Read Fermat's Last Theorem Online
Authors: Simon Singh
relationship with Gauss 117â18, 119
strategy for Fermat's Last Theorem 115â17
Gibbon, Edward 109
Globe, Le
239
Gödel, Kurt 146, 157,
158
, 159
undecidable statements 159â63
Goldbach, Christian 90
Gombaud, Antoine 43â4
Government Code and Cypher School 170â75
gravity, theories of 18, 23
group theory 250â51
Grundgesetze der Arithmetik
(Frege) 152, 154
Guardian
272
hammers, harmony of 15
Hardy, G.H. 1, 2â4, 49â50, 165, 166, 179â80, 191
Riemann hypothesis telegrams 73
Hecke algebras 299â300
Hein, Piet 277
Heisenberg, Werner 162
Hellman, Martin 104
Hermite, Charles 3
hieroglyphics 212
Hilbert, David 101â3, 147,
151
, 157
and basic axioms 149â50
and Fermat's Last Theorem 226â7, 268
23 problems 150, 160, 162, 163
Hilbert's Hotel 102â3
Hippasus 54
History of Mathematics
(Montucla) 112
Hodges, Andrew 176
Hypatia 109, 111
hyperbolic space 201
Iamblichus 14â15
Illusie, Luc 278, 281
imaginary numbers 90, 93â6, 125â6
induction, proof by 231â2, 322â3
infinite descent, method of 90â91
infinity 59, 101â3, 177â8
International Congress of Mathematicians Berkeley (1986) 221, 222
Paris (1900) 150
intuition, and probability 44â5
invariants 141, 142, 219
Inventiones Mathematicae
277
irrational numbers 50, 54, 90â92
Iwasawa theory 259, 260, 296, 297â8
Journal de Mathématique pures et appliquées
248
Kanada, Yasumasa 51
Katz, Nick
262
, 263â5, 278â80, 281
knot invariants 142, 219
KolyvaginâFlach method 259â61, 263â5, 279â80, 281, 293, 297â8
Königliche Gesellschaft der Wissenschaften
135â7, 277
Königsberg bridge puzzle 83â5
Kovalevsky, Sonya 111
Kronecker, Leopold 50
Kummer, Ernst Eduard 123â8,
124
, 134â5, 176â7
L
-series 188
Lagrange, Joseph-Louis 96, 114, 239
Lamé, Gabriel 116, 120â27,
121
Landau, Edmund 110, 143â4
Langlands, Robert 213, 306
Langlands programme 213â14, 254
Last Problem, The
(Bell) 6, 30, 33, 73
Le Blanc, Antoine-August 114
see also
Germain, Sophie Legendre, Adrien-Marie 116
Leibniz, Gottfried 93
liar's paradox 161
Libri-Carrucci dalla Sommaja, Count Guglielmo 113, 241
light, nature of 204â5
limping triangles 65
Liouville, Joseph 124â5, 248, 249
Lipman, Joseph 283
Littlewood, John Edensor 179
Lodge, David 177â8
logic, mathematical 148â9
logicians 148â9, 162
loopiness, in rivers 17â18
Loyd Sam 138â42
Loyd's puzzle
see
â14â15' puzzle
lyre, tuning strings on 14â17
M
-series 201â2, 204â5, 211, 251â3
magnetism, and electricity 204â5
Mahler 314
Mathematical Magic Show
(Gardner) 63
mathematical proof 20â21, 23â6
Mathematician's Apology, A
(Hardy) 2â3, 49â50, 166
mathematicians
collaboration amongst 4â5
and compulsion of curiosity 164â6
in India and Arabia 58â60, 93
mathematical life 2â4
require absolute proof 147â8
secretive nature 40â41
self-doubt of 78â9
youthfulness 3
mathematics
contradictory nature of 152, 154â7
foundation for science 26â7
objective subject 28
relationship with science 17, 18
in seventeenth century 39â40
Mathematics of Great Amateurs
(Coolidge) 39
Mathematische Annalen
192
Mazur, Barry 211â12, 221, 265, 267, 270, 271, 277
Mersenne, Marin, Father 40â42
Method, The
(Heiberg) 48
meticulous librarian, tale of 154â5
Milo 9, 27â8
Mirimanoff, Dimitri 177
Miyaoka, Yoichi 254, 256â7
Miyaoka inequality 256
modular forms 195, 199â202
and elliptic equations 202, 204â5, 209â15
Monde, Le
272
Montucla, Jean-Ãtienne 112
moon, predicting phases of 81â2
Moore, Professor L. T. 47
Mozans, H.J. 119
musical harmony, principles of 14â17
My Philosophical Development
(Russell) 154
natural numbers 91
negative numbers 90â94
network formula 85â8
New York, subway graffiti 257
New York Times
254, 272â3, 282
Newton, Isaac 18, 47, 80, 81
Nixon, Richard Milhous 46â7
Noether, Emmy 110â11
nothingness, concept of 59
number line 92, 94â5, 185â6
numbers
definition of 150, 152
relationships between 11
numerals, Indo-Arab 59â60
Oberwolfach symposium (1984) 215â19, 221
Olbers, Heinrich 115
order and chaos 17
overestimated prime conjecture 179
Paganini, Nicolò 63
parallelism, philosophy of 254, 257
parasites, life-cycles 106â7
particle physics 22â3
Pascal, Blaise 40, 43â4, 45â6
Penrose, Roger 198
Penrose tilings 198â9
People
274, 290â91
perfect numbers 11â13
philosopher, word coined by Pythagoras 10
pi (Ï) 17â18, 50â53, 166
Picturegoers, The
(Lodge) 177â8
Pillow Problems
(Dodgson) 138
Pinch, Richard 285
Plato 109
Poges, Arthur 37, 74
Poincaré, Jules Henri 199
points (dice game) 43
polynomials 237
Portraits from Memory
(Russell) 160
prime numbers 70â71
almost primes 308
and Fermat's Last Theorem 99â100
Germain primes 116
infinity of 100â101, 102â3
irregular primes 126â7, 177
practical applications 103â7
333,333,331 not prime 178
twin primes 308
Principia Mathematica
(Russell and Whitehead) 156â7
probability 43â7
counter-intuitive 44â5
Problèmes plaisants et delectables
(Bachet) 61
puzzles, compendiums of 138
Pythagoras
abhors irrational numbers 50, 54â5
at Croton 9â10, 27â8
death 28
and mathematical proof 26
and musical harmony 14â17
and perfect numbers 12â13
and study of numbers 7
travels 7â8
Pythagoras' equation 28
âcubed' version 30â32
and Fermat's Last Theorem 32, 65â6
whole number solutions 28â30
Pythagoras' theorem 6â7, 19â20, 26, 333â4
Pythagorean Brotherhood 9â11, 13, 27â8, 49, 50, 108
Pythagorean triples 28â30, 65, 338
quadratic equations 236â7
quantum physics 162
quartic equations 237
quintic equations 237â8, 239â40, 245, 248â9
Ramanujan, Srinivasa 3
Raspail, François 242â3
rational numbers 11
rearrangement of equations 216
recipes, mathematical 8, 237
reductio ad absurdum
49â50, 53â4
reflectional symmetry 196
Reidemeister, Kurt 142
religion, and probability 46
Reynolds 323
Ribenboim, Paulo 144
Ribet, Ken
220
, 229, 267, 270â71, 272,
276
, 288â9, 304
Fermat Information Service 282
and significance of TaniyamaâShimura conjecture 221â3
Riemann hypothesis 73
river ratio 17â18
Rivest, Ronald 104
Rosetta stone 212
Rossi, Hugo 46â7
rotational symmetry 195â6
Rubin, Professor Karl 268â9, 300
Russell, Bertrand, 22, 44, 147,
153
, 160
Russell's paradox 152, 154â7
St Augustine (of Hippo) 12
Sam Loyd and his Puzzles: An Autobiographical Review
138
Samos, Greece 8â9
Sarnak, Peter 285â6, 291
Schlichting, Dr F. 144â6
scientific proof 21â2
scientific theories 22â3
scrambling and unscrambling messages 103â5, 168, 170â75
Segre 314
Selmer groups 287
Shamir, Adi 104
Shimura, Goro
193
, 191â5, 202, 203,
206
relationship with Taniyama 205, 207, 209
and TaniyamaâShimura conjecture 209â10, 272, 274
Shimura-Taniyama conjecture
see
TaniyamaâShimura conjecture Silverman, Bob 284
Sir Isaac Newton Institute, Cambridge 4â5, 266
Sir Isaac Newton's Philosophy Explain'd for the Use of Ladies
(Algarotti) 112
6, perfection of 11â12
Skewes, S. 179â80
Skewes's number 180
sociable numbers 63â4
Socrates 109
Somerville, Mary 113
square, symmetries of 195â6
square-cube sandwiches 64, 184
square root of one 93
square root of two 53â4, 91â2, 312â4
strings
and particles 23
vibrating 15â17,
16
Suzuki, Misako 207, 208
symmetry 195â202
Taniyama, Yutaka
190
, 191â5, 202, 203
death 205, 207â8
influence of 209
and TaniyamaâShimura conjecture 202, 204â5
TaniyamaâShimura conjecture 205, 209â15
and Fermat's Last Theorem 216â19, 221â3
Wiles and 215, 223, 225â31, 232, 258â61, 263â5, 274, 304
Taniyama-Weil conjecture
see
TaniyamaâShimura conjecture
Tartaglia, Niccolò 40â41
Taylor, Richard 285,
292
, 293, 296, 297, 299â300
Thales 26
Theano 9â10, 107â8
theorems 21, 71â2
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 196â9
Titchmarsh, E. C. 166
Tokyo, international symposium (1955) 203
translational symmetry 196â7
trichotomy, law of 148
truels 167, 343
Turing, Alan Mathison 167â176
uncertainty principle 161â2
undecidability theorems 159â63
von Neumann, John 159, 167
Wagstaff, Samuel S. 176
Wallis, John 38, 42, 64
weighing problem 61, 337â8
Weil, André 160, 210
Weil conjecture
see
TaniyamaâShimura 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 5â6, 33, 77â8
graduate student days 180â81, 183
tackles elliptic equations 183, 184â5, 188, 189
and TaniyamaâShimura conjecture 215, 223, 225â31, 232, 258â61, 263â5, 274
uses Galois's groups 251â3, 258, 296
announces proof of Fermat's Last
Theorem 1â2, 5, 33â5,
34
, 266â72
reaction of media 272â4
mathematical celebrity 274, 290â91
submits proof for verification 277â9
proof flawed 279â91, 293, 296
proof revised 296â300
proof published 304â5
wins Wolf Prize 308
collects Wolfskehl Prize 308
and the future 309
Wiles, Nada 230, 265, 281, 298â9
Wolf Prize 306
Wolfskehl, Paul
132
, 133â5
Wolfskehl Prize 135â7, 143â6, 268
Zagier, Don 254
zero, function of 58â9
FERMAT'S LAST THEOREM
Simon Singh received his PhD from the University of Cambridge. A former BBC producer, he directed the BAFTA award-winning documentary film
Fermat's Last Theorem
and wrote the best selling book of the same name. He is also the author of
The Code Book
and
Big Bang.
The Code Book
Big Bang
Fourth Estate
An imprint of HarperCollins
Publishers
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Hammersmith
London W6 8JB
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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
The right of Simon Singh to be identified as the author of this work has been asserted by him in accordance with the Copyright, Designs and Patents Act 1988.
A catalogue record for this book is available from the British Library.
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