The best 36 Mathematics books

The Signal and the Noise explains why so many expert predictions today fail spectacularly, and what statistical and probability tools are more up to the task of predicting real-world phenomena.

The Black Swan (2010) offers insights into perceived randomness and the limitations we face in making predictions. Our over-reliance on methods that appeal to our intuition at the expense of accuracy, our basic inability to understand and define randomness, and even our biology itself all contribute to poor decision making, and sometimes to “Black Swans” – events thought to be impossible that redefine our understanding of the world.

Ignorance investigates the strengths and weaknesses of the scientific method and reveals the importance of asking the right questions over the discovery of simple facts. Using real-life examples from history, Ignorance shows that it is our awareness of what we don’t know that drives scientific discovery.

In this book, Ian Stewart focuses on 17 famous equations in mathematics and physics history, highlighting their impact on society. Stewart gives a brief history of the wonders of scientific discovery, and peppers it with vivid examples and anecdotes.

The financial theories you learn about in school are coherent, neat, convenient – and wrong. In fact, they’re so wrong that they might also be dangerous: in underestimating the risk of markets, we inadvertently set ourselves up for catastrophe. The Misbehavior of Markets lays out the flaws of economic orthodoxy, and offers a novel alternative: fractal geometry.

In Simply Complexity, Neil F. Johnson presents an introduction to complexity theory, explaining what complex systems are, where we can spot them in everyday life and how we can benefit from understanding complexity. Although a young field, complexity science already offers us ways to help explain and potentially avoid complex phenomena, such as traffic jams, financial market crashes and modern warfare.

How Not to Be Wrong gives us an intimate glimpse into how mathematicians think and how we can benefit from their way of thinking. It also explains how easily we can be mistaken when we apply mathematical tools incorrectly, and gives advice on how we can instead find correct solutions.

The Structure of Scientific Revolutions (1962) is a groundbreaking study in the history of science and philosophy. It explains how scientists conduct research and provides an interesting (if controversial) explanation of scientific progress.

A Mind for Numbers offers insight into the way our brains take in and process information. It outlines strategies that can help you learn more effectively, especially when it comes to math and science. Even if mathematical or scientific concepts don’t come naturally to you, you can master them with the right kind of dedication and perseverance – and this book will teach you how.

Lean Analytics (2013) offers key advice on how to successfully build your own start-up. It follows a data-based approach to explain how you can use effective metrics to help your organization grow.

The Economist: Numbers Guide (1991) explores a variety of mathematical tools that are exceptionally useful across a range of business environments. These blinks reveal just how simple it is to manage risk by quantifying it, helping improve decision making in the process. The book’s mathematical notions are explained at a basic level, so no prior math knowledge is required.

Everyday, we benefit from huge advances in both scientific theory and practice. What triggered this progress? In The Beginning of Infinity (2011) – a journey through the fundamental fields of science and philosophy – physicist David Deutsch argues that all progress results from one single human activity: the quest for explanations. Human creativity opens up limitless opportunities for progress, making knowledge the “beginning of infinity.”

Numbers Rule Your World (2010) is a guide to statistical reasoning and how you can use concrete statistical information productively to understand as well as improve your world. These blinks walk the reader through the five key principles of statistics and how they can be applied to improve decision making in various contexts.

Soccermatics (2016) highlights the link between the world’s most popular sport and something slightly less popular – math. These blinks will show you how statistical models can help explain the beautiful game, from strategy on the field to tips for beating the spread.

Innumeracy (1988) explains how an aversion to math and numbers pervades both our private and public lives. By examining various real-life examples of innumeracy and its consequences, the book offers helpful solutions to combat this irrational and misguided fear of math.

Though you might not be aware of it, machine learning algorithms are already seeping into every aspect of human life, becoming more and more powerful as they continue to learn from an ever-increasing amount of data. The Master Algorithm (2016) provides a broad overview of what kind of algorithms are already out there, the problems they face, the solutions they can provide and how they’re going to revolutionize the future.

Genius (2011) charts the life and career of brilliant physicist Richard Feynman, from his formative upbringing to his remarkable and lasting contributions to science. Though he’s not as renowned as Albert Einstein, and has no groundbreaking theories to his name, Feynman did change the way scientists look at the world.

The Grand Design (2010) tells the fascinating story of how humans came into being and how we began to use the scientific method to explain both our remarkable growth as a species and the world around us. From the foundational laws of Newton and Einstein to the mind-bending science of quantum physics, find out how far we’ve come and how close we are to answering life’s big questions.

Scale (2017) is a glimpse into the hidden and fascinating world of the mathematical relationships that tie the world together. The blinks describe how such laws connect everything from microscopic organisms to international metropolises, and what they can tell us about the behavior of complex systems.

The Knowledge Illusion (2017) is an in-depth exploration of the human mind. It argues against the view that intelligence is solely an individual attribute, offering compelling arguments for how our success as a species would have been impossible without a community of knowledge.

The Book of Why (2018) introduces basic concepts of statistical methods of argumentation and makes the case for a mathematical model of causation. For decades, the mantra “correlation does not imply causation” has been hammered home by statisticians. The result has been stagnation in many forms of research, and this book aims to push back against this trend.

The Man Who Solved the Market (2019) traces the life of enigmatic hedge fund manager and mathematician Jim Simons. It chronicles his early life as a brilliant geometer who won awards for his math, to his work breaking Soviet codes, all the way through to his success with his hedge fund management firm Renaissance Technologies. Far more than just another investor, Simons changed the world with his math and methods.

The Art of Statistics (2019) is a non-technical introduction to the basic concepts of statistical science. Sidelining abstract mathematical analyses in favor of a more human-oriented approach, it explains how statistical science is helping us to answer questions and tell more informative stories. Stepping beyond the numbers, it also considers the role that the media and psychological bias play in the distortion of statistical claims. In these blinks you’ll find the tools and knowledge needed to understand and evaluate these claims.

When Einstein Walked with Gödel (2018) is an excursion through both the fabric of our reality and the limits of scientific imagination. Combining math and physics with history and philosophy, it sheds light on some of the most important scientific theories of the last three centuries – and examines the turbulent lives of the geniuses who conceived them. 

The Data Detective (2021) is a smart, practical guide to understanding the ways in which statistics –⁠ and our reactions to them –⁠ distort and obscure reality. Using psychological research and illuminating examples, it reveals some of the ways our brains influence how we see data and statistics and how we draw incorrect conclusions as a result. By picking apart our cognitive biases and misconceptions, we gain the ability to see data, and in turn, the world, for what it really is.

The God Equation (2021) is an approachable look at the history and present of theoretical physics. This primer untangles the science behind relativity, string theory, and the search for the elusive “theory of everything.”

The Model Thinker (2018) is a guide to using models to make data talk. In a world inundated with information, it sheds some much-needed light on the patterns underlying the noise – and points us toward the ways we can reveal those patterns for ourselves.

The Emperor’s New Mind (1989) is a timeless argument against the computability of the human mind. Taking you on a fascinating journey through math, computer science, philosophy, and physics, famous mathematician Roger Penrose explains what makes the human mind so special – and what quantum mechanics has to do with consciousness.

Chaos (1987) delves into the most recent theoretical revolution in physics: chaos theory. In the 1970s, scientists began discovering that the world doesn’t behave as neatly as classical physics suggests. From the weather to animal populations to our heartbeats – irregularities, disorder, and chaos pervade our universe. And yet, there seems to be a strange order to the chaos of life. Chaos explores the history of this new science, revealing its startling findings, and pondering its implications.

Zero (2000) is the fascinating story of a number banned by the ancient Greeks and worshipped by ancient Indians. Zero – as well as its twin, infinity – is a number that’s been at the heart of both mathematics and philosophy over the centuries.

The Great Mental Models Volume 3 (2021) is the third book in a series that shows how mental models from various disciplines can be applied to make positive changes to your life. This volume focuses on mental models from systems and mathematics. It demonstrates how you can use cognitive tools to improve everything from decision-making and relationships to healthy eating and personal productivity.

Don’t Trust Your Gut (2022) turns that tried-and-true wisdom about trusting your gut on its head. Not only does trusting your gut instinct often lead you to make the wrong decision, there’s a pretty foolproof method to ensure you make the right decision – analyzing the available data and acting on it.

How to Measure Anything (2007) challenges the notion that certain things can’t be measured, arguing instead that with the right tools and perspectives, everything is quantifiable. It provides insightful methodologies and real-world examples to guide readers on how to turn seemingly immeasurable concepts into tangible data, ultimately helping to make more informed decisions.

How to Read a Financial Report (1980) serves as a comprehensive guide that demystifies the complexities of evaluating a company's fiscal health. It explores balance sheets and income reports, clarifies the fundamentals of financial ratios, and explains any accompanying notes, offering tools for a clear and confident assessment of a business's economic status.

Bank Investing (2021) helps you navigate the intricate maze of bank financial statements with ease. Dive deep into credit analysis, master the dance of regulations and interest rates, and get a front-row seat to the dynamic world of banking mergers and acquisitions. You'll not only be able to decipher bank metrics with flair but harness them to guide your investment choices like a seasoned pro.

Relativity (1916) plunges you into the revolutionary world of physics, challenging your perceptions of space, time, and the cosmos. Dive deep into the groundbreaking ideas that reshaped our understanding of the universe. It's not just a scientific journey – it's a transformative experience that will redefine the reality you live in.