Fermat's Last Theorem
Singh (Simon)
Source: Singh (Simon) - Fermat's Last Theorem
Paper - Abstract

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Contents

    Forward by John Lynch – ix
    Preface – xvii
  1. ’I Think I’ll Stop Here’ – 1
    • 23 June 1933, Cambridge
    • The Last Problem
      … Book by E.T. Bell
    • Everything is Number
      … Pythagoras
    • Absolute Proof
      … The Problem of the Mutilated Chessboard
    • An Infinity of Triples
      … Integral solutions of Pythagoras’ Theorem
    • From Pythagoras’ Theorem to Fermat’s Last Theorem
      … There are no integer solutions for n>2 to equation xn + yn = zn
  2. The Riddler – 37
    • Fermat
    • The Evolution of Number Theory
    • Diophantus of Alexandria
    • Birth of a Riddle
    • The Marginal Note
    • The Last Theorem Published at Last
  3. A Mathematical Disgrace – 77
    • The Mathematical Cyclops
      … Euler
    • The Konigsberg Bridge Problem
    • V + R – L = 1
    • A Petty Pace
      … Proofs for n = 3, 4, …
    • Monsieur Le Blanc
      … Sophie Germain
    • Gauss
    • The Sealed Envelopes
      … Gabriel Lame, Augustin Cauchy & Ernst Kummer
  4. Into Abstraction – 133
    • Paul Wolfskehl
    • The Era of Puzzles, Riddles and Enigmas
      … Sam Lloyd and the 14-15 Puzzle
    • The Foundations of Knowledge
      … David Hilbert, Gottlob Frege, Bertrand Russell
      … Kurt Godel’s two theorems of undecidability
      … The liar (and other) paradoxes
    • The Compulsion of Curiosity
    • The Brute Force Approach
      … Alan Turing, Bletchley Park
    • The Graduate
      … Andrew Wiles & John Coates
      … Clock arithmetic
      … Elliptic Equations
  5. Proof by Contradiction – 191
    • Yutaka Taniyama & Goro Shimura
    • Modular Forms and symmetry
    • Wishful Thinking
      … The Taniyama-Shimura Conjecture
    • Death of a Genius
    • Philosophy of Goodness
      … Robert Langlands’ Unification Conjectures
    • The Missing Link
      … Frey’s Elliptic Equation
      … Ken Ribet
  6. The Secret Calculation – 225
    • The Attic Recluse
    • Duelling with Infinity
    • Evariste Galois
    • Toppling the First Domino
    • ’Fermat’s Theorem Solved?’
      … Yoichi Miyaoka’s “proof” using Differential Geometry
    • The Dark Mansion
    • The Method of Kolyvagin & Flach
      … Nick Katz
    • The Lecture of the Century
    • The Aftermath
  7. A Slight Problem – 277
    • The Carpet Fitter
    • The Nightmare Email
      … Naom Elkies’ “Counter-example” (April Fool)
    • Richard Taylor
    • The Birthday Present
      … Iwasawa Theory
  8. Grand Unified Mathematics – 303
    • Great Unsolved Problems
      … Perfect Numbers
      … Goldbach’s Conjecture (every even number is the sum of two primes)
      … Kepler’s Sphere-packing problem
    • Silicon Proofs
      … The Four-colour problem
    • The Prize
  9. Appendices – 333
    • The Proof of Pythagoras’ Theorem
    • Euclid’s Proof the SQRT(2) is Irrational
    • The Riddle of Diophantus’ Age
    • Bachet’s Weighing Problem
    • Euclid’s Proof that there are an Infinite Number of Pythagorean Triples
    • The Proof of the Dot Conjecture
    • Straying into Absurdity
      … “Proof” that 2=1
    • The Axioms of Arithmetic
    • Game Theory and the Truel
    • An Example of Proof by Induction
  10. Suggestions for Further Reading – 347

Text Colour Conventions (see disclaimer)

  1. Blue: Text by me; © Theo Todman, 2020
  2. Mauve: Text by correspondent(s) or other author(s); © the author(s)



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