Suggested Books

“Mathematics was born and nurtured in a cultural environment. Without the perspective which the cultural background affords, a proper appreciation of the content and state of present-day mathematics is hardly possible.” – R.L. Wilder

Anyone who knows me, knows that I love to read about math and physics.  This page lists some of my favorites books – books for anyone interested in math or science. (This list is always expanding so come back from time to time to check for updates.)   If you have any suggestions or questions, please contact me by leaving a comment or sending me an email at musingsonmath@gmail.com.

To make it easier for you to search, I have broken down the list into categories:

• Biographical
• Mathematical History
• Topics in Mathematics
• Mathematical Philosophy
• Mathematical Theory
• Physics

Happy reading!

 

My Top 5 Picks for Students … or maybe 6?

1. The Man Who Loved Only Numbers by Paul Hoffman
2. Men of Mathematics by E.T. Bell
3. Journey Through Genius:The Great Theorems of Mathematics by William Dunham
4. The Education of T.C. Mits by Lillian R. Lieber
5. A Mathematician’s Apology by G.H. Hardy
6. Letters to a Young Mathematician by Ian Stewart

BIOGRAPHICAL

PAUL ERDOS

The Man Who Loved Only Numbers by Paul Hoffman

This is absolutely my favorite book on Paul Erdos (probably one of my favorites overall as well.)  A great book – very humorous describing the life and genius of one of the world’s greatest mathematicians.

My Brain is Open by Bruce Schechter

A shorter biography than the one above.  Not as much of a discussion of mathematics but still a good read.

CARL FRIEDRICH GAUSS

Gauss – Titan of Science by G. Waldo Dunnington

This is the only biography of Gauss available.  Considered the greatest   mathematician of all time, it is a must read by all fans of mathematics.

KURT GODEL

Incompleteness by Rebecca Goldstein

This is both a biography and a look into one of the most controversial theorems in all of mathematics.  To say Godel was unique is an understatement.  To say he was a genius is equally an understatement.  At times, the book can be quite academic in nature.  However, it does not disappoint.  It is a great look into one the 20th Century’s greatest minds.

PAUL HALMOS

I Want to be a Mathematician: an automathography by Paul Halmos

This book is considered an autobiography.  However, it is much more than that.  Halmos focuses his book on what it is like to be a mathematician, using his life as the framework for the discussion.  It is a must read for anyone considering a life as a mathematician.

DAVID HILBERT

Hilbert by Constance Reid

This book is a biography of one of the greatest mathematicians of the late 19th and early 20th centuries … perhaps one of the greatest of all time.  Hilbert had the midas touch when it came to mathematics and physics by both solving difficult problems and inspiring new mathematics.  What is great about this biography is that non-mathematical people can enjoy it as much as math geeks.  This has quickly become one of my favorites.

JOHN NASH

a Beautiful Mind by Sylvia Nasar

This is the book that inspired the movie about John Nash.  However, as with most movies, if you want the truth, you should read the book.  It is a tough read but well worth it.

S. M. ULAM

Adventures of a Mathematician by Stanislaw Ulam

This is the autobiography of one of the greatest Polish mathematicians of all time. Ulam was more of an applied mathematician, seeking out applications of mathematics in physics and engineering.  Ulam played a pivotal role in the Manhattan Project (at Los Alamos.)

MATHEMATICAL HISTORY

A History of Mathematics by Carl B. Boyer

A great read outlining the history of mathematics from the ancient times through the first half of the 20th Century.  It can be a little technical but is extremely informative and allows us to see into the mind of the great mathematical geniuses.

Men of Mathematics by E.T. Bell

A classic.  Probably the most famous of all books written about the history of mathematicians.  Sometimes criticized for embellishing the truth, it is nevertheless a must read by all.

TOPICS IN MATHEMATICS

The Calculus Wars by Jason Socrates Bardi

So, who invented Calculus … Leibniz or Newton?  This books delves into the history of one of the greatest battles in all of mathematics.

e:  The Story of a Number by Eli Maor

Everything you have ever wanted to know about one of the most important mathematical constants every discovered.  Extremely informative with a good bit     of history.

The Education of T.C. Mits by Lillian R. Lieber

This is both a unique and classic book written about the paradox and application of mathematics to world around us.  It ranges from the practical to the philosophical, written in a very fast pace style.  Topics range from the basic to the bizarre.  Well worth the read!

Euler:  The Master of Us All by William Dunham

The most prolific mathematician of all time is of course Leonhard Euler.  Dunham outlines many of his great discoveries using mathematics that most high school students could follow.  This is an incredible read, allowing us a small taste of the genius that was Euler!

The Fifth Postulate by Jason Socrates Bardi

One of history’s greatest unsolved mathematics problems concerned the proof of Euclid’s Fifth Postulate or, as it is more commonly known, the Parallel Postulate.  This book gives a great historical overview of the attempts to prove the Parallel Postulate as well as thought process leading to its eventual rejection.  It is an extremely entertaining read and has some great biographies of Gauss, Lobachevsky and Bolyai.  As with most math books written today, it keeps a “general interest” audience in mind and steers clear of the heavy-duty mathematics of non-Euclidean geometry.  However, it still gives the reader a good overview of the birth of this field.

The Golden Ratio by Mario Livio

One of the greatest mysteries of mathematics is the Golden Ratio.  Known and used for thousands of years, this constant keeps popping up in math and science.  This book explores the math behind this famous ratio, where to find it and even where not to find it.  It is a great read for teachers.  Thanks to one of my former students for giving it to me.

Journey Through Genius: The Great Theorems of Mathematics by William Dunham

One of my all time favorites.  This book highlights some of the greatest theorems of mathematics.  It is written in such a way that it handles the difficult material with ease.  It fills in the gaps that the textbook cannot.  This is a must read!

The Equation that Couldn’t Be Solved by Mario Livio

Ever wonder why there is a Quadratic, Cubic, and Quartic Formula but no Quintic? This book explains the history of the elusive and impossible search for a formula to solve the general Quintic Equation.  While futile in all efforts to find the formula, the search led to the invention of an entirely new branch of mathematics – abstract algebra.

Mathematical Scandals by Theoni Pappas

Some people think that math is boring.  This book proves that statement incorrect. Included are about a dozen stories of some of the greatest scandals ever to rock the mathematical world.  A great book for teachers who like to include a bit of history into some of their drier lectures.

The Riemann Hypothesis: The Greatest Unsolved Problem in Mathematics by Karl Sabbagh

Probably the greatest of all unsolved mathematical problems.  If proven true, the Riemann Hypothesis will once and for all explain the distribution of prime numbers.  As you read this book, you quickly realize that this is just the tip of the iceberg.  Besides having additional applications in physics and engineering, the most frightening fact … if proven true, it will render most encryption methods obsolete!

MATHEMATICAL PHILOSOPHY

Letters to a Young Mathematician by Ian Stewart

A short book given to me by a former student.  It is one my most prized books. It is written in the form of letters discussing what it is like to be a mathematician and what is needed to become one.  A must read for all math teachers!

A Mathematician’s Apology by G.H. Hardy

Hardy, one of greatest of all number theorists, wrote this book as his mathematical abilities began to wane.  It is touching and sad to read about his coming to terms with realizing that his best years are behind him.  However, it is well worth the read.  There are ‘one of a kind descriptions’ of how mathematics is as much an art as a science.  He allows the reader to see how much joy and pleasure mathematics offers those who choose to explore it.

The Mathematical Experience by Philip J. Davis and Reuben Hersh

Written as a collection of loosely linked essays, this book explores some history, theory, applications and philosophy of mathematics.  It is a fun book offering insights that you just cannot find anywhere else.

MATHEMATICAL THEORY

Chaotic Dynamics by G.L. Baker and J.P. Gollub

A great book on the applications of chaos theory and nonlinear dynamics.  This is a very technical book and requires a good grasp of college level mathematics.

Goldbach Conjecture edited by Wang Yuan

Anyone who knows me, knows that Goldbach’s Conjecture is an obsession of mine. This books includes some of the research into proving this conjecture.  This is again a very technical book that requires a good grasp of Analytic Number Theory.

An Introduction to the Theory of Numbers by G.H. Hardy and E.M. Wright

The all time classic book on Elementary Number Theory.  Anyone who has an interest in number theory needs to read this book.  It requires college level mathematics, but is well worth the time.

Number Theory and Its History by Oystein Ore

A great book on the history and theory of Elementary Number Theory.  What I like about this book is that Ore goes out of his way to present the theory in such a way that those without a great deal of mathematical training can still understand it.

Solved and Unsolved Problems in Number Theory by Daniel Shanks

A very technical book that outlines some of the major solved and unsolved problems in number theory.  What I like here is that Shanks organizes the book by first detailing the known theory and then leads you into the unsolved problems in that particular area.  A very difficult read so make sure you have a pencil and paper ready!

PHYSICS

Einstein by Walter Isaacson

This is the very popular and recent biography written by the one of the best modern-day biographers.  I have read several biographies on Einstein and I have to say, this one is my favorite.  While the book has been criticized for avoiding various parts of Einstein’s life and discoveries, I think it is the best for presenting Einstein as a person.  If you are a fan of Einstein or want to be introduced to him, this is a must read!

Einstein Defiant by Edmund Blair Bolles

This book outlines the historical developments of Quantum Mechanics through the lives of the physicists who developed it.  While he focuses on the great Einstein – Bohr (biography) debates, all aspects all dealt with.  If you are interested in learning more about Quantum Mechanics, this is a must read!

The Einstein Theory of Relativity by Lillian R. Lieber

A classic book on Relativity.  This book has inspired generations of physicists since the 1950’s, including one of my professors, Dr. Jantzen.  (Thanks to his help as editor and as the author of the introduction, the book lives again.)  Be warned – this book has some math in it – even some topics beyond Calculus.  However, you can still get a lot out of it – even if you avoid the math.  Who would do such a thing?

Einstein’s Theory of Relativity by Max Born

Yes, THAT Max Born … noble laureate and one of the greatest physicists of the 20th century (biography).  Using the history of physics as his outline, Born explains Relativity for someone without formal training in physics.  For those of you with some mathematical inclination, there are plenty of formulas to look at and admire (or skip if you are afraid.)  However, the math he uses is primarily algebra so most students should be able to follow it.

The Great Physicists from Galileo to Einstein by George Gamow

This is a great book.  In addition to the remarkable theories of these physicists, Gamow (a world-famous physicist himself) also delves into the lives of these individuals.  He puts it all into historical context so that you can get a full picture of the physics of the times.

Was Einstein Right?  Putting General Relativity to the Test by Clifford M. Will

Updated as late as 1993, this book deals with the scientific evidence supporting Einstein’s Theory of Relativity.  In addition to the evidence, he does a great job explaining all of the aspects of the theory in terms that most anyone can learn from.

Who Got Einstein’s Office by Ed Regis

The setting is the Institute for Advanced Study, home to Einstein for the last 20 years of his life.  Regis focuses his book on the lives of the mathematicians and scientists who called the Institute home.  It is great book honoring the lives and eccentricities of some of the greatest minds in 20th century math and science.