Read Fermat's Last Theorem Online
Authors: Simon Singh
Extrait d'une lettre de M. Kummer a M. Liouville, by E.E. Kummer,
J. Math. Pures et Appl.
12
(1847), 136. Reprinted in
Collected Papers
, Vol. I, edited by A. Weil, 1975, Springer.
A Number for Your Thoughts
, by Malcolm E. Lines, 1986, Adam Hilger. Facts and speculations about numbers from Euclid to the latest computers, including a slightly more detailed description of the dot conjecture.
3.1416 and All That
, by P.J. Davis and W.G. Chinn. 1985, Birkhäuser. A series of stories about mathematicians and mathematics, including a chapter about Paul Wolfskehl.
The Penguin Dictionary of Curious and Interesting Numbers
, by David Wells, 1986, Penguin.
The Penguin Dictionary of Curious and Interesting Puzzles
, by David Wells, 1992, Penguin.
Sam Loyd and his Puzzles
, by Sam Loyd (II), 1928, Barse and Co.
Mathematical Puzzles of Sam Loyd
, by Sam Loyd, edited by Martin Gardner, 1959, Dover.
Riddles in Mathematics
, by Eugene P. Northropp, 1944, Van Nostrand.
The Picturegoers
, by David Lodge, 1993, Penguin.
13 Lectures on Fermat's Last Theorem
, by Paulo Ribenboim, 1980, Springer. An account of Fermat's Last Theorem, written prior to the work of Andrew Wiles, aimed at graduate students.
Mathematics: The Science of Patterns
, by Keith Devlin, 1994, Scientific American Library. A beautifully illustrated book which conveys the concepts of mathematics through striking images.
Mathematics: The New Golden Age
, by Keith Devlin, 1990, Penguin. A popular and detailed overview of modern mathematics, including a discussion on the axioms of mathematics.
The Concepts of Modem Mathematics
, by Ian Stewart, 1995, Penguin.
Principia Mathematica
, by Betrand Russell and Alfred North Whitehead, 3 vols, 1910, 1912, 1913, Cambridge University Press.
Kurt Gödel, by G. Kreisel, Biographical Memoirs of the Fellows of the Royal Society, 1980.
A Mathematician's Apology
, by G.H. Hardy, 1940, Cambridge University Press. One of the great figures of twentieth-century mathematics gives a personal account of what motivates him and other mathematicians.
Alan Turing: The Enigma of Intelligence
, by Andrew Hodges, 1983, Unwin Paperbacks. An account of the life of Alan Turing, including his contribution to breaking the Enigma code.
Yutaka Taniyama and his time, by Goro Shimura,
Bulletin of the London Mathematical Society
21
(1989), 186â196. A very personal account of the life and work of Yutaka Taniyama.
Links between stable elliptic curves and certain diophantine equations, by Gerhard Frey,
Ann. Univ. Sarav. Math. Ser.
1
(1986), 1â40. The crucial paper which suggested a link between the TaniyamaâShimura conjecture and Fermat's Last Theorem.
Genius and Biographers: the Fictionalization of Evariste Galois, by T. Rothman,
Amer. Math. Monthly
89
(1982), 84â106. Contains a detailed list of the historical sources behind Galois's biographies, and discusses the validity of the various interpretations.
La vie d'Evariste Galois, by Paul Depuy,
Annales Scientifiques de l'Ecole Normale Supérieure
13
(1896), 197â266.
Mes Memoirs
, by Alexandre Dumas, 1967, Editions Gallimard.
Notes on Fermat's Last Theorem
, by Alf van der Poorten, 1996, Wiley. A technical description of Wiles's proof aimed at mathematics undergraduates and above.
An elementary introduction to the Langlands programme, by Stephen Gelbart,
Bulletin of the American Mathematical Society
10
(1984), 177â219. A technical explanation of the Langlands programme aimed at mathematical researchers.
Modular elliptic curves and Fermat's Last Theorem, by Andrew Wiles,
Annals of Mathematics
141
(1995), 443â551. This paper includes the bulk of Wiles's proof of the TaniyamaâShimura conjecture and Fermat's Last Theorem.
Ring-theoretic properties of certain Hecke algebras, by Richard Taylor and Andrew Wiles,
Annals of Mathematics
141
(1995), 553â572. This paper describes the mathematics which was used to overcome the flaws in Wiles's 1993 proof.
You can find a set of websites about Fermat's Last Theorem on Simon Singh's website:
[http://www.simonsingh.com]
The pagination of this electronic edition does not match the edition from which it was created. To locate a specific passage, please use the search feature of your e-book reader.
Page numbers in
italic
refer to illustrations
Abel, Niels Henrik 3
absolute proof 21â7, 147
absurdities, mathematical 143, 341
Academy of Sciences, French 119, 238
prize for proving Fermat's Last Theorem 120â28
ACE (Automatic Computing Engine) 175
Adleman, Leonard 104
Adler, Alfred 2
Agnesi, Maria 109â10, 111, 119
Alexandria 47â9, 57â8, 109
Alexandrian Library 48â9, 57â8
Algarotti, Francesco 112
algorithms 81
amicable numbers 62â3
Anglin, W. S. 77
Annals of Mathematics
303
April fool e-mail 293â5
Arago, François 79
Arakelov, Professor S. 254
Archimedes 48, 112
Aristotle 59
arithmetic algebraic geometrists 254â5
Arithmetica
(Diophantus) 42, 57, 58, 60, 61, 62
Clément-Samuel Fermat's edition
68â9
, 70
and elliptic equations 184
Fermat's marginal notes 62, 66â7, 70, 89
Latin translation
56
, 61, 62
and Pythagorean triples 65
axioms 21, 149, 155, 156
of arithmetic 342â3
consistency of 159â60
Babylonians 7â8, 20, 59
Bachet de Méziriac, Claude Gaspar 61â2
Latin translation
of Arithmetica 56
, 61, 62
Problèmes plaisants et delectables
61
weighing problem 61, 337â8
Barnum, P. T. 138
Bell, Eric Temple 6, 30, 33, 39, 73, 115
Bernoulli family 79â80
birthdays, shared, probability of 44â5
Bombelli, Rafaello 93â4
Bonaparte, Napoleon 117, 124, 232, 234
Bourg-la-Reine 232, 234, 238
Brahmagupta 59
bridges, mathematical 212
Bulletin of the London Mathematical Society
207
calculus 18, 46â7
Cantor, Georg 101â2
Cardano, Girolamo 40â41
Carroll, Lewis 138
Cauchy, Augustin Louis 120â28,
122
, 238, 239
chessboard, mutilated, problem of 24â6
Chevalier, Auguste 245, 248
Chudnovsky brothers 51
Churchill, Sir Winston Leonard Spencer 174
cicadas, life-cycles 106â7
Circle Limit IV
(Escher)
200
, 201
City of God, The
(St Augustine) 12
Clarke, Arthur C. 23
clock arithmetic 185â8
closed groups 250â51
Coates, John 180,
182
, 183, 189, 211,226,229, 260, 266,270, 284, 303â4
code breaking 103â5, 168, 170â75
Cohen, Paul 162â3
Colussus (computer) 175
commutative law of addition 149
completeness 91â2, 149â50, 160
complex numbers 95, 126
computers
early 175, 176
unable to prove Fermat's Last Theorem 177â8
unable to prove TaniyamaâShimura conjecture 231
conjectures 72
unifying 305
Constantinople 60
continuum hypothesis 163
contradiction, proof by 49â50, 53â4, 155
Conway, Professor John H. 291
Coolidge, Julian 39
cossists 40
counting numbers 11
Cretan paradox 161
Croton, Italy 9, 27â8
cryptography 103â5, 168, 170â75
crystallography 199, 310
cubic equations 237
Curiosa Mathematica
(Dodgson) 138
Cylon 27â8
d'Alembert, Jean Le Rond 96
Dalton, John 22
Darmon, Henri 294, 295
Deals with the Devil
74
defective numbers 11
slightly 13
Descartes, René 41, 42, 63, 249
Deuring 192
Devil and Simon Flagg, The
37, 74
d'Herbinville, Pescheux 243, 247, 248
Diderot, Denis 82â3
differential geometry 254, 256
Diffie, Whitfield 104
Digby, Sir Kenelm 38, 64
Diophantine problems 57
Diophantus of Alexandria 55, 57
riddle of his age 55, 57, 336â7
Diophantus' Arithmetica Containing Observations by P. de Fermat 68â9
, 70
Dirichlet, Johann Peter Gustav Lejeune 116, 127, 188
disorder parameters 140â42
Disquisitiones arithmeticae
(Gauss) 115
Dodgson, Reverend Charles 138
domino effect 232
dot conjecture problem 128â9, 339â40
du Motel, Stéphanie-Félicie Poterine 243, 248
Dudeney, Henry 138
Dumas, Alexandre 241â2
E
-series 188â9, 204â5, 211, 251â3
Ãcole Normale Supérieure 240
Ãcole Polytechnique 113â14, 236
economics, and calculus 46
Eddington, Sir Arthur 133
Egyptians, ancient 7â8
Eichler 195
Eiffel Tower 119
Einstein, Albert 17, 18, 110
electricity, and magnetism 204â5
Elements
(Euclid) 49, 53, 55, 125
elephant and tortoise fable 160
Elkies, Noam 179, 293â5
elliptic curves 183
elliptic equations 183â5, 187â9, 202
families of 261, 265
Frey's elliptic equation 216â19, 221â2
and modular forms 202, 204â5, 209â15, 305
Enigma code 168â74
Epimenides 161
Escher, Mauritz 201
Euclid
infinite number of Pythagorian triples proof 65, 338
infinity of primes proof 100â101
and perfect numbers 13
proves that 2 is irrational 53. 334â6
and
reductio ad absurdum
49, 53â4
unique factorisation proof 125
Euler, Leonhard 33, 63,
76
attempts to solve Fermat's Last Theorem 88â9, 90, 96
blindness and death 96â8
forsakes theology 79â80
and Königsberg bridge puzzle 83â5
phases of the moon algorithm 81â2, 97
proves existence of God 82â3
proves network formula 85â8
solves prime number theorem 70â71
Euler's conjecture 178â9
Evens, Leonard 284
Eves, Howard W. 225
excessive numbers 11
slightly 13â14
factorisation, unique 125â6
Faltings, Gerd 255â6, 257, 300
Fermat, Clément-Samuel 67, 70
Fermat, Pierre de
36
amateur mathematician 39
Arithmetica
61, 62, 65â7
calculus 46â7
career in civil service 37â9, 60â61
death 67
education 37
and elliptic equations 184
and Father Mersenne 41â2
ill with plague 38â9
observations and theorems 70â73
probability theory 43â4, 45â6
reluctant to reveal proofs 42
Fermat's Last Theorem
challenge of 72â4
computers unable to prove 177â8
Miyaoka's âproof 254â7
partial proofs by computer 177
Germain's method 115â17
n
= 3 (Euler) 90, 96, 99
n
= 4 (Fermat) 89â90, 98â9
n
= 5 (Dirichlet and Legendre) 116
n
= 7 (Lamé) 116
n
= irregular prime (Kummer and Mirimanoff) 176â7
publication of 70
and Pythagoras' equation 32, 65â7
scepticism as to existence of proof 128
simplicity of statement 6, 73
and TaniyamaâShimura conjecture 216â19, 221â3, 266
and undecidability 163â4, 166
why called âLast' 72
Wiles's proof
see
Wiles, Andrew
Fermatian triple 66
finite simple groups Flach, Matheus 260
four-colour problem 319â26
four-dimensional shapes 255â6
four-dimensional space 201
Fourier, Jean Baptiste Joseph 239
â14â15' puzzle 139â42, 219
fractions 11, 53, 90â91
Frege, Friedrich Ludwig Gottlob 150, 152, 154
Frey, Gerhard 215â19
Frey's elliptic equation 216â19, 221â2
friendly numbers 62â3
fundamental particles of matter 22â3
fundamental theorem of arithmetic 125
fundamental truths 148â9
Furtwängler, Professor P. 157, 159
Galileo Galilei 39
Galois, Ãvariste 3,
233
birth 232
duel with d'Herbinville 243, 247, 248
education 234â6, 240
final notes 243,
244
, 245,
246
, 247, 248
funeral 247â8
and group theory 250â51, 252â3
and quintic equations 238, 239â40, 245, 248â9
revolutionary career 238â9, 240â43
game theory 167â8, 343â4
Gardner, Martin 63, 146
Gauss, Carl Friedrich 114â15, 116, 117â18, 119, 179
geometry 7â8, 322
rubber-sheet 322
Gerbert of Aurillac 60
Germain, Sophie 107,
108
, 111â14, 119
career as a physicist 118â19
and Ãvariste Galois 240â41