The best math books

24 authors have picked their favorite books about math and why they recommend each book.

Soon, you will be able to filter by genre, age group, and more. Sign up here to follow our story as we build a better way to explore books.

Shepherd is reader supported. When you buy through links on our website, we may earn an affiliate commission (learn more).

A Mind For Numbers

By Barbara Oakley,

Book cover of A Mind For Numbers: How to Excel at Math and Science (Even If You Flunked Algebra)

Oakley is best known for her co-instruction of Learning How to Learn, one of the most popular Coursera courses that has had millions of students. This book offers a science-driven perspective for how to get good at math. Oakley walks her talk too, specializing in linguistics she only became a professor of engineering later, despite some difficulties with math.


Who am I?

I'm a writer, programmer, traveler and avid reader of interesting things. For the last ten years I've been experimenting to find out how to learn and think better. I don't promise I have all the answers, just a place to start. 


I wrote...

Ultralearning: Master Hard Skills, Outsmart the Competition, and Accelerate Your Career

By Scott Young,

Book cover of Ultralearning: Master Hard Skills, Outsmart the Competition, and Accelerate Your Career

What is my book about?

Learn a new talent, stay relevant, reinvent yourself, and adapt to whatever the workplace throws your way. Ultralearning offers nine principles to master hard skills quickly. This is the essential guide to future-proof your career and maximizes your competitive advantage through self-education.

Scott H. Young incorporates the latest research about the most effective learning methods and the stories of other ultralearners like himself—among them Benjamin Franklin, chess grandmaster Judit Polgár, and Nobel laureate physicist Richard Feynman, as well as a host of others, such as little-known modern polymath Nigel Richards, who won the French World Scrabble Championship—without knowing French.

How Not to Be Wrong

By Jordan Ellenberg,

Book cover of How Not to Be Wrong: The Power of Mathematical Thinking

This book is not about computing, but it is relevant in an indirect way. I love this book, since it is written in such an engaging style and illustrates with many examples that math is not a dry subject to be practiced only by mathematicians but helps everyone to solve real-world problems. The book shows how important it is to be precise in describing problems and that applying a little mathematical rigor goes a long way in solving them. Ellenberg describes mathematics as the “extension of common sense by other means.” In a similar way, I view computer science as the extension of problem-solving methods (aka “algorithms”) by other means. 


Who am I?

I’m a professor of computer science at Oregon State University. My research focus is on programming languages, but I also work on computer science education and outreach. I grew up in Germany and moved to the United States in 2000. Since computer science is a fairly new and not widely understood discipline, I am interested in explaining its core ideas to the general public. I believe that in order to attract a more diverse set of people to the field we should emphasize that coding is only a small part of computer science.


I wrote...

Once Upon an Algorithm: How Stories Explain Computing

By Martin Erwig,

Book cover of Once Upon an Algorithm: How Stories Explain Computing

What is my book about?

According to popular culture, computer science is all about coding. This is a tragic misconception that deters many creative students from exploring the field while at the same time disappointing those that only want to code.

At its core, computer science is the science of systematic problem solving, which critically involves the design of representations and their transformations. A precisely described method for solving a problem is called an algorithm, and computation is the execution of an algorithm. My book emphasizes that everybody uses algorithms (and thus computes) all the time—often without a machine, and it explains the major topics of computer science based on everyday examples and well-known stories, without the need to learn how to code.

Bracelets for Bina's Brothers

By Rajani LaRocca, Chaaya Prabhat (illustrator),

Book cover of Bracelets for Bina's Brothers

This adorable picture book by Rajani LaRocca and illustrated by Chaaya Prabhat is about a girl named Bina who wants to make bracelets for her brothers for Raksha Bandhan, a Hindu holiday. Through this sweet story, the book explores patterns and sequences, introducing kids to math concepts in a fun and playful way.


Who am I?

I love encouraging kids to explore engineering, design, and technology! I am a former Google product designer for kids and families. I started writing to address a growing need for coding education, particularly for girls and kids of color. Stories are a wonderful way to demonstrate concepts and to invite kids to approach STEM with creativity and imagination. I picked a range of books for this post, from non-fiction to fantastic, because different kids will respond to different kinds of stories. Through these books, I hope that kids will find inspiration and tools for creative problem-solving, for STEM and beyond.


I wrote...

Invent-a-Pet

By Vicky Fang,

Book cover of Invent-a-Pet

What is my book about?

Katie is an ordinary girl who longs for an extraordinary pet--something more spectacular than a simple goldfish. Then one day Katie comes home to find a gift from her mother: a mysterious machine designed to help her create that one-of-a-kind creature. Each time she feeds different items into the machine, out comes a marvelously colorful new animal--like a purple monkey, rainbow-spotted horse, and green bunny! But none of them is just right. Through trial and error, Katie figures out the formula for her absolutely perfect SURPRISE pet.

The Beginner's Guide to Constructing the Universe

By Michael S. Schneider,

Book cover of The Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art, and Science

According to Michael Schneider, "The universe may be a mystery, but it's no secret." This book is a comprehensive yet simple visual guide to understanding the hidden meaning in the mathematical composition of all physical form. It is fun and fascinating to discover the sacred geometry visible throughout nature, in flowers, crystals, plants, shells, and the human body. You don't have to be a mathematician to see the beauty and symmetry of these patterns in every expression of God's creation, once revealed.


Who am I?

Lilli Botchis, PhD, is a psycho-spiritual counselor, educator, and vibrational medicine developer with four decades of experience in advanced body/soul wellness and the development of higher consciousness. Her expertise includes botanicals, gems, color, flower essences, bio-energy therapies, and holographic soul readings. Lilli is an alchemist, mystic, and translator of Nature’s language as it speaks to our soul. A brilliant researcher in the field of consciousness, she understands the interconnectedness of Nature and the human being and is known as an extraordinary emissary of the natural world. Lilli has been inducted into the Sovereign Order of St. John of Jerusalem, Knights Hospitaller. Many seek her out for her visionary insights and compassionate wisdom.


I wrote...

Awakening the Holographic Human: Nature's Path to Healing and Higher Consciousness

By Elizabeth E. Botchis,

Book cover of Awakening the Holographic Human: Nature's Path to Healing and Higher Consciousness

What is my book about?

Awakening the Holographic Human is a comprehensive reference book on healing and higher consciousness through the use of the natural intelligence found in flowers, herbs, gems, color, the human energy system, and the astrological archetypes. It is for anyone interested in physical, psycho-spiritual, and emotional healing; personal and/or planetary transformation; the development of higher states of consciousness; and actualizing human potential.

This book takes one on a journey in learning how to live in a transpersonal state, not limited by conditions and beliefs, but invoking the Mystery, the sacred, the sublime beauty of being human. Written in a beautifully lyrical style, as one reader wrote, this book is more than a body of knowledge—it is a transmission of love and wisdom. In this book, Lilli reveals the light-encoded intelligence within each of Nature’s healing gifts. She shares her knowledge so that anyone can understand the nature of their personal reality and how to expand beyond it into something greater: the holographic human.

What Is Mathematics, Really?

By Reuben Hersh,

Book cover of What Is Mathematics, Really?

Reuben Hersh is responsible for a revolution in the way we look at mathematics. His main idea is very simple: mathematics is something that is created by human beings. Isn’t that obvious, you say? Not if you believe that mathematics is there even before life itself, that it is built into the nature of reality in some way. In philosophy, this view is called Platonism. Hersh had the radical but obvious idea that if we want to understand what mathematics is we should look at what mathematicians actually do when they create mathematics. Like all great ideas it can be stated very simply but the implications are enormous.  His ideas are what got me started writing my own books about math and science.


Who am I?

I'm a mathematician but an unusual one because I am interested in how mathematics is created and how it is learned. From an early age, I loved mathematics because of the beauty of its concepts and the precision of its organization and reasoning. When I started to do research I realized that things were not so simple. To create something new you had to suspend or go beyond your rational mind for a while. I realized that the learning and creating of math have non-logical features. This was my eureka moment. It turned the conventional wisdom (about what math is and how it is done) on its head.


I wrote...

How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics

By William Byers,

Book cover of How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics

What is my book about?

If you love mathematics then this book will show you where the beauty and profundity that you love comes from. Most people mistakenly think that mathematics is nothing but logic, something like an AI program.  This book demonstrates that something very different is going on. Mathematics makes use of non-logical features like ambiguity, contradiction, and paradox. It is precisely these non-logical features that make math profound. The book demonstrates this with fascinating examples from all levels of math.

Profundity comes from being able to look at an idea from more than one point of view. Profound ideas often come from resolving situations of conflict, for example, zero resolves the conflict of having something that stands for nothing. Maybe I should have called the book, “mathematics beyond logic”.

Proofs and Refutations

By Imre Lakatos,

Book cover of Proofs and Refutations

Lots of people have a priori ideas about what mathematics is all about but Lakatos had the brilliant idea of looking at what actually happened. His book is all about one famous theorem: “for all regular polyhedra, V – E + F =2, where V is the number of vertices, E is the number of edges, and F is the number of faces.  Think of a cube where V=8, E = 12, F = 6.  

We tend to think that mathematics proceeds from a well-defined hypothesis to conclusion. But that is only the finishing step. Along the way the definitions keep changing as do the hypotheses and even the conclusion. Everything is moving! This is what makes doing mathematics so exciting!


Who am I?

I'm a mathematician but an unusual one because I am interested in how mathematics is created and how it is learned. From an early age, I loved mathematics because of the beauty of its concepts and the precision of its organization and reasoning. When I started to do research I realized that things were not so simple. To create something new you had to suspend or go beyond your rational mind for a while. I realized that the learning and creating of math have non-logical features. This was my eureka moment. It turned the conventional wisdom (about what math is and how it is done) on its head.


I wrote...

How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics

By William Byers,

Book cover of How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics

What is my book about?

If you love mathematics then this book will show you where the beauty and profundity that you love comes from. Most people mistakenly think that mathematics is nothing but logic, something like an AI program.  This book demonstrates that something very different is going on. Mathematics makes use of non-logical features like ambiguity, contradiction, and paradox. It is precisely these non-logical features that make math profound. The book demonstrates this with fascinating examples from all levels of math.

Profundity comes from being able to look at an idea from more than one point of view. Profound ideas often come from resolving situations of conflict, for example, zero resolves the conflict of having something that stands for nothing. Maybe I should have called the book, “mathematics beyond logic”.

The Philosophical Baby

By Alison Gopnik,

Book cover of The Philosophical Baby: What Children's Minds Tell Us about Truth, Love, and the Meaning of Life

This is another book about the new research into how babies think. I am excited about this research because of its implications for how people learn mathematics and how researchers create math. This book taught me something important about how we all think. Gopnik distinguishes between what she calls flashlight consciousness and lantern consciousness. Flashlight is the way adults think. You focus on one thing at a time and give it your full attention. But babies, she claims, use their minds differently. Their lantern consciousness is unfocused and is aware of the big picture all at once.  

So what happens to lantern consciousness when you grow up? The answer is that creative individuals use it and alternate between lantern and flashlight consciousness. When we are creating or learning something new, we have to drop back to lantern consciousness. Logic comes from flashlight consciousness and, by itself, will never produce anything…


Who am I?

I'm a mathematician but an unusual one because I am interested in how mathematics is created and how it is learned. From an early age, I loved mathematics because of the beauty of its concepts and the precision of its organization and reasoning. When I started to do research I realized that things were not so simple. To create something new you had to suspend or go beyond your rational mind for a while. I realized that the learning and creating of math have non-logical features. This was my eureka moment. It turned the conventional wisdom (about what math is and how it is done) on its head.


I wrote...

How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics

By William Byers,

Book cover of How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics

What is my book about?

If you love mathematics then this book will show you where the beauty and profundity that you love comes from. Most people mistakenly think that mathematics is nothing but logic, something like an AI program.  This book demonstrates that something very different is going on. Mathematics makes use of non-logical features like ambiguity, contradiction, and paradox. It is precisely these non-logical features that make math profound. The book demonstrates this with fascinating examples from all levels of math.

Profundity comes from being able to look at an idea from more than one point of view. Profound ideas often come from resolving situations of conflict, for example, zero resolves the conflict of having something that stands for nothing. Maybe I should have called the book, “mathematics beyond logic”.

Alex Through the Looking-Glass

By Alex Bellos,

Book cover of Alex Through the Looking-Glass

This is a sequel to Alex Bellos's bestseller Alex's Adventures in Numberland, but more focused on applications of mathematics to the real world, especially through physics. Many of these were known to me, particularly when they involved calculus, but I greatly enjoyed Alex's distinctive and novel way of putting across sophisticated ideas, in part by interspersing them with personal interviews with mathematicians of all kinds.  


Who am I?

I am an applied mathematician at Oxford University, and author of the bestseller 1089 and All That, which has now been translated into 13 languages. In 1992 I discovered a strange mathematical theorem – loosely related to the Indian Rope Trick - which eventually featured on BBC television. My books and public lectures are now aimed at bringing mainstream mathematics to the general public in new and exciting ways.


I wrote...

The Wonder Book of Geometry: A Mathematical Story

By David Acheson,

Book cover of The Wonder Book of Geometry: A Mathematical Story

What is my book about?

What is the quickest route to mathematics at its best? 

In this book, I try to show how geometry can provide the answer, by drawing on its rich history, quirky personalities, and practical applications. Throughout, I highlight elegant methods of deduction and the most surprising results, and claim that, in this way, anyone can begin to enjoy some of the wonders of mathematics within just half an hour of starting.

Teaching and Learning Algebra

By Doug French,

Book cover of Teaching and Learning Algebra

This may seem an odd choice, but as a maths popularizer I need to know all that I can about why some people find the main elements of the subject so difficult. I found Doug French's book exceptionally helpful in this respect, even though it is aimed principally at high school teachers. This is partly because he focuses throughout on the most important mathematical ideas and difficulties. Moreover, the scope is wider than the title suggests, for he also ventures imaginatively into both geometry and calculus.


Who am I?

I am an applied mathematician at Oxford University, and author of the bestseller 1089 and All That, which has now been translated into 13 languages. In 1992 I discovered a strange mathematical theorem – loosely related to the Indian Rope Trick - which eventually featured on BBC television. My books and public lectures are now aimed at bringing mainstream mathematics to the general public in new and exciting ways.


I wrote...

The Wonder Book of Geometry: A Mathematical Story

By David Acheson,

Book cover of The Wonder Book of Geometry: A Mathematical Story

What is my book about?

What is the quickest route to mathematics at its best? 

In this book, I try to show how geometry can provide the answer, by drawing on its rich history, quirky personalities, and practical applications. Throughout, I highlight elegant methods of deduction and the most surprising results, and claim that, in this way, anyone can begin to enjoy some of the wonders of mathematics within just half an hour of starting.

Mathematics for the Million

By Lancelot Hogben,

Book cover of Mathematics for the Million: How to Master the Magic of Numbers

This book has haunted me for years. For what is it, exactly, that gives it such enduring popularity? After all, it was first published in 1936, yet is still in print today. In his autobiography, Hogben remarks on the importance of eye-catching illustrations but speculates that its success may instead be because the book contains – most unusually for a 'popular' work – exercises and answers, making it more suitable for self-teaching. Whatever the real answer, his book must surely have something to teach anyone – like myself – who aspires to bring mainstream mathematics to life for the general public.


Who am I?

I am an applied mathematician at Oxford University, and author of the bestseller 1089 and All That, which has now been translated into 13 languages. In 1992 I discovered a strange mathematical theorem – loosely related to the Indian Rope Trick - which eventually featured on BBC television. My books and public lectures are now aimed at bringing mainstream mathematics to the general public in new and exciting ways.


I wrote...

The Wonder Book of Geometry: A Mathematical Story

By David Acheson,

Book cover of The Wonder Book of Geometry: A Mathematical Story

What is my book about?

What is the quickest route to mathematics at its best? 

In this book, I try to show how geometry can provide the answer, by drawing on its rich history, quirky personalities, and practical applications. Throughout, I highlight elegant methods of deduction and the most surprising results, and claim that, in this way, anyone can begin to enjoy some of the wonders of mathematics within just half an hour of starting.

Or, view all 103 books about math

New book lists related to math

All book lists related to math

Bookshelves related to math