Description
Book SynopsisAround 1637, the French jurist Pierre de Fermat scribbled in the margin of his copy of the book Arithmetica what came to be known as Fermat''s Last Theorem, the most famous question in mathematical history. Stating that it is impossible to split a cube into two cubes, or a fourth power into two fourth powers, or any higher power into two like powers, but not leaving behind the marvelous proof he claimed to have had, Fermat prompted three and a half centuries of mathematical inquiry which culminated only recently with the proof of the theorem by Andrew Wiles.
This book offers the first serious treatment of Fermat''s Last Theorem since Wiles''s proof. It is based on a series of lectures given by the author to celebrate Wiles''s achievement, with each chapter explaining a separate area of number theory as it pertains to Fermat''s Last Theorem. Together, they provide a concise history of the theorem as well as a brief discussion of Wiles''s proof and its implications. Requiring li
Table of ContentsQuasi-Historical Introduction.
Remarks on Unique Factorization.
Elementary Methods.
Kummer's Arguments.
Why Do We Believe Wiles?
More Quasi-History.
Diophantus and Fermat.
A Child's Introduction to Elliptic Functions.
Local and Global.
Curves.
Modular Forms.
The Modularity Conjecture.
The Functional Equation.
Zeta Functions and L -Series.
The ABC-Conjecture.
Heights.
Class Number of Imaginary Quadratic Number Fields.
Wiles' Proof.
Appendices.
Index.
