Accessible Mathematical Texts for the Curious
Bold texts are very highly recommended!
A * indicates that the text has more technical information and might be more challenging for readers
without a background in mathematics.
Overviews / Multiple Subjects
The Joy of X - Steven Strogatz
Series of digestible articles on multiple subjects in math, adapted from Strogatz’ articles
in the NYTimes. Strogatz has a gift of bringing mathematics down to the real world. Any reader
can find a lot of easy and understandable information here.
The Mathematical Experience - P.J. Davis & R. Hersh
What is it that mathematicians actually do? People think of mathematicians as supremely
sure and smart, when the work of mathematicians is founded on analogy and guesswork. The
authors analyze proofs, Euclid, Cantor, and the idea of aesthetics in mathematics.
What Is Mathematics? - R. Courant & H. Robbins
What people learn as mathematics in school is often boring and disconnected from the
work that mathematicians actually do. This wide-ranging book touches on a number of subjects
and looks at them from a perspective of wonder, rather than boring memorization.
From Here to Infinity - Ian Stewart
An overview of many big ideas and enigmatic problems in mathematics. Covers some of
the major breakthroughs that happened in the years before it was published in 1996.
Beyond Numeracy, J.A. Paulos
A follow-up to Innumeracy - Paulos writes a light introduction to many topics in
mathematics, intended for the non-technical reader.
*The Calculus of Friendship - Steven Strogatz
A series of letters between Strogatz and his high school math teacher, in which they
discuss everything from calculus problems to divorce. Strogatz uses examples from nature to
analyze calculus, the science of change and motion.
The Penguin Dictionary of Curious and Interesting Numbers, D. Wells
A dictionary-style overview of interesting numbers and sequences. It contains short
entries on a variety of numbers and patterns.
Group Theory in the Bedroom, and Other Mathematical Diversions - Brian Hayes
Collection of charming, accessible essays about various topics in modern mathematics.
“If you ever lie awake pondering the complexities of the universe, you may have a soul buddy in
Brian Hayes.”
History of Mathematics
A History of Mathematics - Carl B. Boyer & Uta C. Merzbach
A broad history of mathematics, ranging from Greeks, to Chinese, Arabic, European, and
American mathematicians. It provides a history of the mathematicians themselves as well as
distilling the mathematical ideas to their most digestible forms. It is a useful resource for
teachers wishing to show the story behind mathematical discovery.
Makers of Mathematics, S. Hollingdale
A readable history of mathematics as seen through the lens of great mathematicians.
Hollingdale analyzes mathematics through the lives and works of Archimedes, Descartes,
Fermat, Pascal, and many more. The emphasis is biographical, but mathematical ideas are also
introduced and explored.
Mathematics Education
Rethinking Mathematics - E. Gutstein & B. Peterson
Powerful account of modern mathematics education that challenges teachers to radically
change the way that we approach teaching mathematics. The book brings social justice to the
forefront in the mathematics classroom, rather than making it a one-off activity.
A Mathematician’s Apology - G.H. Hardy
An essay from 1940 that provides an insight into the workings of a mathematician’s
mind, the beauty of mathematics, and a self-justification for Hardy of his work as a
mathematician.
A Mathematician's Lament - Paul Lockhart
An essay about how school mathematics divorces the study of math from the joy of math.
It makes an analogy to art, music, and poetry, where students are encouraged to discover and
create before learning abstract principles. In mathematics classes, students learn the abstract
without context and without playing. Lockhart encourages math classes to be flipped, so that
students have context with which to understand the material.
Innumeracy, John Allen Paulos
A discussion of mathematical illiteracy and the dangers of our misconceptions of many
fundamental concepts in mathematics.
Proofs Without Words - Roger B. Nelsen
Visual representations of mathematical ideas that will help visual learners in the
classroom. The book is divided into different sections which focus on different domains of
mathematics. These visual proofs can supplement analytic proofs in the classroom.
Mathematics in Nature
Is God a Mathematician - Mario Livio
The book is an analysis of the lives and accomplishments of great mathematicians,
providing a lens through which to understand the universe. The central question is: if
mathematics so well explains the universe, is it really an abstract construction of the human
mind? Do we see God’s work in mathematics?
Five Equations that Changed the World - M. Guillen
Each chapter focuses on a different law of physics that governs natural phenomena. The
book analyzes how mathematical ideas predict and describe natural phenomena which are
difficult to analyze without modern mathematics.
It Must Be Beautiful - Ed. G Farmelo
A collection of essays on equations in modern science. The central idea is that nature
must be governed by simple and beautiful ideas which are all related. Nature is too ordered to
not be governed by beautiful equations.
Statistics & Economics
The Signal and the Noise, Nate Silver
Silver has made a career out of using big data and mathematical modeling to accurately
predict things. In this book he examines good and bad predictions and the public’s faulty
understanding of probability and uncertainty.
Freakonomics, S. Dubner & S. Leavitt
Easy, digestible applications of math and statistics to unusual situations. Dubner and
Leavitt analyze gang economics, abortion rates, and a number of other real-world situations. A
great book that shows how math can be used in a variety of contexts.
Networks, Crowds & Markets - David Easley and Jon Kleinberg
Today’s world is more connected than ever before. Using mathematics, this book
explores the connections in today’s global economy and internet. The book analyzes how
connectedness affects society, economies, and epidemics, using applied mathematics.
The (Mis)behavior of Markets: A Fractal View of Financial Turbulence - Benoit Mandelbrot &
Richard Hudson
The mathematics behind modern financial markets through chaos theory, written by one
of the great modern mathematicians.
Mathematics for Young Readers
Sir Cumference series - Cindy Neuschwander
Sir Cumference and Lady Di of Ameter take young readers on a journey through
mathematical ideas, framed in an King Arthur-esque world. As the knight valiantly tries to save
Lady Di, he encounters mathematical problems along the way. These books are great for young
kids, as they gently introduce the mathematics in the context of an engaging picture book.
What’s Your Angle, Pythagoras - Julie Ellis
Similar to Sir Cumference, this picture book teaches mathematical concepts in the
context of a story. Young Pythagoras is always getting in trouble, but he discovers the theorem
that bears his name on a trip to Egypt.
Fractals, Googols, and Other Mathematical Tales - Theoni Pappas
Pappas introduces mathematical concepts in a light-hearted way, personifying
mathematical concepts and making them part of a story. Pappas follows Penrose, a cat, through
his adventures through the mathematical world.
Analysis of a Single Number or Concept
Fermat’s Engima - Simon Singh
History of the 350 year drive to prove Fermat’s Last Theorem, a remarkable result that
Fermat established but did not prove. Hundreds of mathematicians have labored to prove the
theorem without success.
The Music of the Primes - Marcus du Sautoy
An engaging read about the history of number theory and the ongoing attempt to find a
formula that predicts where prime numbers will appear. Although there are infinitely many
primes, the distribution of primes is, so far, impossible to predict.
*The Universe in Zero Words - D. Mackenzie
A large collection of equations and numbers that have been enormously influential in the
development of modern mathematics and science. Each equation has only about 1000 words
about it, so it could be a good light introduction to many different concepts, but the language is
rather technical sometimes.
A History of Pi - P. Beckmann
A non-technical introduction to pi and the many places it shows up in the natural world
and in mathematical laws.
Zero - Charles Seife
Seife presents a historical overview of zero, from its innocent beginnings, to its banned
existence in the middle ages, to its complicated relation with modern physics. The idea of zero is
so fundamental to modern mathematics, but so difficult to reconcile with other theoretical
sciences.
e: The Story of a Number - Eli Maors
The importance of e and where it appears in natural and manmade objects.
The Equation That Couldn't Be Solved - M. Livio
The history of the mathematical laws behind symmetry and the development of group
theory.
Finding Moonshine: A Mathematician’s Journey Through Symmetry, Marcus Du Sautoy
Why symmetry is inherently pleasing and the discovery of mathematical principles
behind it.
Biographies
Surely You’re Joking, Mr Feynman, R.P. Feynman
Extremely engaging and fun autobiography of one of the greatest modern physicists. He
tells not only how his education and intelligence shaped his career, but also of his exploits
breaking into his colleague’s safes and picking up women.
The Man Who Knew Infinity, R. Kanigel
Biography of the Indian mathematician Srinivasa Ramanujan, an unschooled and selftaught mathematical genius from the slums of Madras. Ramanujan collaborated with one of the
pre-eminent mathematicians in England and left behind a legacy that still holds fresh ideas.
The Man Who Loved Only Numbers, Paul Hoffman
This biography of the great mathematician Paul Erdos shows the quirks and madness
behind his mathematical work. He would show up on other mathematician’s doorsteps and live
there for several weeks or months while he solved a mathematical problem. Upon solving the
problem, he would move on to the next mathematician.
My Brain is Open: The Mathematical Journeys of Paul Erdös - Bruce Schecter
Another biography of the life of Paul Erdos, detailing his collaborations with various
mathematicians and the ideas Erdos explored. The title, “My Brain is Open,” is what Erdos
would say when he appeared on a mathematician’s doorstep.
The Archimedes Codex - R. Netz & W. Noel
The story of a medieval prayer book that contains many of Archimedes’ lost works.
The Strangest Man - Graham Farmelo
Biography of Paul Dirac, the youngest theoretician to ever win the Nobel Prize in
Physics. Dirac, a contemporary of Einstein, was an eccentric man who was quite brilliant and
legendary. This book draws upon previously undiscovered letters and archives to describe his
life and personality.
In Code - Sara Flannery
The memoir of Sara Flannery, whose groundbreaking research on internet cryptography
led to her international fame as mathematician at the age of 16.
Chaos Theory
The Drunkard’s Walk, Leonard Mlodinow
A math book you actually can’t put down - Mlodinow writes about our innate inability to
comprehend randomness and use it in predictions and uncertainty. He address chaos theory in its
modern applications as well as hilarious applications of correlation vs causation.
Chaos, J. Gleick
One of the first texts that introduced the relatively new theory of chaos. It addresses the
development of the field as well as its applications.
Does God Play Dice, Ian Stewart
An engaging book about the applications of prediction and chaos theory, and how it is
used in many different fields from weather forecasting to understanding the solar system.
Fractals: Images of Chaos, H. Lauwerier
A basic mathematical introduction to fractal geometry, the mathematics behind chaos
theory. A great introduction for the reader with a basic mathematics education.
Cryptography
The Code Book, Simon Singh
A history of encryption and the impact of codes on wars, nations, and individuals. Singh
writes about the times and personalities of code-breaking as well as the technical explanations
behind the mathematics of cryptography.
*The Mathematics of Ciphers, S.C. Coutinho
An introduction to the algorithms of number theory and their use in cryptography. It also
covers some elementary number theory concepts and historical contexts. May be a bit technical
for those with a more limited mathematical education.