Why am I passionate about this?

I love mathematics and truly believe that “Functions Describe the World.” I'm deeply satisfied that I've spent my professional life discovering new mathematics and explaining known mathematics to others. I was an undergraduate at the University of Texas, Austin, got my PhD from Brown University, then spent three years as a G.C. Evans Instructor at Rice University, before moving to Williams, where I've been ever since. Besides writing All the Math You Missed (But Need to Know for Graduate School), I've also written Algebraic Geometry: A Problem Solving Approach (with a number of co-authors) and Electricity and Magnetism for Mathematicians: A Guided Path from Maxwell’s Equations to Yang-Mills, and a number of research articles.  


I wrote

All the Math You Missed: (But Need to Know for Graduate School)

By Thomas A. Garrity,

Book cover of All the Math You Missed: (But Need to Know for Graduate School)

What is my book about?

People who are starting graduate school in mathematics are full of hopes and dreams to become great mathematicians. That is good.…

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The books I picked & why

Book cover of Hilbert

Thomas A. Garrity Why did I love this book?

David Hilbert was one of the great mathematicians of the early twentieth century. He also created an entire research environment at the University of Göttingen, founded on the fundamental assumption that there is a deep unity behind all of mathematics (an assumption that in part motivated me to write All the Math You Missed). From this school much of the mathematical triumphs of the last 100 years have sprung (especially from the revolutionary work rotating around the mathematics of Emmy Noether in the 1920s in Göttingen). At least that is my impression from reading this book. It inspires young mathematicians to believe that it is indeed possible that “mathematics is the ultimate description of reality.” It certainly had that effect on me as a college junior worrying about my future life.  

By Constance Bowman Reid,

Why should I read it?

4 authors picked Hilbert as one of their favorite books, and they share why you should read it.

What is this book about?

"It presents a sensitive portrait of a great human being. It describes accurately and intelligibly on a nontechnical level the world of mathematical ideas in which Hilbert created his masterpieces. And it illuminates the background of German social history against which the drama of Hilberts life was played. Beyond this, it is a poem in praise of mathematics." -SCIENCE


Book cover of Adventures of a Mathematician

Thomas A. Garrity Why did I love this book?

Ulam was a Polish mathematical prodigy, publishing significant mathematics by the time he was 20. He was part of the rich Polish math community centered around Stefan Banach. Unlike most, he was heading to the United States in 1939 (with his younger brother) when Germany invaded Poland. All the rest of his family were murdered by the Nazis. He on the other hand ended up in Los Alamos, providing critical help on the Manhattan Project. Later in life, he wrote this book, his autobiography. Based on his history, one could well think that it would be a book full of tragic grief. Instead, it is a pean to the joys of doing mathematics and of living a life full of mathematics, without downplaying the horrors of the mid-twentieth century. 

By S. M. Ulam,

Why should I read it?

2 authors picked Adventures of a Mathematician as one of their favorite books, and they share why you should read it.

What is this book about?

This autobiography of mathematician Stanislaw Ulam, one of the great scientific minds of the twentieth century, tells a story rich with amazingly prophetic speculations and peppered with lively anecdotes. As a member of the Los Alamos National Laboratory from 1944 on, Ulam helped to precipitate some of the most dramatic changes of the postwar world. He was among the first to use and advocate computers for scientific research, originated ideas for the nuclear propulsion of space vehicles, and made fundamental contributions to many of today's most challenging mathematical projects. With his wide-ranging interests, Ulam never emphasized the importance of his…


Book cover of Prime Obsession: Berhhard Riemann and the Greatest Unsolved Problem in Mathematics

Thomas A. Garrity Why did I love this book?

Most mathematicians believe that the Riemann Hypothesis is the most important open question in mathematics, including me. But it is almost impossible to explain why this is such a central concern. This book is one of the attempts to explain to the non-mathematician why the Riemann Hypothesis is so important. As a partial spoiler alert, it has to do with the nature of prime numbers, which in part explains the title. It is not a book to read in one sitting, but it with a little work is great for seeing, at least in part, the big picture.

By John Derbyshire,

Why should I read it?

1 author picked Prime Obsession as one of their favorite books, and they share why you should read it.

What is this book about?

The definitive story of the Riemann Hypothesis, a fascinating and epic mathematical mystery that continues to challege the world.

In 1859, Bernhard Riemann, a little-known thirty-two year old mathematician, made a hypothesis while presenting a paper to the Berlin Academy titled  “On the Number of Prime Numbers Less Than a Given Quantity.”  Today, after 150 years of careful research and exhaustive study, the Riemann Hyphothesis remains unsolved, with a one-million-dollar prize earmarked for the first person to conquer it.

Alternating passages of extraordinarily lucid mathematical exposition with chapters of elegantly composed biography and history, Prime Obsession is a fascinating and…


Book cover of Gamma: Exploring Euler's Constant

Thomas A. Garrity Why did I love this book?

Gamma is a number, though little understood. Even its most basic properties are still unknown. We don’t even know if it is a rational number (a ratio of integers). This wonderful book explains why anyone would care. While it does require some mathematical background, anyone who has had calculus and is willing to read the book with a notepad and pen next to them in order to check and explore the formulas on their own will come away with a true appreciation of gamma and its impact. 

By Julian Havil,

Why should I read it?

1 author picked Gamma as one of their favorite books, and they share why you should read it.

What is this book about?

Among the many constants that appear in mathematics, ?, e, and i are the most familiar. Following closely behind is ?,, or gamma, a constant that arises in many mathematical areas yet maintains a profound sense of mystery. In a tantalizing blend of history and mathematics, Julian Havil takes the reader on a journey through logarithms and the harmonic series, the two defining elements of gamma, toward the first account of gamma's place in mathematics. Introduced by the Swiss mathematician Leonhard Euler (1707-1783), who figures prominently in this book, gamma is defined as the limit of the sum of 1…


Book cover of Euclid's Elements

Thomas A. Garrity Why did I love this book?

This is the bestselling textbook of all time. Euclid’s Elements has been the model for correct thinking for thousands of years. The traditional year-long course on axiomatic reasoning about geometry was easily my favorite course in high school. In fact, I sort of assumed that I was slow in that I could not “see” the underlying axioms in other classes. I simply did not realize that the other high school subjects were not axiom-based. 

The story goes that as a young prairie lawyer, Abraham Lincoln carried around with him a tattered copy of the Elements so that he could learn how to think (even though he never really had much formal education). I hope this is true. Even more so, I want to believe that he developed his profound oratorial skill from the power behind Euclid.

By Dana Densmore (editor), Thomas L. Heath (translator),

Why should I read it?

1 author picked Euclid's Elements as one of their favorite books, and they share why you should read it.

What is this book about?

The classic Heath translation, in a completely new layout with plenty of space and generous margins. An affordable but sturdy sewn hardcover student and teacher edition in one volume, with minimal notes and a new index/glossary.


Explore my book 😀

All the Math You Missed: (But Need to Know for Graduate School)

By Thomas A. Garrity,

Book cover of All the Math You Missed: (But Need to Know for Graduate School)

What is my book about?

People who are starting graduate school in mathematics are full of hopes and dreams to become great mathematicians. That is good. But most are suddenly confronted with the cold hard fact that they are expected to know a daunting breadth of mathematics, a breadth that few actually have or even could have had. This book is an attempt to help my younger future colleagues. 

Each of its twenty chapters covers a key part of the math needed for graduate school. All beginning graduate students know the math in some of the chapters. Hardly any are comfortable with the material in all of the chapters. This book will help them “get into the game,” concentrating on why the math in each chapter is important and pointing them to resources to learn more. 

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Book cover of What Walks This Way: Discovering the Wildlife Around Us Through Their Tracks and Signs

Sharman Apt Russell Author Of What Walks This Way: Discovering the Wildlife Around Us Through Their Tracks and Signs

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