“This will never be a civilized country until we expend more money for books than we do for chewing gum.” – Elbert Hubbard

Here are some books that I’ve found to be especially fascinating/enlightening/readable. Some of them are reference books and not meant to be read cover-to-cover, but some can be read like a novel. Within each category, I’ve tried to organize the books according to their (approximate) level of difficulty, starting with the easiest. This list only includes my favorite mathematical books, so I’ll add a caveat: it is essential to read papers too! At some point in the future I might attempt to expand this list to include must-read papers in my area. But for now, here are a few recommendations from my shelf:


Mathematics for the non-Mathematician:

My Best Mathematical and Logic Puzzles, Martin Gardner

Gödel’s Proof, Ernest Nagel

The Colossal Book of Mathematics, Martin Gardner

A Mathematician’s Apology, G. H. Hardy

Calculus Made Easy, Silvanus P. Thompson

Gödel, Escher, Bach: An Eternal Golden Braid, Douglas Hofstadter

Geometry and the Imagination, David Hilbert and Stephan Cohn-Vossen

Mathematics: From the Birth of Numbers, Jan Gullberg


Topology, Measure Theory, Dynamics, and Analysis:

Topology, James Munkres

Counterexamples in Topology, Steen and Seebach

Measure, Topology, and Fractal Geometry, Gerald Edgar

Visual Complex Analysis, Tristan Needham

Principles of Mathematical Analysis, Walter Rudin

The Elements of Integration and Lebesgue Measure, Robert Bartle

Measure and Category, John Oxtoby

An Introduction to Chaotic Dynamical Systems, Robert Devaney

General Topology, Ryszard Engelking

The Handbook of Set-Theoretic Topology

Open Problems in Topology


Set Theory and Foundations:

Mathematical Logic (Parts I and II), Cori and Lascar

A Shorter Model Theory, Wilfrid Hodges

Set Theory: An Introduction to Independence Proofs, Kenneth Kunen

The Axiom of Choice, Thomas Jech

Multiple Forcing, Thomas Jech

Classical Descriptive Set Theory, Alexander Kechris

Set Theory: on the Structure of the Real Line, Baroszynski and Judah

The Higher Infinite, Akihiro Kanamori

Set Theory, Thomas Jech

The Handbook of Set Theory


Other Books:

Mathematics and its History, John Stillwell

Greek Mathematical Works (parts I and II)

Geometry: Euclid and Beyond, Robin Hartshorne

On Numbers and Games, John Conway

Lecture on the Hyperreals, Robert Goldblatt

Graph Theory, Frank Harary

Elements of Information Theory, Cover and Thomas

Ramsey Theory, Graham, Rothschild, and Spencer

Algebra in the Stone-Cech Compactification, Hindman and Strauss

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