Fermat’s Last Theorem: From Fermat to Wiles



When historians come to judge the mathematics of the twentieth century, I am confident that they will regard it as a golden age, for both the emergence of brilliant new ideas and the solution of longstanding problems (the two are, of course, not unrelated). In the latter category, Fermat’s Last Theorem (FLT) is neither the most ancient nor the latest example. In the late 1990s, Thomas Hales solved Kepler’s Sphere-Packing Problem, posed in 1611, and Grigori Perelman proved the Poincaré Conjecture, proposed in 1904. Of course, the Riemann Hypothesis, the Goldbach Conjecture, and other outstanding problems are still unresolved.


Elliptic Curve Elliptic Curf Integer Solution Diophantine Equation Unique Factorization 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    A. D. Aczel, Fermat’s Last Theorem: Unlocking the Secret of an Ancient Mathematical Problem, Four Walls Eight Windows, 1996.Google Scholar
  2. 2.
    W. W. Adams and L. J. Goldstein, Introduction to Number Theory, Prentice-Hall, 1976.Google Scholar
  3. 3.
    K. Barner, Paul Wolfskehl and the Wolfskehl Prize, Notices Amer. Math. Soc. 44 (1997) 1294–1303.MATHMathSciNetGoogle Scholar
  4. 4.
    I. G. Bashmakova, Diophantus and Diophantine Equations (translated from the Russian by A. Shenitzer), Math. Assoc. of America, 1997.Google Scholar
  5. 5.
    Z. I. Borevich and I. R. Shafarevich, Number Theory, Academic Press, 1966.Google Scholar
  6. 6.
    N. Bourbaki, Elements of the History of Mathematics, Springer-Verlag, 1994.Google Scholar
  7. 7.
    J. Buhler, R. Crandell, R. Ernvall, and T. Metsänkylä, Irregular primes and cyclotomic invariants to four million, Math. Comp. 61 (1993) 151–153.CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    B. Cipra, New heights for number theory. In What’s Happening in the Mathematical Sciences, Amer. Math. Soc., Vol. 5, 2000, pp. 3–11.Google Scholar
  9. 9.
    B. Cipra, Princeton mathematician looks back on Fermat proof, Science 268 (26 May 1995) 1133–1134.Google Scholar
  10. 10.
    B. Cipra, A truly remarkable proof. In What is Happening in the Mathematical Sciences, Amer. Math. Soc., Vol. 4, 1994, pp. 3–7.Google Scholar
  11. 11.
    D. A. Cox, Introduction to Fermat’s Last Theorem, Amer. Math. Monthly 101 (1994) 3–14.CrossRefMATHMathSciNetGoogle Scholar
  12. 12.
    H. Darmon, A proof of the full Taniyama-Shimura-Weil Conjecture is announced, Notices Amer. Math. Soc. 46 (1999) 1397–1401.MATHMathSciNetGoogle Scholar
  13. 13.
    K. Devlin, F. Gouvêa, and A Granville, Fermat’s Last Theorem, a theorem at last, MAA Focus 13 (August 1993) 3–4.Google Scholar
  14. 14.
    J. P. Dowling, Fermat’s Last Theorem, Math. Mag. 59 (1986) 76.CrossRefMathSciNetGoogle Scholar
  15. 15.
    H. M. Edwards, Fermat’s Last Theorem: A Genetic Introduction to Algebraic Number Theory, Springer-Verlag, 1977.Google Scholar
  16. 16.
    S. Gelbart, An elementary introduction to the Langlands Program, Bulletin Amer. Math. Soc. 10 (1984) 177–219.CrossRefMATHMathSciNetGoogle Scholar
  17. 17.
    D. Goldfeld, Beyond the Last Theorem, The Sciences 36 (March/April 1996) 34–40.Google Scholar
  18. 18.
    F. Gouvêa, A marvellous proof, Amer. Math. Monthly 101 (1994) 203–222.CrossRefMATHMathSciNetGoogle Scholar
  19. 19.
    K. Ireland and M. Rosen, A Classical Introduction to Modern Number Theory, Springer-Verlag, 1982.Google Scholar
  20. 20.
    I. Kleiner, The roots of commutative algebra in algebraic number theory, Math. Mag. 68 (1995) 3–15.CrossRefMATHMathSciNetGoogle Scholar
  21. 21.
    G. Kolata, Andrew Wiles: A math whiz battles 350-year-old puzzle, Math. Horizons (Winter 1993) 8–11.Google Scholar
  22. 22.
    J. Kramer, Über den Beweis der Fermat-Vermutung II, El. Math. 53 (1998) 45–60.CrossRefMATHGoogle Scholar
  23. 23.
    J. Kramer, Über die Fermat-Vermutung, El. Math. 50 (1995) 12–25.MATHGoogle Scholar
  24. 24.
    B. Mazur, Number theory as gadfly, Amer. Math. Monthly 98 (1991) 593–610.CrossRefMATHMathSciNetGoogle Scholar
  25. 25.
    R. Murty, A long standing mathematical problem is solved: Fermat’s Last Theorem, Can. Math. Soc. Notes 25 (Sept. 1993) 16–20.Google Scholar
  26. 26.
    H. Pollard and H. G. Diamond, The Theory of Algebraic Numbers, 2nd ed., Math. Assoc. of Amer., 1975.Google Scholar
  27. 27.
    P. Ribenboim, Fermat’s Last Theorem for Amateurs, Springer-Verlag, 1999.Google Scholar
  28. 28.
    P. Ribenboim, 13 Lectures on Fermat’s Last Theorem, Springer-Verlag, 1979.Google Scholar
  29. 29.
    K. A. Ribet and B. Hayes, Fermat’s Last Theorem and modern arithmetic, American Scientist 82 (March-April 1994) 144–156.Google Scholar
  30. 30.
    J. H. Silverman, A Friendly Introduction to Number Theory, Prentice Hall, 1997.Google Scholar
  31. 31.
    J. H. Silverman and J. Tate, Rational Points on Elliptic Curves, Springer-Verlag, 1992.Google Scholar
  32. 32.
    S. Singh, Fermat’s Enigma: The Quest to Solve the World’s Greatest Mathematical Problem, Penguin, 1997.Google Scholar
  33. 33.
    S. Singh and K. Ribet, Fermat’s last stand, Scientific Amer. 277 (November 1997) 68–73.CrossRefGoogle Scholar
  34. 34.
    J. Stillwell, Mathematics and Its History, 2nd ed., Springer-Verlag, 2002.Google Scholar
  35. 35.
    A. van der Poorten, Notes on Fermat’s Last Theorem, Wiley, 1996.Google Scholar
  36. 36.
    S. M. Wagstaff, The irregular primes to 125000, Math. Comp. 32 (1978) 583–591.MATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsYork UniversityTorontoCanada

Personalised recommendations