From: bobs@rsa.com
Subject: Re: Wiles' proof of FLT
Date: Wed, 27 Jan 1999 14:39:35 GMT
Newsgroups: sci.math
Keywords: What to study to understand Wiles' proof

In article <36ADFF7D.D7E98F06@rdg.ac.uk>,
  Kevin Anderson <@rdg.ac.uk> wrote:
> A survey question: How many people on this NG understand the proof? (I
> don't.)

I have read it 4 times. I can lay claim to understanding 10 to 15% of the
proof.

>
> For those that do, what books would you recommend to start off learning
> about  the methods used in Wiles' proof?

I mean no insult, but if you don't have sufficient background to already know
the areas of math that are involved, then the books that will be required
will probably number in the dozens.

Start with Rotman's Homological Algebra  and Shafarevich's Algebraic
Geometry. Also Apostol's Intro to Analytic No. Theory,	Vol 2.	(for the
elementary stuff about modular forms) Toss in Koblitz's book on Elliptic
Curves and Modular Forms  and Silverman's two books on Arithmetic of Elliptic
Curves as well.  Add  Serre's "A Course in Arithmetic"	for an understanding
of p-adic rings/fields.  I don't know of any books covering Mazur's  Ring 
Deformation theory. Nor of a good book on Hecke Algebras.

We are talking a minimum of 5 years of intensive graduate-level study for
 someone who already has a high level of mathematical maturity.  Keep in
mind that Wiles taught a course on some of the stuff in the proof and his
grad students all dropped out; it was too tough.

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