文档介绍：Preface
It is now well known that Fermat’s last theorem has been proved. For
more than three and a half centuries, mathematicians — from the
great names to the clever amateurs — tried to prove Fermat’s famous
statement. The approach was new and involved very sophisticated
theories. Finally the long-sought proof was achieved. The arithmetic
theory of elliptic curves, modular forms, Galois representations, and
their deformations, developed by many mathematicians, were the
tools required plete the difficult proof.
Linked with this great mathematical feat are the names of TANI-
YAMA, SHIMURA, FREY, SERRE, RIBET, WILES, TAYLOR.
Their contributions, as well as hints of the proof, are discussed in
the Epilogue. This book has not been written with the purpose of
presenting the proof of Fermat’s theorem. On the contrary, it is writ-
ten for amateurs, teachers, and mathematicians curious about the
unfolding of the subject. I employ exclusively elementary methods
(except in the Epilogue). They have only led to partial solutions
but their interest goes beyond Fermat’s problem. One cannot stop
admiring the results obtained with these limited techniques.
Nevertheless, I warn that as far as I can see — which in fact is
not much — the methods presented here will not lead to a proof of
Fermat’s last theorem for all exponents.
vi Preface
The presentation is self-contained and details are not spared, so
the reading should be smooth.
Most of the considerations involve ordinary rational numbers and
only occasionally some algebraic (non-rational) numbers. For this
reason I excluded Kummer’s important contributions, which are
treated in detail in my book, Classical Theory of Algebraic Num-
bers and described in my 13 Lectures on Fermat’s Last Theorem
(new printing, containing an Epilogue about recent results).
There are already — and there will be more — books, mono-
graphs, and papers explaining the ideas and steps in the proof of
Fermat’s theorem. The