83 books directly related to math 📚

The Greatest Adventure deals with mutated dinosaurs in Antarctica, which sounds like something out of a 1950s horror film but which Bell uses as the basis for an… show more.

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… show more.

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… show more.

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.  

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.

As an adult, I found the same author’s Mathematics for the Million a bit crass and utilitarian but I pardon him everything for a wonderful first experience.

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… show more.

This remarkable book is authored by Francis Su, the past president of the Mathematical Association of America. The author describes human flourishing as follows: “a wholeness of being and doing, of realizing one’s potential and helping others do the same, of acting with honour and treating others with dignity.” He explains how human beings, of all ages and ability levels, can experience flourishing through the doing of mathematics.

In each of the final twelve chapters, the author explores a trait of mathematics, how it relates to our journey as humans, and how the development of each trait enables us to… show more.

For decades, the most famous opening chord in rock and roll was an unsolved problem, since no one could reproduce it. But in 2004, Jason Brown, a professor at Dalhousie University, used mathematics to recreate the opening chord of the Beatles hit song, “A Hard Day’s Night”. I remember when newspapers around the world reported on Jason’s findings, as I was at Dalhousie at the time, as one of Jason’s Ph.D. students.

Jason’s Beatles story serves as the final chapter in this wonderful book, a collection of short vignettes about how mathematics relates to every aspect of our lives, including… show more.

The idea of a fourth dimension grabbed the public’s attention in the late 19th and early 20th centuries. Before Minkowski and Einstein popularized time as the fourth dimension, people were enthralled by the mind-expanding idea of a possible fourth physical dimension perpendicular to our three. Edwin Abbott was one of the first authors to write about this idea for a popular audience. His 1884 novella Flatland beautifully illustrates by analogy how to view higher dimensions by telling the story of two-dimensional figures (polygons and circles) encountering a being who lives in the third dimension. Flatland is also a satirical take… show more.

One of my favorite professors, Gretchen Martinet, used this to teach a course called “Mathematical Statistics” when I was at the University of Virginia. It is an extremely profound course full of dense but fundamental mathematical proofs in classical statistics. 

You will learn why the formula for the normal distribution is the way it is, why the sum of squares appears everywhere in statistics, and how to fit a linear regression by hand. In the same way calculus elevates our understanding of rates of changes, the book elevates your understanding of samples, averages, and distributions. Quant trading requires an intuitive… show more.

Many undergraduate mathematics books – even those aimed at new students – are dense, technical, and difficult to read at any sort of speed. This is a natural feature of books in a deductive science, but it can be very discouraging, even for dedicated students. Houston’s book covers many ideas useful at the transition to proof-based mathematics, and he has worked extensively and attentively with students at that stage. Consequently, his book maintains high mathematical integrity and has lots of useful exercises while also being an unusually friendly read.

Mathematics requires accurate calculation, and students sometimes think that getting the right answer is enough. But mathematics is also about valid logical arguments, and the demand for clear communication increases through an undergraduate degree. Students, therefore, need to learn to write professionally, with attention to general issues like good grammar, and mathematics-specific issues like accuracy in notation, precision in logical language, and structure in extended arguments. Vivaldi’s book has a great many examples and exercises, and students could benefit from studying it systematically or from dipping into it occasionally and reflecting on small ways to improve.

I read Cosmos when I was young and it inspired the love of science I still carry today. I found Sagan’s musings about the pale blue dot mesmerizing, and the science was thrilling. I ended up going to Space Camp when I was 14 and Governor’s School for Physics when I was 16 to further my scientific knowledge. When I wrote A Paradox of Fates, I used some of the science I learned in Governor’s School to explain time travel, which has always been a fascinating subject to me.

The world is a complicated place, and it is often difficult to see it clearly. Mathematical tools like logic and proofs let us understand it better. This popular book is a more modern and less technical primer in thinking about the world through a mathematical lens. 

For many readers, it will open the eyes as to why much of that math you learned in school was there in the first place, and refresh your thinking about it. Statistical reasoning is particularly important in today’s data-driven world, and this book will help you realize when someone is lying to you through… show more.

Love and Math is a mathematical autobiography, seamlessly interweaving an inspiring personal journey with profound mathematical ideas. Born in the Soviet Union, Frenkel aspired to become a professional mathematician, only to see his hopes crushed by entrenched antisemitism at Moscow State University – home to the premier mathematics program in the country. While sitting for the entrance exam, he was confronted by two advanced graduate students who were sent to question him personally and make sure he failed. Rejected but undeterred, Frenkel turned instead to an informal network of top-flight but marginalized Soviet mathematicians, who like him were denied employment… show more.

I’m interested in how mathematicians create mathematics but this book made me realize that learning mathematics is also a form of creativity. Each of us has created our understanding of mathematics as we were growing up. We are all creative!  

What is amazing about this book is that even children as young as six months possess rudimentary mathematical concepts, in particular, the concept of number. (Actually, Carey shows children have two distinct ways of thinking about numbers). The concept of number is built-in. That’s amazing to me! The mastery of counting numbers, 1,2,3,… is a great creative leap in the… show more.

This book might as well be called Introduction to machine learning, and it is probably one of the only books truly deserving of the title. Did you know neural networks have been used for decades to scan checks at the bank? They are called Boltzman Machine. Have you ever heard of how decision trees were used in old-school data mining? You could only get them from proprietary software packages from the early 2000s.

In quant trading, you will constantly face compute power constraints, so it is invaluable to understand the mathematical foundations of the most old-school machine learning methods… show more.

Picking up this short picture book, I expected a dose of Phantom Toolbooth-esque wordplay. Not at all. This five-minute love story, about a line yearning for a dot, somehow enlarges into a meditation on geometric structure itself. From such a brief book, I didn’t expect new insights about how simple geometry underlies our most intricate thinking—but then again, that’s what delightful visuals will do for you.

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… show more.

I have always liked the classical geometry of triangles and circles, but Matt Parker's book helped me go way beyond that and broaden my whole outlook. And the attractively hand-drawn diagrams and zany humour just added to the whole experience. After all, how many maths authors do you know who decide to build a computer out of 10,000 dominoes, just to calculate 6 + 4? 

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… show more.

Polya was a great mathematician who knew what counted (after all, he made major contributions to combinatorics, the mathematics of counting). He thought hard about what he was doing when working on problems in mathematics, developing a mental process that lead to creative breakthroughs and solutions. Polya’s problem-solving method is broadly applicable to domains other than mathematics, and this book features many nice puzzles to improve your thinking.

Algorithm design is challenging because it often requires flashes of sudden insight which seem to come out of the blue. But there is a way of thinking about problems that make such… show more.

Have you ever been to a mathematics lecture where the speaker wore a tuxedo and baffled the audience with his mystifying knowledge of numbers? Well, I have and the speaker was Arthur Benjamin, who combined mathematics and magic. He even displayed this knowledge with Stephen Colbert on his earlier show The Colbert Report. It is our good fortune that he describes much of this mathematical wizardry in this fascinating book. 

There are books that simply tell us (or perhaps remind us) how mathematics can be interesting and fun. This delightful book is one of the best, describing how mathematics can be amazing, surprising, and beautiful, all at the same time. While mathematics has helped people accomplish so many things that we may have never dreamed of, this book shows us that mathematics can be popular as well. 

We love all of David Macauley’s books. He uses hand-drawn black-and-white illustrations to describe the enormous effort and complicated processes involved in building some of the most magnificent structures in the world, from cathedrals to castles to pyramids. Cathedral was his first, and we think the best. Although intended for young readers, there are many builders, engineers, and architects that find wonder in Macauley’s work. 

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… show more.

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. 

Mathematicians are constantly baffled by the public’s lack of awareness, not just of what mathematics does, but what it is. Today’s technological society functions only because of a vast range of mathematical concepts, techniques, and discoveries, which go far beyond elementary arithmetic and algebra. This was one of the first books to tackle these misunderstandings head on. It does so by examining not just the math and what it’s used for, but the social structures, the ‘conditions of civilization’ that have brought us to this curious state: utterly dependent on math, almost universally unaware that we are. 

I was given this book when I was about 15, and devoured it. It is an eclectic collection of mathematical paradoxes, fallacies, and curiosities so strange that they seem impossible. Mathematical magic tricks, a proof that all numbers are equal, a proof that all triangles are isosceles, a curve whose length is infinite but whose area is finite, a curve that crosses itself at every point, a curve that fills the interior of a square. Infinities that are bigger than other infinities. The Saint Petersburg Paradox in probability, a calculation that you should pay the bank an infinite amount of… show more.

One of the friendliest routes into mathematics, for many people, is its history. In math, unlike many sciences, ideas last indefinitely. Pythagoras’s Theorem is about 4,000 years old, understood in ancient Babylon a thousand years before Pythagoras was born. It was true then, and it is still true today. The history of math tells of the construction of a towering edifice, with each new level built on top of the previous ones. There are many histories of mathematics, but none quite like this one. The author is a much-loved English TV personality, famous for his enthusiasm for math and his… show more.

This book loves to pretend to be a Raymond Chandler type thriller with a hard-boiled detective, but what might be a stereotype is offset by the detective's past and his personal struggle with depression, as well as a romantic interest in his client, an attractive female mathematician who hires him to figure out why three different mathematicians she contacted about the exact same topic have all died recently.  

Pieces are gathered and put together bit by bit to form a well-balanced mystery complete with false leads and a twist at the end. What makes this novel quite unique is the… show more.

They say that Plato was not a mathematician but was a maker of mathematicians. The same could be said of Martin Gardner, a prolific author who wrote, among many other things, the “Mathematical Games” column for Scientific American for a quarter of a century. Although all his books are excellent, The Colossal Book of Mathematics is a great entry point to Gardner’s oeuvre. It consists of what Gardner viewed as his 50 best Scientific American columns along with addenda containing updated material on each topic. With topics like topology, geometry, recreational mathematics, the infinite, and probability, each article is an… show more.

Everyone knows what probability is, and we all understand how a coin flip works, but not everyone can explain the optimal betting strategies for a roulette table. We don’t study probability to understand the likelihood of events. We study probability to understand the expected outcomes of business processes that depend on those events.

In other words, this book won’t just teach you about probabilities, it will teach you about business strategies associated with those probabilities. It will help you answer a question like: How do I maximize the profit on this life insurance policy, given this set of survival probabilities?… show more.

This is one of my favorite underappreciated statistics books of all time. Non-parametric statistics can be otherwise described as statistics without assumptions. The entire goal of this field of study is to prove X is greater than Y without making any assumptions about the underlying distributions of X or Y. The methods are different, and they require more data than other methods, but the learning journey is invaluable.

I personally believe that modern machine learning is simply the modeling section of the school of non-parametric statistics. Working through this book will give you a much deeper understanding of why… show more.

The book is a well-curated collection of the essential mathematical concepts that form ML. You may experience a cultural shock jumping to this book from the previous one, because the writing in this book is a bit formal. However, it is the missing but necessary piece for building solid foundations for practical ML. You will find it more valuable combining the intuition behind ML that you gained previously. And the explanations in the book are succinct and from the ML perspectives. For instance, partial derivatives are explained in terms of neural network weight optimization. I wish the concepts in Linear… show more.

This book provides a systematic account of how to understand and structure mathematical proofs. Its approach is almost entirely syntactic, which is the opposite of how I naturally think – I tend to generate arguments based on examples, diagrams, and conceptual understanding. But that difference, for me, is precisely what makes this book so valuable. Solow gives a no-nonsense, practical, almost algorithmic approach to interpreting logical language and to tackling the associated reasoning. His book thereby provides the best answer I know of to the “How do I start?” problem so often encountered when students begin constructing proofs.  

Research in cognitive psychology has revealed a lot about human learning and how to make it more effective. Most mathematics students – and indeed their professors – know very little about this research or how to apply it. Weinstein and Sumeracki’s book explains how psychologists generate evidence on learning, gives a basic account of human cognitive processing, explains some strategies for effective learning, and gives tips for applying them. It is not about mathematics and it certainly will not make advanced mathematics simple, but I think that we would all have an easier time if we were more aware of… show more.

This is a classic and for good reason. I love the idea of putting each thing you have to do on its own piece of paper because once you do, you can organize and manage everything on your plate. You can triage and prioritize what needs to happen when, in any area of your life. And the “Someday/Maybe” file is a great way of retaining ideas and plans that aren’t a priority right now.

First published in 1937, this lovely book is a true classic. In two volumes Bell brings to life 30 or so mathematicians, from Archimedes to Cantor. When first reading the book many years ago I had remembered some of the names from school and college, but only as labels to theorems or equations, and I felt taken into a delightful new realm of knowledge – I could now think of Fermat, Lagrange, Gauss, and Riemann as people. And I began to want to know more about the scientists whose names I had heard in school and college. Bell’s book had… show more.

Among my children’s bedtime stories The Number Devil was a favourite. It’s about a boy who finds his school maths lesson dull and pointless. One night in his dreams he gets visited by the Number Devil, who introduces him to the astonishing patterns to be found in numbers. By making the lead character a maths-sceptic, the author carries the reader along so that we are all drawn into the hidden beauty of mathematics. The book has wonderful colour illustrations, which adds to its charm. Parents love it too.

Hailed by educators throughout the world, Howard Gardner’s theory of multiple intelligences has been applied to hundreds of classrooms and schools. It shatters the theory that being smart is only measured by math and English skills. Through scientific and unquestionable documented historical research. Goodbye to SATs. Now we can acknowledge that geniuses can also be measured by linguistics, music, mathematical, spatial, body, and personal intelligence. A politician, athlete, architect, dancer, or musician can be brilliant in what they do but may not be able to write, speak, or do mathematics. We have known this to be our experience but now… show more.

Forget the tape measure. Leave the fractions, decimals, and mathematics behind. Long before the tape measure was a universal adornment on the woodworker’s belt, people designed furniture, houses, bridges, and cathedrals using nothing more than simple whole number ratios. This slender tome will show you how to do just that and will entertain you along the way. 

I admire James Gleick’s Chaos. Who doesn’t? It’s a landmark book, a masterpiece of science writing. But let’s be real: it’s not exactly a beach read, is it? If Chaos is a complex aged wine, then this book is a simple autumn cider: a photographic collage of nature’s fractals, sweetened with a splash of Gleick’s lyrical prose.

I stumbled on this in a used bookstore. What a find! The old-school, kid-friendly illustrations lead swiftly from simple beginnings (“What happens when you stretch a painting?”) to the depths of undergraduate topology. I haven’t used this in the classroom yet, but honestly, I could imagine busting it out with anyone from first-graders to first-year PhD candidates.

It’s a little weird that this book should find a place on my list. It’s a book about how society has become resistant to anything that is difficult and painful and the kinds of people that we have become as a result. But mathematics is difficult! To understand mathematics you have to think hard, sometimes for a long time. Moreover understanding something hard is discontinuous, it requires a leap to a new way of thinking. You have to start with a problem and this problem might be an ambiguity or a contradiction. A is true and B is true but… show more.

One way of enlivening any presentation of mathematics is by including some history of the subject, but this only really works if there is some serious scholarship behind it. I especially like Hollingdale's book, partly because of the concise writing style, and partly because of the unusually good balance between history and mathematics itself. The calculus, in all its various forms, with some aspects going right back to the Ancient Greeks, is treated especially well.

This book is a brilliant interweaving of politics, history, and intrigue, with characters living ordinary lives, described in the spirit of a Russian novel. With one story threading into another, the book moves us forwards. We fly over the tall mountains, misty valleys, and green fields of current abstract maths and fundamental physics to witness the true beauties of truth. And in the end, Stewart confesses: “No one could have predicted that a pedantic question about equations could reveal the deep structure of the physical world, but that is exactly what's happened.”

As with many of Stewart’s books, Why Beauty… show more.

This classic book, in board book form or paperback, is spare of words with bold pictures. A red carpet and green walls are set against a child’s bright yellow gown. A tender story mixes in elementary math, offering the charm of counting backwards. Soothing for bedtime, it’s one of my favorite gifts for the very youngest.

Are you stuck on a single sentence that keeps expanding but goes nowhere? Then tame it by cutting it down and finishing it off now. Ian Hacking is the master of the subject-verb-predicate sentence in historical writing. And this book, in addition to being a model of stylistic clarity, changes how we think about modernity, mathematics, danger, and risk. You’ll never be afraid of being clear again.

It is fair to say that many people—even those who loved mathematics as students—view mathematics as having always existed. The idea that definitions and theorems that fill our school textbooks were created or discovered by human beings is something that has never crossed their mind. In fact, mathematics has a long, fascinating, and rich history, and William Dunham’s Journey Through Genius is a perfect introduction to the topic. Dunham expertly writes about the history of topics like geometry, number theory, set theory, and calculus in a way that is entertaining, understandable, and rigorous. After finishing Journey Through Genius, readers… show more.

This is the tender and intriguing story of a brilliant math professor with a peculiar problem--ever since a traumatic head injury, he has lived with only eighty minutes of short-term memory. The other main character is a young Housekeeper, with a ten-year-old son, who is hired to care for him. Each day, the characters are reintroduced to one another, while the Professor’s long-term memories open up new directions for them all, creating close bonds and a strange familiar unit. It’s a simple story but it has remained with me for some reason – perhaps because memory is so key to… show more.

This fine book is about learning the relationships between what is seen in an image, and what is known about the world. It’s a counterpart to our book on feature extraction and it shows you what can be achieved with the features. It’s not for those who shy from maths, as is the case for all of the books here. So that you can build the techniques, Simon’s book also includes a wide variety of algorithms to help you on your way.

That Steven Strogatz, Cornell Professor and longtime New York Times columnist, is unsurpassed as an expositor of mathematics, goes without saying. No one can make the abstract and technical appear simple and intuitive like Strogatz. In Infinite Powers he takes on the Calculus -- the central pillar of modern mathematics that is also the bane of many a high-school student. It is an immensely powerful field, and at its core is a concept that is both counter-intuitive and paradoxical: the infinite.

The roots of the calculus, we learn, go back to the ancient Greeks, whose notions of the infinite were… show more.

The author explains the importance of abstraction in logic, demonstrating its three main components: paths made of long chains of logic, packages made of a collection of concepts structured into a new compound unit, and pivots to build bridges to previously disconnected places.

Eugenia Cheng does an excellent job of abstracting principles of logic to better understand challenging real-world societal issues such as affirmative action and cancer screening. I found it quite compelling to understand how and why she came to her positions on various issues, through her axiom that "avoiding false negatives is more important than avoiding false positives."… show more.

This is a deep and beautifully elegant overview of the ideas underlying statistical inference. It is the finest concise outline I know of the foundations, dealing with the key concepts and ideas in an accessible way. Written by one of the leading creators of modern statistics, without unnecessary mathematics or superfluous detail it includes a balanced description of the fundamentals of distinct schools of thought, such as Bayesian and frequentist schools. The book did not exist when I started learning statistics, but I am certain I would have understood the discipline’s subtleties much sooner if it had.

Gödel (1906-1978) is, like Newton, an unpromising subject for biography. He was antisocial and mentally unstable. His obsessive fear of being poisoned led eventually to him starving himself to death. 

Rebecca Goldstein is a professor of philosophy with a deep interest in logic and the foundations of mathematical truth – the applecart that Gödel overturned in 1931 with his tremendous paper on the incompleteness of axiomatic systems. She is also an experienced novelist. This combination makes her just the right person to construct a gripping story out of Gödel’s weirdness and world-shaking importance.

I well remember when Erdos came to MIT to visit my wonderful friend Gian-Carlo Rota. He traveled without money and without a place to stay. He depended entirely on friends. What he offered in return was something of much greater value: his ideas. A mathematician searches everywhere for the right problems to work on – not easy, not random, but opening a door from what we know to what we don't know. Erdos gave that ideal gift to his friends. If you wrote a paper with him, your Erdos number is 1.  

Ekeland’s book is an entwinement of philosophical views of scientists with metaphysics dealing with nature’s directives. It’s an embroidery of lively anecdotes involving illustrious individuals and great historical moments of human decisions. We go through the Peloponnesian Wars, Venetian concessions to the Hapsburg emperor Maximilian, Darwin’s voyage to the Galapagos, and other enriching accounts. His explanations are clear, elegant, fluid, exhilarating, and suspenseful, reminding me of the effortless style of Richard Feynman. While reading, I felt compelled by a force of nature and purpose to learn about the best of all possible worlds.   

More than any other, this book influenced me most about wanting to study mathematics. Of course, I was young at the time and strongly partial to Einstein’s remark, “This is beyond doubt the most interesting book on the evolution of mathematics which has ever fallen into my hands.” Many years later, when I exhaustively tried to find the book in any bookstore I passed, it was out of print. So I suggested it to my publisher, who immediately acquired the rights and republished it under my editing guidelines. It is the quintessential lure into mathematics for readers of any age.   

The full title of this wonderful book is The Theory That Would Not Die: How Bayes' Rule Cracked the Enigma Code, Hunted Down Russian Submarines, and Emerged Triumphant from Two Centuries of Controversy. Bayes’ Theorem is a one-line mathematical formula, named after a Scottish church minister, that calculates the updated probability of an event occurring given new information that we receive.  Applications of Bayes’ Theorem are diverse and profound, from recommendation systems to automated translation algorithms to weather prediction.

This well-researched book does a deep dive into the most important characters of mathematical statistics over the past three centuries, and… show more.

John Urschel is an African-American mathematician specializing in graph theory, who recently completed his Ph.D. in mathematics at MIT. But he is better known for his football career, as a starting offensive lineman for the Baltimore Ravens. Six of Urschel’s papers were completed while he was still in the National Football League.

Mind and Matter is John Urschel’s memoir, co-authored with his wife Louisa Thomas. Each chapter alternates between football and mathematics, and how his success on the field translated to success in the classroom, and vice-versa. I loved how accessible the book is, for readers of all ages, and… show more.

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.

The Four Color Problem was one of the most baffling questions in mathematics for over 120 years. First posed in 1852, it asks whether every map can be colored with four colors, or fewer, so that regions adjacent along a boundary have different colors. The answer (yes) was finally obtained in 1976, with massive computer assistance. This method was initially controversial, but the result is now firmly established. This highly readable account, with full-color illustrations, opens up the history and the personalities who tackled this topological enigma, as well as making the mathematics comprehensible. The path to the final solution… show more.

Kornbluh’s book is an incredible revelation. It shows that psychoanalysis provides an insistence on a formal interpretation that allows it to have a privileged critical position relative to capitalism. By showing capitalism’s formal impasses, psychoanalysis provides the perfect supplement to a Marxist critique and opens up possibilities for envisioning a non-capitalist future. The book uses realist fiction as a way to envision the formal critique of capitalism and really makes one want to read the books under discussion. I have taught this book to students, and they love it more than any other I’ve ever used. 

I didn’t want to leave older children out of this list. This book would make a fantastic gift for a child who loves science but considers themselves “too old” for picture books. This beautifully illustrated chapter book features children who followed their curiosities and questions to real discoveries that helped the world! A very inspiring read.

An enthralling, fictional description of a young scientist (Einstein) and his dreams/thoughts about space, time, relativity, and the nature of reality. The book fictionalizes Einstein’s dreams in 1905, his “Annus Mirabilis” (“Miracle Year”), in which he wrote four fundamental papers, including one on his theory of Special Relativity. While this is a work of fiction, the physics concepts are beautifully explained.

The number Pi, of course, has no history; like any other number, it is what it is and exists outside of time and space. But the human understanding of Pi has a rich history indeed, beginning with the discovery that the circumference of a circle is more than three times, but less than four times, its radius. The centuries brought better estimates, better ways of discovering new estimates, the discovery that Pi is irrational, the recognition that it has a habit of popping up in areas of mathematics that appear to have nothing to do with circles, and a slew… show more.

Are you still here? Good. Because by now you are probably reading to tackle some university-level courses in quantum physics, right? Well, with your background in pop quantum physics all you need to get there is a little more abstraction. So, if you have the stomach for a bit of mathematics, Quantum Mechanics: The Theoretical Minimum by Leonard Susskind is your ticket to the big show! (Don’t say I didn’t warn you about the math, though.)

While studying computer networks, Claude Shannon did something pretty impressive. He reformulated the majority of classical statistics from scratch using the language and concepts of computer science. 

Statistical noise? There’s a new word for that; it’s called entropy. Also, it turns out it is a good thing, not a bad thing because entropy is equal to the information content or a data set. Tired of minimizing the squared error of everything? That’s fine, minimize the log of its likelihood instead. It does the same thing. This book challenges the assumptions of classical statistics in a way that fits neatly… show more.

Climate fiction, or “cli-fi” as it is now known, lets readers imagine the world about which scientists are warning, a world where climate-fueled extremes upend humanity’s everyday existence. This book tells the story of a Midwestern math whiz who studies “worst-case scenarios” for a living. When one of those scenarios collides with his own life, action, adventure, and love follow.

David Hilbert was the most important mathematician at the dawn of the 20th century. In 1900, he gave the mathematical community its homework for the next 100 years setting out the list of open problems that had to be solved by 2000. While to the rest of the mathematicians, he may have appeared as their professor, he was also the class clown. As colorful and funny as he was brilliant, you cannot but come away loving this great mathematical genius.

When I was asked to review this book, my first instinct was to decline. Newton (1642-1727) was a towering genius but a dull fellow, with no interest in other human beings. He often published anonymously for fear that, he explained: "Public esteem, were I able to acquire and maintain it … would perhaps increase my acquaintance, the thing which I chiefly study to decline." How can a biographer make such a person interesting?

The author dodges very nimbly around this problem, giving us an account, not so much of the man as of his reputation and influence. Perhaps this means… show more.

This is the most fun book that has ever been written about the famous philosophical challenges posed by the proper interpretation of quantum mechanics. It is extremely difficult to say what the real world could possibly be like considering that quantum mechanics is so accurate at predicting our observations of it. Albert is a wonderful guide to this problem. His book is genuinely funny and down-to-earth (yes, I mean it!) and it introduces only as much technical and scientific machinery as is absolutely necessary. There is no other quantum mechanics book quite like this one.

The Three Body Problem is a real-life unsolved math problem concerning the motion of three bodies (think a star and two orbiting planets), all acting on each other by the pull of gravity. Given their positions and movements at times, what will happen in the future? Will they eventually fly away or fall into the star?  

The Three Body Problem is also a mathematical mystery by Catherine Shaw (a pen name – shhh), set in Cambridge in Victorian times, which contains three actual dead bodies, all of the mathematicians working on the eponymous problem. Another mathematician, who knew all three… show more.

Weinstein takes the age-old question – what is literature? – and transforms it into why we (would want to) read literature. For him, literature changes us, allows us to be someone else, and provides us insight into the world we inhabit, and many more worlds we haven’t. He reads a broad array of works, from Sophocles to James Joyce and Toni Morrison, and thinks about such issues as identification, empathy, and sympathy with those we come to ‘know’ through our reading.