, Don 254
zero, function of 58–9
About the Author
FERMAT’S LAST THEOREM
Also by the Author
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Copyright
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First published in paperback by Fourth Estate in 2002 (reprinted 4 times)
First published in Great Britain in 1997 by Fourth Estate
Copyright © 1997 by Simon Singh
Foreword copyright © 1997 by John Lynch
Line illustrations by Jed Mugford
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