Mathematics reading recommendations

This page includes recommendations largely intended for casual reading that nonetheless build subject-specific intuition or provide insight into the discipline. For recommendations better suited to formal learning, see mathematics learning recommendations.

About mathematics as a discipline

These books provide excellent insight into the kind of work that mathematicians do, without requiring the readers to grasp a lot of mathematics.

Book	Author	ISBN and purchase links
Mathematics: A Very Short Introduction	Timothy Gowers	ISBN 978-0192853615, Amazon paperback
The Mathematical Experience	Philip J. Davis, Reuben Hersh	ISBN 978-0395929681, Amazon paperback
Love and Math: The Heart of Hidden Reality	Edward Frenkel	ISBN 978-0465050741, Amazon hardcover
Introduction to Mathematical Thinking	Keith Devlin	ISBN 978-0615653631, Amazon paperback

Mathematical history

Further information: Books about mathematics history

Book	Author	ISBN and purchase links	Why we're recommending it
The Music of the Primes: Searching to Solve the Greatest Mystery in Mathematics	Marcus du Sautoy	ISBN 978-0062064011, Amazon paperback	This book is one of the best books for a general audience on the history 19th and 20th century mathematical research. It focuses on the Riemann Hypothesis, which is one of the most famous unsolved mathematical problems, but manages to tie together many different threads, which offers the reader a sense of perspective. Art of Problem Solving founder Richard Rusczyk named it one of his favorite math popularization books. The book requires no mathematical background.
The Code Book: The Science of Secrecy from Ancient Egypt to Quantum Cryptography	Simon Singh	ISBN 978-0385495325, paperback	This book gives a history of the mathematical field of cryptography, which has affected society on many levels. Students who have learned first year high school algebra are probably equipped to understand the book.
Journey through Genius: The Great Theorems of Mathematics	William Dunham	ISBN 978-0140147391, Amazon paperback	This book presents highlights from the history of mathematics. In doing so, it gives a sense for mathematics as a human intellectual accomplishment. A number of mathematicians remember it as their favorite math book from their high school days. It's accessible to students who have learned most of high school geometry and second year algebra.
Euler: The Master of Us All	William Dunham	ISBN 978-0883853283, Amazon paperback	This book is a survey of some of the most significant work of Leonhard Euler, who's one greatest mathematicians who ever lived. It's accessible to students who have learned calculus.

Higher math

Book	Author	ISBN and purchase links	Why we're recommending it
Concrete Mathematics: A Foundation for Computer Science	Ronald L. Graham, et. al.	ISBN 978-0201558029, Amazon paperback	This is a book about discrete math. It's good preparation for certain parts of advanced computer programming.
The Shape of Space	Jeffrey Weeks	ISBN 978-0824707095, Amazon paperback	This book introduces the reader to hyperbolic geometry in two and three dimensions, giving the reader a glimpse of modern geometry. It's accessible to readers who have learned high school geometry
Integers, Polynomials, and Rings: A Course in Algebra	Ronald S. Irving	ISBN 978-0387201726, Amazon paperback	This is a very gentle introduction to the mathematical field called abstract algebra. It's accessible to a high schooler who has learned second year high school algebra, and has some very pretty material.
A Primer of Analytic Number Theory: From Pythagoras to Riemann	Jeffrey Stopple	ISBN 978-1853710162, Amazon paperback	This is an introduction to one of the central areas of mathematical research. It's accessible to students who have learned calculus, and will help reinforce your understanding of calculus.