[Turkmath:6890] Güzel ve mühim bulmasam paylaşmazdım:

[yilmaz akyildiz]

Why don't Andrew Wiles and his colleagues write an expanded book of 1000
pages, explaining his proof step by step to everybody?


Actually, Wikipedia has an article about Wiles' proof of Fermat's Last
Theorem, and it contains an overview of the proof. In principle, you could
go through it step by step and thereby learn the proof.

However, if you do not have at least an undergraduate education in
mathematics, it will take you anywhere from 5 to 10 years of intensive
study in order to decompose this theorem into pieces that you can
understand.

This is because Wiles' proof requires the study of modular elliptic curves,
which require knowledge of both algebraic and analytic number theory.

Algebraic number theory of that level requires knowledge of algebraic
extensions, Galois extensions, Galois cohomology, and algebraic geometry.
To understand those, you need to have already studied some commutative ring
theory, algebraic topology, Galois groups, basic number theory and category
theory. This means that you already need to have a strong grounding in
group theory and point set topology.

Studying analytic number theory won't be any easier. You need to understand
what Hecke eigenforms are, so you better know at least a little
representation theory, and you should absolutely have a very strong
background in automorphic forms. To do that, you again need to have a
strong ring/group theory background, but you will also need to know
Fourier, complex, and some functional analysis. To understand those, you
need real analysis, and to understand that you need to have studied
calculus.

This isn't meant to be exhaustive list, by the way---the full proof might
very well contain other bits of mathematical theory that I have missed here
(I do not study modular elliptic curves, and so I have not personally read
Wiles' proof, even though I have a very rough idea of the sort of
ingredients that go into it).

If the book really pushed to only include material directly relevant to
proving the theorem, you could maybe push it to be just a 1000 pages---but
this would come at the cost that it would become completely unintelligible.
If you wanted a book that was at least somewhat readable, I would guess
that it would need to be around 10,000 pages or more.

Unfortunately, no one other than the author(s) would ever read it. I don't
think even Wiles' mother could force herself to slog through all of that...
......
The book by Simon Singh does a nice job for the layman:

https://images.app.goo.gl/oKiyvYY4bWT4AE5Q7

Yayınevine toplu sipariş vermiş ve öğrencilerime bu kitabı aldırmış BU ve
GS daki  derslerimde yan kitap olarak okutmustum. Çok tavsiye eder,
çevirenini de kutlarım.

…...
Bir başkası demiş ki:
I actually thought that the proof was not that hard to follow. But then
someone pointed out to me that I was reading a proof of the Pythagorian
Theorem….
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