Cover image for Fermat's last theorem for amateurs
Title:
Fermat's last theorem for amateurs
Author:
Ribenboim, Paulo.
Personal Author:
Publication Information:
New York : Springer, [1999]

©1999
Physical Description:
xii, 407 pages : illustrations ; 25 cm
Language:
English
Subject Term:
ISBN:
9780387985084
Format :
Book

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QA244 .R53 1999 Adult Non-Fiction Non-Fiction Area
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Summary

Summary

In 1995, Andrew Wiles completed a proof of Fermat's Last Theorem. Although this was certainly a great mathematical feat, one shouldn't dismiss earlier attempts made by mathematicians and clever amateurs to solve the problem. In this book, aimed at amateurs curious about the history of the subject, the author restricts his attention exclusively to elementary methods that have produced rich results.


Reviews 1

Choice Review

In Maine they tell this joke: A 75-year-old man answers the door and sees a beautiful 25-year-old woman. "Oh, I must have the wrong place," she says; "Right place, but you're just 50 years too late," is his reply. And just so, this beautiful book arrives decades too late, for it barely tries to sketch Wiles's recent monumental proof of Fermat's Last Theorem (or even the 150-year-old partial success of Kummer and the 90-year-old criterion of Wieferich), but merely documents all that mathematicians had achieved up to Wiles's time by strictly elementary means. Call it an obsessive survey of a three-and-half-century obsession; but will new generations of mathematicians, amateur or professional, share the obsession now with the problem already solved? Sadly, very few mathematicians as yet understand Wiles's proof thoroughly, and despite a flurry of publication, no one seems ready to bring Wiles even to the common mathematician, much less to the common person. (As for Kummer, see Ribenboim's earlier 13 Lectures on Fermat's Last Theorem, CH, Jun'80.) Like a Rachmaninoff piano concerto, this most typical production of an epoch arrives after the close of that era. Highly recommended, though predicting the usage it will see seems impossible. Upper-division undergraduates and up. D. V. Feldman; University of New Hampshire


Table of Contents

The Problem
Special Cases
4 Interludes
Algebraic Restrictions on Hypothetical Solutions
Germain's Theorem
Interludes 5 and 6
Arithmetic Restrictions on Hypothetical Solutions and on the Exponent
Interludes 7 and 8
Reformulations, Consequences, and Criteria
Interludes 9 and 10
The Local and Modular Fermat Problem
Epilogue
Appendix A References to Wrong Proofs
Appendix B General Bibliography
Name Index
Subject Index