Hey, math people! The University of Cambridge prepared a unique list of math books you should read in 2022.
This list of interesting math books you should read is mainly intended for sixth-formers planning to take a degree in mathematics. However, everyone who likes mathematics should look at some very suitable items for less experienced readers, and even the most hardened mathematician will probably find something new here.
What are the most useful math books you should read?
The range of mathematics books now available is enormous. This list contains a few suggestions that you should find helpful. They are divided into three groups: historical and general which aim to give a broad idea of the scope and development of the subject; recreational, from problem books which aim to keep your brain working, to technical books, which give you insight into a specific area of mathematics and include mathematical discussion; and textbooks which cover a topic in advanced mathematics of the kind that you will encounter in your first year at university.
Alright, buckle up, because we’re about to dive into the mind of a guy who was, by all accounts, so unbelievably brilliant and simultaneously so unbelievably weird that people called him “the strangest man”. We’re talking about Paul Dirac, the British physicist who, if you haven’t heard his name alongside Einstein or Newton, you absolutely should have. And Graham Farmelo’s “The Strangest Man: The Hidden Life of Paul Dirac, Mystic of the Atom“ is here to explain why.
First off, let’s get the core deal with Dirac. This dude was a pioneer of quantum mechanics, snagged a Nobel Prize for Physics (the youngest theoretician ever to do so, mind you), and basically reshaped our understanding of the universe. Michael Frayn even called the book “a monumental achievement – one of the great scientific biographies”. Pretty high praise.
But here’s where the “Strangest Man” part really kicks in:
The Man Himself: A Human Robot with a Hidden Heart?
Imagine a genius so pathologically reticent that his postcards home were only about the weather. Yeah, that was Dirac. He was described as strangely literal-minded, legendarily unable to communicate or empathize, and a loner. Reviewers throw around terms like “bona fide eccentric,” “nerd,” “geek,” and “social misfit”. One even suggested he had “the emotional depth of a carrot”. Ouch.
Part of this seems to stem from a pretty brutal childhood. His very strict father would single out young Paul for one-on-one suppers where they only spoke French. Dirac deeply resented this and blamed those “excruciating evenings” for his extreme reticence, even vowing never to speak French again as an adult. This tough upbringing seemingly molded him into the “introverted master of clear thought” he became.
Despite all this, there’s a softer side. He showed loyalty to his family and friends and apparently cried when Einstein died, not because he lost a friend, but because “science had lost an invaluable scientist”. He also had a soft spot for Disney classic movies and “Odyssey 2001“. See? Not all circuits and no soul.
The Brain Power: Pulling Reality Out of Thin Air (with Math)
Now, for the mind-blowing stuff he actually did.
- Antimatter, Baby! Dirac’s greatest triumph was hypothesizing the existence of antimatter (the positron). Get this: he didn’t look at any experimental data. He just “messed around with the equations for the electron”, found a “beautiful and elegant” way to manipulate them, and voilà, predicted a particle that was like an electron but “opposite in nature”. Less than five years later, experimentalists found it. This prediction was “motivated solely by faith in pure theory, without any hint from data”. That’s like predicting a whole new species of animal just by looking at a blueprint of existing animals and realizing the blueprint implies something else must be there. Wild.
- Quantum Everything: He played a major role in establishing quantum mechanics and was a pioneer of Quantum Field Theory (QFT) and Quantum Electrodynamics (QED). His work on magnetic monopoles even became some of the basis for string theory.
- The Textbook that Wouldn’t Die: His quantum mechanics textbook, written in 1930, is still in print and used as a standard today. When Albert Einstein himself admitted he had problems following some of Dirac’s equations, and he was called the “greatest English physicist since Isaac Newton“, you know you’re dealing with someone operating on a different plane.
Dirac’s secret sauce? A unique blend of “part theoretical physicist, part pure mathematician, part engineer“. His engineering training gave him a visual thinking ability and a deep belief in mathematical beauty and elegance. If an equation wasn’t beautiful, it probably wasn’t right. This led him to do “apparently unsound things that would annoy the mathematical purists”, like inventing the Dirac delta-function, which wasn’t mathematically respectable for decades, but he just knew it was right.
The Book Itself: Peeking Behind the Reticent Curtain
Farmelo, who is a senior research fellow at the Science Museum, London, and an associate professor of physics at Northeastern University, US, managed to write over 500 pages about this incredibly reserved man. He had access to Dirac’s personal papers, which is a true treasure for anyone trying to understand such a private individual.
The book is praised for being “incredibly detailed” about Dirac’s personal life and successfully bringing “so many of the characters in Dirac’s circle to life”. It covers not just Dirac, but also the “rise and golden age of quantum mechanics”, featuring giants like Einstein, Bohr, Heisenberg, Pauli, Born, Fermi, and Oppenheimer. It also paints a rich historical panorama, showing how science intertwined with World War II, the Cold War, and the Manhattan Project. It’s a “superb work” and an “excellent biography”.
Now, some folks had a little beef:
- Science Light: A recurring criticism is that while the personal life is super rich, the scientific details are “practically glossed over”. Some wished Farmelo had gone deeper into the physics, lamenting that “every time Farmelo recounted an amazing achievement of Dirac’s I felt as if I had been rushed through it”. However, to Farmelo’s credit, he aims to explain Dirac’s work in “general terms, without any scary equations”, making it accessible to non-physicists.
- The “A” Word (Autism): This is a hot topic in the reviews. Farmelo “postulates that he suffered from a high functioning form of autism”, and some reviewers found the “case that Dirac was solidly on the spectrum” to be “extremely compelling”. But others were “a little leery of this new trend to classify every genius as autistic lately”. Some felt the author’s psychological analysis was “superficial”, “uninformed”, or based on “unreliable sources”, even perpetuating “fallacious negative stereotypes about autism”. So, that’s a whole rabbit hole the book goes down, with mixed results for readers.
The Verdict: Is It Worth Your Precious Brain Calories?
Absolutely. “The Strangest Man” is “a fascinating glimpse into the birth of quantum mechanics, through the life of a man who was at once one of the pillars of the community and yet still an outsider”. It’s for anyone fascinated by “the lives of brilliant outsiders”, the history of science, or just how some brains work in ways that are, well, strange.
It perfectly encapsulates why Niels Bohr, another titan of physics, once said: “Dirac was the strangest man”. And after reading this, you’ll totally get it. It’s a journey into the mind of a guy who didn’t just walk the path of science; he built his own, guided by an almost mystical faith in mathematical beauty, and pulled new realities into existence from pure thought.
Have you ever wondered about the minds behind the most profound mathematical discoveries? Paul Hoffman’s “The Man Who Loved Only Numbers: The Story of Paul Erdős and the Search for Mathematical Truth” offers a masterful biography, providing a vivid portrait of one of the 20th century’s most eccentric and influential mathematicians, Paul Erdős. This book isn’t just for math enthusiasts; it’s a fascinating look into a singular human being whose life was as unconventional as his genius.
Paul Erdős: The Wandering Monk of Mathematics
Erdős was, by all accounts, a unique individual, incomparable even among other singular men like Albert Einstein. He was a mathematical nomad, wandering the world and living primarily from the kindness of fellow mathematicians. Possessions meant little to him; he carried just a suitcase with a single change of clothes, considering private property a nuisance. His dedication to mathematics was absolute: he often thought about theorems, conjectures, and problems for as much as 18 to 20 hours a day, sometimes aided by amphetamines and coffee. His sole passion, religion, and goal in life was the solving of mathematical problems.
His eccentricities extended to his personal language: he called children “epsilons” (after the mathematical term for a small positive infinitesimal quantity), women “bosses,” men “slaves,” alcohol “poison,” and music “noise”. God was affectionately, or perhaps provocatively, referred to as “The Supreme Fascist” or “The S.F.,” the imagined owner of “The Book” where all elegant mathematical proofs reside.
Despite his seemingly unworldly focus, Erdős was a deeply compassionate and generous man. He gave away much of his meager income to charities, friends, and even panhandlers. He loved children and had a genius for setting each person, regardless of their level, the perfect problem to intrigue and stretch them. His life was a testament to the idea that knowledge doesn’t necessarily lead to material wealth or influence; he simply wouldn’t allow it.
A Pioneer of Mathematical Collaboration
One of the most remarkable aspects of Erdős’s career was his prolific collaboration. He co-authored over 1,400 to 1,500 published papers with more than 500 different people, a quantity of work matched only by the 18th-century mathematician Leonhard Euler. This collaborative style was so notorious that it led to the creation of the “Erdős number”: if you published a paper with him, your number is 1; if you published with someone who has an Erdős number of 1, yours is 2, and so on. Low numbers are highly sought after in the mathematical community. For Erdős, mathematics was always a social activity; he was generous with his ideas, prioritizing the solution of a problem over being the first to prove it himself.
Hoffman’s Skillful Narrative
Paul Hoffman, who knew and interviewed Erdős for about ten years, provides a clear and informative portrait of this unique individual. The book skillfully weaves together Erdős’s life story with accessible explanations of complex mathematical concepts, making it a layman’s guide to startling mathematical discoveries. Even for those who struggled with math in school, the book has a way of making the subject understandable and incredibly exciting. It introduces readers to the world of pure mathematics, its historical background, and the lives and psychology of many famous mathematicians beyond Erdős himself, such as Cantor, Fermat, Gauss, and Andrew Wiles.
While primarily focused on Erdős, the book also provides insight into the turbulent 20th-century history of Hungary and how political events impacted Erdős’s life and travel, especially as a Hungarian Jew affected by WWII and the Cold War.
A Balanced Perspective
Some readers note that while the book excels at portraying Erdős the man, Hoffman’s acknowledged lack of a strong mathematical background leads to a few minor “mathematical glitches” in his explanations, such as confusing “amicable numbers” with “friendly numbers” or describing non-Euclidean geometry. Others felt the book occasionally deviates from Erdős, including too many anecdotes about other mathematicians or focusing extensively on figures like Ron Graham. However, these are generally considered minor quibbles given the book’s overall success in humanizing Erdős and making his world accessible. The title, “The Man Who Loved Only Numbers,” might also be seen as slightly misleading, as Erdős was demonstrably a caring person interested in more than just numbers.
“The Man Who Loved Only Numbers” is an engaging and entertaining read. It’s a wonderful journey into the mind of a genius and the fascinating world of mathematics, showing how a life entirely devoted to an infinite field can be both profound and humorous. If you’re interested in an inspiring story about dedication, collaboration, and the sheer beauty of mathematical truth, even if you’re not a mathematician, this book is well worth picking up. It truly made me wish I had stuck with my math classes!
Richard Feynman is the kind of person who makes you feel both inspired and a little inadequate all at once. Brilliant, endlessly curious, and armed with a wicked sense of humor, he is thoroughly unlike the buttoned-up academic stereotype. “Surely You’re Joking, Mr. Feynman!“ invites readers into the quirky, borderline chaotic life of one of the 20th century’s most brilliant minds. If you’re a fan of the best physics books, this one is an absolute must-read.
What Is This Book About?
This isn’t your typical autobiography, and that’s what makes it so engaging. Rather than a straightforward narrative, “Surely You’re Joking, Mr. Feynman!“ is more like sitting down for coffee with someone disarmingly candid and riotously funny. The book is a series of anecdotes about Richard Feynman‘s life and escapades, touching on everything from quantum physics to cracking safes at Los Alamos. Yes, the man who revolutionized physics also had a knack for breaking into file cabinets!
Feynman’s genius wasn’t just confined to his lab. His curiosity extended to playing the bongo drums, deciphering ant trails, and pulling pranks on Nobel-level physicists. This collection of stories brilliantly distills that childlike wonder and relentless drive to know how things work down to a highly entertaining read.
Why It’s One of the Best Physics Books (Even if You Don’t Like Physics)
Physics might not be your thing, and that’s totally okay. The beauty of this book is that it doesn’t hit you over the head with formulas or complex theories. Instead, Feynman’s enthusiasm for figuring things out is contagious. His stories sneak in serious science lessons without feeling at all preachy.
For example, his chapters on quantum mechanics and his work at Los Alamos during the Manhattan Project are peppered with humor and surprises. Somehow, he makes superfluidity and nuclear physics seem like they’re part of a wild adventure. This is why the book stands out among the best physics books—not because it’s a dense lecture, but because it’s a glimpse into the playful mind of a scientific icon.
What Makes Feynman Different?
Reading this book, you begin to understand why Feynman felt like an outlier even among geniuses. Feynman didn’t just know physics; he lived it. He sought to understand everything at its core level, ruthlessly cutting through jargon and pretentiousness. Even when he was exploring abstract topics like quantum electrodynamics, his practical approach and irreverent humor made him refreshingly relatable.
But what makes Feynman so endearing is that he wasn’t satisfied limiting himself to physics or his career. He fully embraced life’s curiosities, whether that meant learning to draw, playing in samba bands, or unlocking the mysteries of bureaucracy purely for fun.
Not Your Traditional Scientific Hero
What I love most about this book is how human it makes Feynman feel, without diminishing his brilliance. He pokes fun at himself and the world around him. Whether he’s hilariously recounting his misadventures in Brazil or calling out the inefficiencies in education systems, Feynman is always genuine. His ability to cut through pretense and see the wonder of the world is arguably his greatest strength.
This quality makes the book endlessly inspiring. By the time I turned the last page, all I wanted to do was look at the world with a little more curiosity and not be afraid of asking questions, no matter how “silly” they might seem.
Why You Should Read It
If you’ve got a fascination with science, a love for lively personalities, or are exploring the best physics books to start your reading list, this book is practically screaming your name. But even beyond that, it’s a story about passion, curiosity, and living boldly.
You don’t have to know a thing about quantum mechanics to walk away with valuable lessons. Feynman reminds us that brilliance and playfulness don’t have to live in separate corners. Sometimes, the best ideas come when you’re fooling around and having fun.
A Final Thought (and Why You Should Pick It Up Now)
Feynman’s stories don’t just entertain; they make you think. He constantly challenged himself and the conventions around him. Whether he was feeling out of place among Nobel laureates or just seeing the humor in a mundane situation, Feynman lived life on his own terms.
Perhaps the best physics books aren’t just about science but about the scientist behind the theories. This book isn’t just a chronicle of a brilliant mind; it’s a call to action for all of us to approach life with curiosity, humor, and boldness.
If you haven’t read “Surely You’re Joking, Mr. Feynman!“ yet, stop pondering and grab a copy. Settle in, and prepare to be inspired (and entertained) by the curious adventures of Richard Feynman, the ultimate proof that science and fun really can go hand in hand.
In the Music of the Primes, Marcus du Sautoy tells the illuminating, authoritative, and engaging story of Bernhard Reimann and the ongoing quest to capture the holy grail of mathematics—the formula to predict prime numbers.
Oliver Sacks, the author of The Man Who Mistook His Wife for a Hat, calls The Music of the Primes “an amazing book. . . . I could not put it down once I had started.” Simon Winchester, the author of The Professor and the Madman, writes, “this fascinating account, decoding the inscrutable language of the mathematical priesthood, is written like the purest poetry.
Marcus du Sautoy’s enthusiasm shines through every line of this hymn to the joy of high intelligence, illuminating as it does so even the darkest corners of his most mysterious universe.”
A wonderful collection of ninety-two photographic portraits of some of the greatest mathematicians of all time can be seen in Mathematicians. The beautiful photos by renowned photographer Mariana Cook are supplemented by concise autobiographical prose written by each mathematician. Cook portrays the vivacious and colorful personalities of these outstanding thinkers. Together, the images and text portray a broad collection of people committed to the fascinating study of mathematics.
Readers are introduced to young and old mathematicians, dads and children, spouses and wives through the fascinating black-and-white photographs. They include Fields Medal winners, people just starting out in their significant careers, and established luminaries in the field. As the mathematicians discuss how they became interested in mathematics, why they love the subject, how they stay motivated in the face of mathematical challenges, and how their greatest contributions have paved new paths for future generations, their candid personal essays reveal unique and wide-ranging thoughts, opinions, and humor. David Blackwell, Henri Cartan, John Conway, Pierre Deligne, Timothy Gowers, Frances Kirwan, Peter Lax, William Massey, John Milnor, Cathleen Morawetz, John Nash, Karen Uhlenbeck, and numerous other mathematicians are among those mentioned in the book.
This photography collection is an inspiring tribute to mathematicians everywhere, conveying the beauty and excitement of mathematics to individuals both inside and beyond the subject.`
Sofya Vasilievna Kovalevskaya, a professor of mathematics at the University of Stockholm, published her memories of growing up in Russia in the middle of the nineteenth century in 1889. Professor Kovalevskaya was already well-known on a global scale, albeit perhaps not for the reasons she should have been: less as the accomplished mathematician she was than as a “mathematical lady”—a strange but intriguing phenomenon.
Her novel became popular right away. She had originally intended for it to be published in Swedish, the language of her chosen country.
Discover the world of mathematics like never before in this beautifully written and thought-provoking book, The Mathematical Experience. Whether you’re a cultivated thinker or a practicing mathematician, The Mathematical Experience offers a unique vantage point to explore the vast landscape of mathematics.
More than just a mathematics book, The Mathematical Experience delves into the philosophy, psychology, history, and biographies of mathematicians. It is a comprehensive guide to the mathematical experience in all its forms.
Perfect for liberal arts students, future teachers, or anyone interested in mathematics, this book includes term paper topics, essay assignments, problems, computer applications, and suggested readings. It is a valuable resource for any mathematics course or as casual reading material.
This new edition delves into the fundamental issues of mathematics that are often overlooked. It provides an excellent initiation into the more challenging aspects of the subject, helping readers acquire a real understanding of mathematics.
Written by distinguished mathematicians, this book offers a clear and engaging exploration of the Queen of Sciences. Get ready to be entertained and enlightened as you dive into the fascinating world of mathematics.
“Martin Gardner is solely responsible for the development of the field of “recreational mathematics,” whether he is talking about hexaflexagons, number theory, Klein bottles, or the meaning of “nothing.” The most well-known essays from Gardner’s illustrious “Mathematical Games” column, which appeared in Scientific American for twenty-five years, are collected in The Colossal Book of Mathematics. Inspiring readers to look beyond numbers and formulae and explore the application of mathematical principles to the mysterious world around them, Gardner’s collection of captivating puzzles and mind-bending paradoxes opens mathematics accessible to the general public. This collection of essays is a substantial and conclusive memorial to Gardner’s contributions to mathematics, science, and culture. The topics covered in the essays range from basic algebra to the twisting surfaces of Mobius strips, from an endless game of Bulgarian solitaire to the impossibility of time travel.
The Colossal Book of Math tackles a wide range of topics in its twelve sections, each strikingly brought to life by Gardner’s sharp insight. Gardner expertly leads us through complex and wondrous worlds by starting with topics that appear to be simple: using basic algebra, we consider the fascinating, frequently hilarious, linguistic and numerical possibilities of palindromes; using simple geometry, he dissects the principles of symmetry that the renowned mathematical artist M. C. Escher uses to create his unique, dizzying universe. Few contemporary philosophers combine a deep aesthetic, and imaginative impulse with a strict scientific skepticism like Gardner does. For instance, in his breathtaking investigation of “The Church of the Fourth Dimension,” he masterfully imagines the geographical possibilities of God’s presence in the world as a fourth dimension, at once “everywhere and nowhere,” bridging the gap between the worlds of science and religion.
Gardner enables the reader to further engage difficult subjects like probability and game theory, which have bedeviled shrewd gamblers and illustrious mathematicians for generations, with unlimited wisdom and his signature humor. Gardner consistently demonstrates his ferocious intelligence and sweet humor, whether disproving Pascal’s wager with elementary probability, creating musical patterns with fractals, or unraveling a “knotted doughnut” using basic topology. Hexaflexagons, “Nothing,” and “Everything,” as well as the reassuringly familiar “Generalized Ticktacktoe” and “Sprouts and Brussel Sprouts” are both confronted in his writings. He expertly navigates these mind-bogglingly obscure themes, and with addenda and recommended reading lists, he enriches these great essays with a fresh perspective.
Gardner is admired by mathematicians, physicists, writers, and readers alike for his immense knowledge and insatiable curiosity, which shine through on every page. The Colossal Book of Mathematics is the largest and most thorough math book ever put together by Gardner and remains a vital resource for both amateur and experienced mathematicians. It is the product of Gardner’s lifetime passion for the wonders of mathematics.”
“So goes the story of Gordius, king of Phrygia, and his tight Knot. However, Alexander the Great simply sliced the Knot with his sword after many had tried and failed. He finally made it as far east as Northern India after conquering the majority of Asia.
Cut the Knot is a collection of probability puzzles designed to stretch the mind and improve logical and mathematical reasoning. These problems and their solutions were originally published on cut-the-knot.org and reflect the work of brilliant minds worldwide. Alexander Bogomolny will walk you through these chosen riddles following a thematic sequence. Before reading their solutions, give them a try. The non-trivial, unexpected solution might be just what you need, as it was for Alexander the Great.”
“This book’s goal is to carefully but untechnically illustrate the distinctions between high-level, research-level mathematics and the kind of mathematics we learn in school. Readers of this book will leave with a deeper grasp of seemingly counterintuitive ideas like infinity, curved space, and imaginary numbers since the most fundamental distinctions are philosophical. The opening chapters discuss general facets of mathematical theory. Following these are talks of more specialized subjects, and the book concludes with a chapter that addresses frequently asked social concerns concerning the mathematical community, such as “Is it true that mathematicians burn out at the age of 25?” Anyone who wants to better grasp mathematics should start with this introduction.”
