Math
The Proof of Fermat’s Last Theorem
Wiles, Andrew
“Modular elliptic curves and Fermat’s Last Theorem”
This paper does a lot of the work to prove that all elliptic curves are modular. A gap remained concerning Hecke algebras.
Taylor, Richard, and Andrew Wiles
“Ring-theoretic properties of certain Hecke algebras”
This paper fills in the gap in Wiles’s proof, completing the proof that all elliptic curves are modular.
Ribet, Ken
“On modular representations of Gal(Q/Q) arising from modular forms”
This paper proves Fermat’s Last Theorem, by connecting the fact that all elliptic curves are modular to FLT.
Analysis
Ahlfors, Lars V.
Complex Analysis
This is a classic textbook on complex analysis.
Buck, R. Creighton
Advanced Calculus
This is the classic text on calculus. Every advanced analysis book that needs a citation for some basic concept from calculus cites this book. It is difficult; far more advanced than a regular calculus textbook.
Lebesgue, Henri
Doctoral Thesis on Integration
Here is Lebesgue’s actual doctoral thesis (in French!) in which he first introduces the Lebesgue integral.
Rudin, Walter
Principles of Mathematical Analysis
The most famous/classic textbook on real analysis.
Spivak, Michael
Calculus
A classic undergraduate textbook. It’s really more of an introduction to real analysis than calculus.
Algebra
Artin, Michael
Algebra
A popular book on algebra. It’s at the level of advanced undergraduate or introductory graduate. It starts in an odd place (for me), matrix operations, and apparently emphasizes linear algebra throughout. I don’t think I like that as much, but it would probably be good to get comfortable with nonetheless.
Fraleigh, John
A First Course in Abstract Algebra
This was my first textbook in abstract algebra.
Stewart, Ian
Galois Theory
When I was learning Galois Theory, we used the first edition of this book, and it was utterly FILLED with errors. It drove me up the wall, and I was always complaining to my teacher Ken Ribet about it, which made him more annoyed with me than I was with Stewart. Not my finest hour. Nonetheless, this book is intended to be an easy-to-follow introduction specifically to Galois Theory, without having to go all the way through abstract algebra to get there. Here is the third edition; maybe the errors have been corrected.
Stewart, James
Calculus – Early Transcendentals
This is my original calculus textbook from way back in college!
Elliptic Curves
Serre, Jean-Pierre
A Course in Arithmetic
Serre was a big figure in the proof of Fermat’s Last Theorem.
Silverman, Joseph
The Arithmetic of Elliptic Curves
I don’t know anything about this book, but I believe it is a book about the arithmetic of elliptic curves.
Modular Forms
Miyake, Toshitsune
Modular Forms
A classic book on modular forms.
Shimura, Goro
Introduction to the Arithmetic Theory of Automorphic Functions
This is the classic textbook on modular forms. This book is probably where most mathematicians in the field first learned the topic. Fermat’s Last Theorem was proven by observing that all elliptic curves are modular, then showing that any solution to Fermat’s Last Theorem can be associated to an elliptic curve, and that that curve would not be modular. Hence, if it is true that all elliptic curves are modular, then it can not be true that there are any solutions to an+bn=cn when n > 2. It was in 1957 that Yutaka Taniyama and Goro Shimura first conjectured that all elliptic curves are modular, which became known as the Taniyama-Shimura conjecture. It is this conjecture that Andrew Wiles proved in 1995 (for “semi-stable” curves—that’s a technical but unimportant detail). This is the textbook that Goro Shimura wrote on the subject in 1971.
Topology
Munkres, James
Topology
This was my textbook in topology (when I should have been studying for law school!).
Statistics
Wasserman, Larry
All of Statistics: A Concise Course in Statistical Inference.
Nothing whatever to do with Fermat’s Last Theorem, this is a popular textbook on statistics.