The most recommended math books

Who picked these books? Meet our 248 experts.

248 authors created a book list connected to math, and here are their favorite math books.
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Book cover of Gödel's Proof

David B. Black Author Of Wartime Software

From my list on teaching and inspiring the best programmers.

Why am I passionate about this?

I started programming in high school and wrote software in many domains for 30 years, from the early ARPA-net to massive credit card software. I wrote a FORTRAN compiler with one assistant in a year. I got hassled to do proper project management. Nightmare. It was all about inflated expectations instead of moving fast and winning. Then in 25 years of venture capital investing, I learned from many young companies how the little startups built quickly and well things that giants like Google literally could not get done. This book and my others spell out what I learned from the little guys who beat the giants.

David's book list on teaching and inspiring the best programmers

David B. Black Why did David love this book?

Nagel’s book is the most understandable explanation I’ve found about one of the most cosmically seminal math proofs: Godel’s incompleteness theorem.

It takes the idea of recursion and self-reference to the ultimate conclusion about truth, understanding, and boundaries of existence. This may sound hootie-tootie, but think of the sequence of abstraction in math: arithmetic, algebra, calculus, etc.

Once you add in recursion (self-reference), you’ve got the most important concepts underlying true understanding and productivity in software – something never discussed in computer science, and certainly not in practical programming.

Think about the so-called Von Neumann computer architecture, which underlies all modern computers – instructions are data, stored in the same place as ordinary data, and some instructions write data that are instructions. This is recursion taken to the next level. 

By Ernest Nagel,

Why should I read it?

2 authors picked Gödel's Proof as one of their favorite books, and they share why you should read it.

What is this book about?

An accessible explanation of Kurt Goedel's groundbreaking work in mathematical logic
In 1931 Kurt Goedel published his fundamental paper, "On Formally Undecidable Propositions of Principia Mathematica and Related Systems." This revolutionary paper challenged certain basic assumptions underlying much research in mathematics and logic. Goedel received public recognition of his work in 1951 when he was awarded the first Albert Einstein Award for achievement in the natural sciences-perhaps the highest award of its kind in the United States. The award committee described his work in mathematical logic as "one of the greatest contributions to the sciences in recent times."
However, few…


Book cover of Chances Are . . .: Adventures in Probability

Larry R. Frank Sr. Author Of Wealth Odyssey: The Essential Road Map for Your Financial Journey Where Is It You Are Really Trying to Go with Money?

From my list on issues that confuse many people about money.

Why am I passionate about this?

Wealth Odyssey is a summary work based on a 12-hour adult education course I taught for 10 years. It’s important to me to educate people through my 29 years in the profession (1994-2023), my focus has always been on helping people first understand that retirement means you’re wealthy enough not to work anymore – working is optional. You don’t need to be rich. Wealth is scalable for any income level and comes from foundation income and investments to supplement that foundation to support your desired lifestyle’s Standard of Individual Living (SOIL) for as long as you live. Your focus should be on your plan and apply a few concepts grounded in well researched evidence.

Larry's book list on issues that confuse many people about money

Larry R. Frank Sr. Why did Larry love this book?

When people think of financial planning, their first thought is investing. Their second thought is retirement.

Kaplans explain risk succinctly: “Everything is possible, yet only one thing happens.” People understand risk but don’t really understand how to apply it rationally to investing (market risks) or to retirement (longevity risk).

But first, having an understanding of what risk is and isn’t, and where it comes from is important before you can apply it to what fuels your plans – markets and longevity.

This book helped me formulate the basic planning concepts I use in my book since personal finance is all about taking risks – as are any other decisions and actions you take in life.

By Michael Kaplan, Ellen Kaplan,

Why should I read it?

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

What is this book about?

A compelling journey through history, mathematics, and philosophy, charting humanity’s struggle against randomness

Our lives are played out in the arena of chance. However little we recognize it in our day-to-day existence, we are always riding the odds, seeking out certainty but settling—reluctantly—for likelihood, building our beliefs on the shadowy props of probability. Chances Are is the story of man’s millennia-long search for the tools to manage the recurrent but unpredictable—to help us prevent, or at least mitigate, the seemingly random blows of disaster, disease, and injustice. In these pages, we meet the brilliant individuals who developed the first abstract…


Book cover of Great Circles: The Transits of Mathematics and Poetry

Joseph Mazur Author Of The Clock Mirage: Our Myth of Measured Time

From my list on narrative merit in mathematics and science.

Why am I passionate about this?

Meaningful communications with people through life, books, and films have always given me a certain kind of mental nirvana of being transported to a place of delight. I see fine writing as an informative and entertaining conversation with a stranger I just met on a plane who has interesting things to say about the world. Books of narrative merit in mathematics and science are my strangers eager to be met. For me, the best narratives are those that bring me to places I have never been, to tell me things I have not known, and to keep me reading with the feeling of being alive in a human experience.

Joseph's book list on narrative merit in mathematics and science

Joseph Mazur Why did Joseph love this book?

Great Circles is a unique tale of the life and works of mathematicians, scientists, philosophers, poets, and other literary figures. It is collections of circles of thoughts and implications that return on themselves as if they are gravitationally attached to some core red dwarf of universal meaning.  

I loved reading this book. One moment I was into the math, and in the next, I was immersed in a relevant poem or was personality attached to some math or a philosophical thought about a connection of a poem with the math. It was a ride more than a read. It is a calming cognitive exercise on tour through and between chapters – mind wandering not permitted-- with a smooth comfort of thought as if Grosholz is in the room (or perhaps in your brain) reading and guiding.  

The poetry is gripping and wonderfully placed between the appropriate background materials. 

By Emily Rolfe Grosholz,

Why should I read it?

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

What is this book about?

This volume explores the interaction of poetry and mathematics by looking at analogies that link them. The form that distinguishes poetry from prose has mathematical structure (lifting language above the flow of time), as do the thoughtful ways in which poets bring the infinite into relation with the finite. The history of mathematics exhibits a dramatic narrative inspired by a kind of troping, as metaphor opens, metonymy and synecdoche elaborate, and irony closes off or shifts the growth of mathematical knowledge.

The first part of the book is autobiographical, following the author through her discovery of these analogies, revealed by…


Book cover of The Real Work of Data Science: Turning Data Into Information, Better Decisions, and Stronger Organizations

Roger W. Hoerl Author Of Statistical Thinking: Improving Business Performance

From my list on AI and data science that are actually readable.

Why am I passionate about this?

As a professional statistician, I am naturally interested in AI and data science. However, in our current information age, everyone, in all segments of society, needs to understand the basics of AI and data science. These basics include such things as what these disciplines are, what they can contribute to society, and perhaps most importantly, what can go wrong. However, I have found that much of the literature on these topics is highly technical and beyond the reach of most readers. These books are specifically selected because they are readable by virtually everyone, and yet convey the key concepts needed to be data-literate in the 21st century. Enjoy!

Roger's book list on AI and data science that are actually readable

Roger W. Hoerl Why did Roger love this book?

This book goes beyond the hype of data science, the details of machine learning methods, and the coding so closely associated with data science. Rather, it emphasizes the real types of problems for which data science may help, and explains the practical issues (“the real work”) that often lead to failure in data science projects.

These issues tend to be overlooked in more technical presentations of data science. They include such critical considerations as defining the right problem to begin with, understanding the “pedigree” (background and quality) of any data used, and ensuring that the right people are involved from the start.

By Ron S. Kenett, Thomas C. Redman,

Why should I read it?

1 author picked The Real Work of Data Science as one of their favorite books, and they share why you should read it.

What is this book about?

The essential guide for data scientists and for leaders who must get more from their data science teams

The Economist boldly claims that data are now "the world's most valuable resource." But, as Kenett and Redman so richly describe, unlocking that value requires far more than technical excellence. The Real Work of Data Science explores understanding the problems, dealing with quality issues, building trust with decision makers, putting data science teams in the right organizational spots, and helping companies become data-driven. This is the work that spells the difference between a good data scientist and a great one, between a…


Book cover of The Biggest Number in the World: A Journey to the Edge of Mathematics

H. Chris Ransford Author Of In Search of Ultimate Reality: Inside the Cosmologist's Abyss

From my list on weird thrilling science universe.

Why am I passionate about this?

As a child, I felt profoundly dissatisfied by the pat and cardboard cutout explanations that some teachers offered for life and the universe: there had to be more! I decided to go into science. The explanatory power of science is 'next level,' to use a contemporary phrase, and unless and until we explore it, we'll miss the beauty and sheer wonder of the universe. Neither should we overly specialize: science is not compartmentalized, but vastly different fields of science feed into and reinforce one another. Popular science has an essential role to play: irrespective of how arcane hard science may appear to be, its story can always be told in everyday words.

H. Chris' book list on weird thrilling science universe

H. Chris Ransford Why did H. Chris love this book?

The first time I came across this wonderful book, I did the inevitable double take: I had happened to study infinity in its many possible renditions, and the title of this superb book seems to be a mistake: an obvious, silly contradiction in terms, because we can always add one to any purported 'biggest number in the world' and thereby immediately produce an even bigger number. Yet...This book describes the weird, weird world of huge numbers, the race amongst a rarefied coterie of aficionados to find ever bigger specific, provable numbers, and much else besides. 

Mind-blowing.

By David Darling, Agnijo Banerjee,

Why should I read it?

1 author picked The Biggest Number in the World as one of their favorite books, and they share why you should read it.

What is this book about?

From cells in our bodies to measuring the universe, big numbers are everywhere

We all know that numbers go on forever, that you could spend your life counting and never reach the end of the line, so there can't be such a thing as a 'biggest number'. Or can there?

To find out, David Darling and Agnijo Banerjee embark on an epic quest, revealing the answers to questions like: are there more grains of sand on Earth or stars in the universe? Is there enough paper on Earth to write out the digits of a googolplex? And what is a…


Book cover of The Mathematician's Mind: The Psychology of Invention in the Mathematical Field

Holger Gzella Author Of Aramaic: A History of the First World Language

From my list on becoming a scholar.

Why am I passionate about this?

I hold the chair of Old Testament at the Faculty of Catholic Theology at Munich University in Germany. My main area of expertise is Semitic languages, though, which is also the field for which I previously held a chair at Leiden University in the Netherlands for fifteen years (eventually, however, Munich made me an offer one cannot refuse). Hence my main occupation concerns the interpretation of ancient texts in exotic languages such as Hebrew, Aramaic, Phoenician, and others, mostly at the baseline of individual words, grammatical forms, and syntactic constructions. Despite the seemingly dry, specialized character of my work, it is, in my view, a lifestyle rather than a job. 

Holger's book list on becoming a scholar

Holger Gzella Why did Holger love this book?

Scholarship, regardless of the particular field, is always a creative process. Craft and method, the fruits of a rigorous education and hard work, are essential prerequisites, but genuine breakthroughs often seem to result from some mysterious incubation: a wild dance of ideas that emerge from the subconscious, stirred up by the keen will to understand something. Only a few of them eventually make it, by way of sensual representations, to the surface of consciousness, where they are formed and articulated by logic and language. In this book, the great French mathematician Jacques Hadamard captivatingly describes his investigation into the psychological underpinnings of creativity. He stresses the role of images and emotions in thought processes. I have always liked his conclusion that every significant invention requires at least some poetic feel.

By Jacques Hadamard,

Why should I read it?

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

What is this book about?

Fifty years ago when Jacques Hadamard set out to explore how mathematicians invent new ideas, he considered the creative experiences of some of the greatest thinkers of his generation, such as George Polya, Claude Levi-Strauss, and Albert Einstein. It appeared that inspiration could strike anytime, particularly after an individual had worked hard on a problem for days and then turned attention to another activity. In exploring this phenomenon, Hadamard produced one of the most famous and cogent cases for the existence of unconscious mental processes in mathematical invention and other forms of creativity. Written before the explosion of research in…


Book cover of The Singularity Is Near: When Humans Transcend Biology

Nicholas Maes Author Of Laughing Wolf

From my list on to understand (and survive) modernity.

Why am I passionate about this?

I am a classicist (Greek and Latin) and a serious student of history. Modernity has obsessed me for the last 10 years, how it unfolds, what its implications are, whether it generates more gains than losses, whether it’s changing us profoundly and whether we can dodge it or not. Because of this interest (which I lecture on often) I am fascinated to see modernity’s gleanings in earlier times and always curious to see what other critics make of it. Because its effects will only grow down the road, the task of understanding its mechanisms and outcomes is one of extreme urgency, as these books illustrate in different ways.

Nicholas' book list on to understand (and survive) modernity

Nicholas Maes Why did Nicholas love this book?

This book is one of the nuttiest I’ve read in its imaginings of a modern world on steroids. The part that teases most is that its predictions might come true.

I know our smartphones and laptops have changed our world, but cures that would extend longevity ad infinitum? Neural interfaces that would connect us directly to the internet? Nanobots that would reduce the cost of goods to zero?

Because the topic of modernity has come to engross me so, the big question always is, “How far will it carry us?” The answer to which (according to Kurzweil) is much farther than you can possibly imagine and much sooner than you think. One should have one’s mind blown every couple of years, and Kurzweil does exactly that.

By Ray Kurzweil,

Why should I read it?

5 authors picked The Singularity Is Near as one of their favorite books, and they share why you should read it.

What is this book about?

"Startling in scope and bravado." -Janet Maslin, The New York Times

"Artfully envisions a breathtakingly better world." -Los Angeles Times

"Elaborate, smart and persuasive." -The Boston Globe

"A pleasure to read." -The Wall Street Journal

One of CBS News's Best Fall Books of 2005 * Among St Louis Post-Dispatch's Best Nonfiction Books of 2005 * One of Amazon.com's Best Science Books of 2005

A radical and optimistic view of the future course of human development from the bestselling author of How to Create a Mind and The Singularity is Nearer who Bill Gates calls "the best person I know at…


Book cover of Beyond Measure: The Hidden History of Measurement from Cubits to Quantum Constants

Alessandro Ferrero Author Of Forensic Metrology: An Introduction to the Fundamentals of Metrology for Judges, Lawyers and Forensic Scientists

From my list on why good measurements can change your life.

Why am I passionate about this?

I’ve worked in the field of metrology for over 40 years, and I love this field of science. During these many years, I realized that instruments have become an often invisible but always present part of our lives and, if we learn to use them correctly, they can improve our lives, while, on the contrary, if we trust them more than we should, they can easily ruin our lives. For this reason, I like to explore also the philosophical implications of metrology and how it can help justice to render fair decisions and I love to share my passion with other people.

Alessandro's book list on why good measurements can change your life

Alessandro Ferrero Why did Alessandro love this book?

When I introduce measurements to my students, I talk about “an exciting adventure across centuries.” I love this book because it tells the long history of measurement, starting from prehistory and arriving at our days as if it were a true, fantastic adventure humankind has lived since the beginning of its existence.

This is not a technical book, nor a book of history, in a strict sense. It is written by a journalist as an adventure novel, telling the story of a fantastic journey across generations to build our present knowledge.

I read it as a novel, eager to discover the next adventure, always discovering players and facts I ignored. 

By James Vincent,

Why should I read it?

2 authors picked Beyond Measure as one of their favorite books, and they share why you should read it.

What is this book about?

From the cubit to the kilogram, the humble inch to the speed of light, measurement is a powerful tool that humans invented to make sense of the world. In this revelatory work of science and social history, James Vincent dives into its hidden world, taking readers from ancient Egypt, where measuring the annual depth of the Nile was an essential task, to the intellectual origins of the metric system in the French Revolution, and from the surprisingly animated rivalry between metric and imperial, to our current age of the "quantified self." At every turn, Vincent is keenly attuned to the…


Book cover of R for Data Science: Import, Tidy, Transform, Visualize, and Model Data

Tilman M. Davies Author Of The Book of R: A First Course in Programming and Statistics

From my list on intro to programming and data science with R.

Why am I passionate about this?

I’m an applied statistician and academic researcher/lecturer at New Zealand’s oldest university – the University of Otago. R facilitates everything I do – research, academic publication, and teaching. It’s the latter part of my job that motivated my own book on R. From first-year statistics students who have never seen R to my own Ph.D. students using R to implement novel and highly complex statistical methods and models, my experience is that all ultimately love the ease with which the R language permits exploration, visualisation, analysis, and inference of one’s data. The ever-growing need in today’s society for skilled statisticians and data scientists means there's never been a better time to learn this essential language.

Tilman's book list on intro to programming and data science with R

Tilman M. Davies Why did Tilman love this book?

For those intending to use R with an eye on the popular 'Tidyverse' suite of packages – which facilitate the handling, manipulation, and visualisation of data setsit's hard to go past this book. From the founding contributors of the RStudio/Tidyverse worlds, this is a great way to learn about this dialect of R against the overarching backdrop of statistical data analysis and data science.

By Hadley Wickham, Garrett Grolemund,

Why should I read it?

1 author picked R for Data Science as one of their favorite books, and they share why you should read it.

What is this book about?

Learn how to use R to turn raw data into insight, knowledge, and understanding. This book introduces you to R, RStudio, and the tidyverse, a collection of R packages designed to work together to make data science fast, fluent, and fun. Suitable for readers with no previous programming experience, R for Data Science is designed to get you doing data science as quickly as possible. Authors Hadley Wickham and Garrett Grolemund guide you through the steps of importing, wrangling, exploring, and modeling your data and communicating the results. You'll get a complete, big-picture understanding of the data science cycle, along…


Book cover of Logicomix: An Epic Search for Truth

Kirsten Menger-Anderson Author Of Doctor Olaf Van Schuler's Brain

From my list on love, loss, and logic in 1930s Vienna.

Why am I passionate about this?

I first learned about life in 1930s Vienna from my grandfather’s memoir: Reminiscences of the Vienna Circle and the Mathematical Colloquium. I was fascinated by the time and place and began to read more about the era, which ultimately served as a setting for my forthcoming novel, The Expert of Subtle Revisions.

Kirsten's book list on love, loss, and logic in 1930s Vienna

Kirsten Menger-Anderson Why did Kirsten love this book?

In the mood for a graphic novel starring Bertrand Russell and a supporting cast of famous thinkers like Whitehead, Frege, Gödel, and Wittgenstein? Logicomix is for you!

Flip to Chapter Six, “Incompleteness,” for a peek of Vienna in the 1930s. The logic and philosophy illustrated throughout provide a great context for the work of Vienna’s famous philosophical circle led by Moritz Schlick, whose 1936 murder provides a chilling contrast to the intellectual pursuits of that time.

By Apostolos Doxiadis, Christos Papadimitriou,

Why should I read it?

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

What is this book about?

This brilliantly illustrated tale of reason, insanity, love and truth recounts the story of Bertrand Russell's life. Raised by his paternal grandparents, young Russell was never told the whereabouts of his parents. Driven by a desire for knowledge of his own history, he attempted to force the world to yield to his yearnings: for truth, clarity and resolve. As he grew older, and increasingly sophisticated as a philosopher and mathematician, Russell strove to create an objective language with which to describe the world - one free of the biases and slippages of the written word. At the same time, he…