The Math and Myth of Coincidence
by Joseph Mazur
(Basic Books; March 29, 2016)
“Mazur gently dashes icy water on our sense of wonder, patiently doing the math to explain multiple lottery winners, ‘remarkable’ accidental scientific discoveries and wrongheaded government policy.”
—Keith Blanchard, Wall Street Journal
"Coupling lively anecdotes with the principles of probability, Joseph Mazur balances the fun of a great coincidence with the logical thinking of a mathematician. With a lightness of touch and a witty turn of phrase, Mazur sweeps aside pseudoscience and conspiracy theories, proving that there are rational explanations for even the most extraordinary events."
"Always entertaining and frequently insightful, “Fluke” is never less than thought-provoking."
--The Wall Street Journal
“Like John Allen Paulos, in Innumeracy (1988), mathematician Mazur takes what could be difficult, abstruse subjects—probability and statistics—and makes them entertaining. The author’s focus is coincidence, in particular our perception of coincidence. He astounds us with some eye-opening facts (it’s actually quite likely that a squirrel might get hit by lightning while crossing a street, even though it sure doesn’t seem all that likely), shows us that seemingly astounding things are actually not that astounding (the same person winning a lottery four times isn’t all that improbable), and explains how it’s our own lack of familiarity with mathematics and the nature of probability that makes things seem wildly unlikely (a certain event might seem rare and unique to us, but in terms of probability, it can be entirely expected). The author draws examples and illustrations from a variety of fields—law enforcement, economics, the sciences—and, when he unavoidably gets into some fairly complicated mathematical discussions, he explains his terms and remembers that, for the most part, his readers aren’t mathematicians. An ideal book, then, for the lay reader who is curious about the nature of coincidence.”
— David Pitt, Booklist
“A lively look at the statistical probabilities of seemingly unlikely events. It is in the early running to be among the best books of the year.” —Sobering Thoughts
"A great read for someone who wants to have fun thinking."
-- The Carroll County Times
In Fluke, he sets out to mathematically disentangle such coincidences from our all-too-human notions of fate and destiny. I say “too human” because we all love a happy coincidence story: as Mazur puts it, “in this enigmatic galaxy, [such stories] validate our longing for individuality”. This is another Mazur hallmark: discursive forays into psychology, physics, philosophy, and history. --Robyn Arianrhod, Cosmos
“Mazur’s thoughtful tour reveals the explanatory power of probability theory in the larger world.”
“A mathematics romp through amazing coincidences… While [Mazur] does not go beyond high school algebra, readers who pay attention will learn the basics of probability, bell curves, standard deviations, hidden variables, and how to calculate the odds of a monkey typing Shakespeare.”
“With charm and clarity, Joseph Mazur leads us through the strange terrain of chance and surprise. He explains why apparently remarkable coincidences are usually more likely than we imagine, because we underestimate how large our world really is. Not so much probability theory as improbability theory! A terrific read, and a welcome antidote to superstition and gullibility.”
—Ian Stewart, author of Professor Stewart’s Incredible Numbers
“Mazur has written a wonderfully insightful book. He shows how it is that our purely psychological expectations about what might happen in the real world, and our culturally acquired notions of order and disorder, often give us a completely false sense of the chance that something will, in fact, occur in the world outside.”
—Richard Lewontin, professor of biology emeritus at Harvard University and author of The Genetic Basis of Evolutionary Change
“Clear, humorous, and grounded in history and culture, Fluke shows you why anything that can happen is bound to happen sometime. But just as rainbows still thrill us when we parse the physics, dissecting bizarre coincidences doesn’t dilute our amazement. Mazur has accomplished the seemingly impossible feat of writing a book for everyone.”
—Marjorie Senechal, editor in chief, Mathematical Intelligencer
“In Fluke, the author takes us on a marvelous guided tour of the world of the unlikely and the improbable. After reading Fluke, you will definitely come away with a deeper understanding of why wildly improbable coincidences may not be so improbable after all.”
—Ronald Graham, chief scientist at the California Institute for Telecommunications and Information Technology
“A Tour de force of masterful writing that weaves together simple and not-so-simple mathematical notions of probability and statistics into various intriguing coincidences form fact and fiction, explaining with nuance various strange phenomena. Mazur’s book will teach you some of this mathematics, leaving you quite equipped to understand the role of chance in your life without resorting to magical thinking.”
—Gizem Karaali, editor of the Journal of Humanistic Mathematics
"The chances are very slim that you'd ever read this blurb. A simple-minded calculation puts the odds at about 50,000 to one against. Yet... here you are. How weird is this seemingly farfetched coincidence? Well, dear reader, you've picked up the right book to answer that question."
—Charles Seife, author of Virtual Unreality: The New Era of Digital Deception
“Joe Mazur’s Fluke walks the reader, hand in steady hand, through the weird and dangerous landscape of extreme probability, distinguishing cause from correlate, and phenomenon from mere coincidence.”
—Jordan Ellenberg, author of How Not To Be Wrong: The Power of Mathematical Thinking
“An exciting addition to the ranks of books exploring the mysteries of chance and coincidence in the vein of The Black Swan and The Improbability Principle.”
—David J. Hand, Professor of Mathematics at Imperial College and author of The Improbability Principle
“Fluke is going to surprise you as a lay reader. You will learn, for instance, that DNA matching is not always clear evidence of guilt in court; and that meeting an acquaintance on your only trip to Disneyland may not be as unlikely as you thought. Mathematician Joe Mazur has written an excellent book, where he shows that probabilistic outcomes are often non-intuitive and unexpected."
—Florin Diacu, author of the award-winning book Megadisasters— The Science of Predicting the Next Catastrophe
Reviews for Enlightening Symbols
From Library Journal
"Mazur delivers a solid exposition of an element of mathematics that is fundamental to its history."
From Publishers Weekly
Mazur's lively and accessible writing makes what could otherwise be a dry, arcane history as entertaining as it is informative."
"[T]his is a good book. It is well written by an experienced author and is full of interesting facts about how the symbols used in mathematics have arisen. It would certainly interest anyone who studies the history of mathematics."--Phil Dyke
From Literary Review
"[I]nformative, highly readable and scholarly."--Brian Rotman
From London Mathematical Society
"Mazur introduces the reader to major characters, weaves in relevant aspects of wider culture and gives a feel for the breadth of mathematical history. It is a useful book for both student and interested layperson alike."--Mark McCartney
From American Mathematical Society Notices
At whatever depth one chooses to read it, Enlightening Symbols has something for everyone. It is entertaining and eclectic, and Mazur’s personal and easy style helps connect us with those who led the long and winding search for the best ways to quantify and analyze our world. Their success has liberated us from “the shackles of our physical impressions of space”—and of the particular and the concrete—“enabling imagination to wander far beyond the tangible world we live in, and into the marvels of generality” [ p. 154]. --Robyn Arianrhod
From The Herald-Tribune
The book is visually exquisite, great care having been taken with illustrations and figures. Mazur's discussion of the emergence of particular symbols affords the reader an overview of the often difficult primary literature. He carefully explains the relative advantages and disadvantages of different notations, allowing readers to see how good notation opens up new realms of thought. Although the book can be enjoyed at many levels, it will most reward those who have some memory of high school algebra and beginning calculus. I can't imagine any reader, however inattentive, escaping without learning a good deal of history and mathematics. For me, the biggest takeaway is the intellectual debt that every human being, no matter in what society, owes to those who went before. --Donald O'Shea
From Mathematical Association of America
Mazur does an excellent job of weaving together a wonderful culturally-rich tapestry, within which he threads the evolution of mathematical notation. His theme is a “tough sell” and therefore the Guggenheim Foundation and his publishers at Princeton University Press should be commended for supporting such an endeavor. --Tushar Das
From The Bulletin of the American Mathematical Society
"Mazur is a master story teller."--John Stillwell
From The European Mathematics Society
Mazur treats only a subset of F. Cajori's monumental A history of mathematical notation (Dover, 1993 first edition 1922) and there is overlap with many other mathematical history books ..., but Mazur adds new findings and insights and it is so much more entertaining than the first and differs from the second because it is much broader and from the third and fourth (which concentrate on the role of zero), and these features make it an interesting addition to the existing literature for anybody with only a slight interest in mathematics or its history.
For full review click here.
From Science Magazine
Joseph Mazur’s Enlightening Symbols: A Short History of Mathematical Notation and Its Hidden Powers is a figurative cabinet rich with such curiosities. However, the book is more than a collection of fun facts about mathematics and the evolution of its language....
As Mazur sets out to address such easily overlooked aspects, he also reaffirms their relevance, showing how rich and complex the topic is....
It is gripping to read about the contributions, big or small, of so many human minds—from real game-changers such as René Descartes, Gottfried Leibniz, and Isaac Newton to less-familiar names such as Robert Recorde (who introduced our equal sign) and François Viète (who used dedicated letters to designate knowns and unknowns in a polynomial equation, an idea later formalized by Descartes)....
Thanks to Mazur’s playful approach to the subject, Enlightening Symbols offers an enjoyable read. --Gaia Donati
Click here for full review in Science
This book, written with the extensive source citations of a scholarly work yet accessible to any reader familiar with arithmetic and basic algebra, traces the often murky origins of this essential part of our intellectual heritage….
This book is a treasure chest of information about how the language of science came to be. We encounter a host of characters along the way, not just great mathematicians and scientists, but scoundrels, master forgers, chauvinists, those who preserved precious manuscripts and those who burned them, all leading to the symbolic language in which we so effortlessly write and do mathematics today. --John Walker
Reviews for What's Luck Got to Do with It?
September 16, 2010: Times Education Supplement
When to hold, when to fold. What makes Exchequers, poker players and other punters go for broke?
Chris Howls gets a tip sheet.... If not a probability primer, this book is essential reading for George Osborne. Read more...
"Appealing to historians, gamblers and mathematicians alike, ‘What’s Luck Got To Do With It?’ has been recommended to anyone working the casino industry. With its broad range of chapters, Mazur’s book is appealing to virtually anyone with an interest in the human psyche. "
"...an entertaining and accessible tour of the history of gambling, the way mathematicians quantify luck and the psychology that keeps gamblers returning to the table. A book worth taking a chance on."
Joseph Mazur is a mathematics professor who’s written books about math for the popular audience, and his writing style is wonderfully suited to discussing a complex subject in a friendly way. Maybe the greatest compliment I can pay Mazur is that he doesn’t come across like a professor in his writing–he’s more like a very interesting guy sitting next to you on a plane ride out to Las Vegas, who’s got several hours worth of anecdotes and an occasional mathematical proof to back them up.
What’s Luck Got to Do With It? tackles what might be the million-dollar question when it comes to gambling: why do people consistently bet against the odds? Demonstrating that he’s not approaching his subject from too great a distance, Mazur treats the reader to a debate between his uncles–two of whom are racetrack devotees, one of whom insists that gambling is a sure path to ruin and warns against feeling to sure that luck is on your side. The book essentially seeks to identify just what luck is, and reconcile it with the dry mechanics of probability and the law of large numbers. Involving history, psychology, and several examples from popular culture,the book uses its mathematical backbone to ask and answer some key questions about gambling and luck.
The book is divided into three parts. The first is an outstanding brief history of gambling from the dawn of time to about 2008. No matter what you’ve read about the topic, you’ll probably still learn something new here. Then Mazur looks into the math of gambling and luck, and relates the underlying theoretical truths that make gambling work the way it does. Along the way Mazur works in several personal anecdotes that keep the reading lively. After laying down the mathematical foundation, Mazur explains “the analysis,” or why people continue to gamble against the odds. He incorporates research about problem gambling, but also addresses non-problem gamblers, who make up the great bulk of the gambling public.
Because Mazur’s not judgmental about luck and gambling, but is analytical, the book is a winner. It’s not just a mathematician telling us that we’ll never hit a million-dollar jackpot–it’s a mathematician looking at why we continue to hope to hit that jackpot. This book should be required reading for anyone in the casino business, and anyone who spends more than a fraction of their disposable income on gambling should find it informative, if nothing else. It’s a reasoned, but also passionate, search for the meaning of luck that may change the way you look at a pair of dice–or your mortgage.
Blending math with memoir, probability with psychology, and heuristics with history, Mazur has written an essential book for anyone who wants to get a better idea of why we consistently bet against the odds. From the betting window to Wall Street, he offers insights into both the mechanics of chance and the enduring appeal that that luck holds for those who wager every day, whether they call it gambling, speculation, or just hoping for the best. Engaging and illuminating, this is a guaranteed winner."
at the University of Nevada, Las Vegas,and author of Roll the Bones: The History of Gambling.
I recommend this book enthusiastically. Mathematical readers will not learn much new mathematics but they will learn quite a bit about history, both of probability and of the social context in which it emerged, and will have a glimpse of the psychological issues arising in the translation of theoretical results to the real world. Non-mathematical readers, conversely, may find in the historical and psychological aspects of the subject a “hook” that will pull them into the mathematics. Finally, Mazur is most in his element when telling stories from his own life; interweaving these stories with related mathematics is a hallmark of Mazur’s work, and a most enjoyable one."
"This is a fascinating book. It's a fresh, funny, philosophical look at gambling by a mathematician who knows what he's talking about, and who has quite obviously thought about gambling for a long time. Mazur isn't afraid to make provocative, opinionated statements. I have not seen a gambling book like this before. I think it will attract a lot of readers."
"This book is significant int hat it offers a lively and diverse collection of gambling-related ideas. Mazur's robust blend of anecdotes, history, psychology, and mathematics differes from other attempts to discuss these ideas. He offers plenty of inights into the questions and issues he raises."
Reviews for Euclid in the Rainforest
Euclid in the Rainforest is a Finalist for the PEN: Martha Albrand Award for First Nonfiction. Also, It has been selected as an Outstanding Academic Titles of the Year 2005 by the library journal Choice.
"In Euclid and the Rainforest, Joseph Mazur brilliantly explores the symbiotic relationship between the physical and the mathematical worlds. He asks the questions: How do we know that the world is what we experience it to be? Can logic guide us through the rainforest of science and math and provide us with a chance to discover the underlying foundation for their truths? In his highly original search, Mazur is a brilliant forester whose graceful pursuit leads him to understanding the logical bases of human reason. Mazur has given us a stylish and seductive book that convinces the mind even as it delights the soul."
A thoroughly readable account of the meaning of truth in mathematics, presented through a series of quirky adventures in the Greek Islands, the jungles around the Orinoco River, and elsewhere. Examines tricky concepts like infinity, topology, and probability through tall tales and anecdotes. Three different kinds of truth are examined: formal classical logic, the role of the infinite, and inference by plausible reasoning. The story of the student who believed nothing except his calculator is an object lesson for everyone who thinks mathematics is just 'sums'.
From Library Journal
“Logic as an academic and intellectual discipline can be overwhelming and dry. But writing with the general reader or undergraduate student in mind, Mazur (mathematics, Marlboro Coll.) successfully explores how mathematical logic and proof are essential building blocks to understanding knowledge and universal truths. In brief chapters, he draws on the philosophy and geometry of the ancient Greeks and incorporates historical vignettes and personal narratives to examine the three types of logic (classical logic, plausible reasoning, and infinity) that we use to determine whether something is true.
Mazur clearly demonstrates how the validity of arguments and truthfulness can be revealed through the rules of logic, debate, and the principals of mathematics. Although there are some simple diagrams and figures, his text is devoid of complex proofs and dense mathematical language; instead, the author has drawn upon his experiences as a formative teacher to create a book rich in content that connects with real-world experiences. Suitable for large public and academic libraries.”
From Science and Theology News
“In Euclid in the Rainforest, one can see Euclid as a metaphor for the sterile and the methodical--the logical, but mechanistic stacking of proven result upon proven result to arrive at an end that is unassailable by anyone, anywhere, anytime. On the other hand, the rainforest conjures up complexity, richness, unexpected sightings and multiple pathways to the clearing called ‘clarity.’ In Joseph Mazur’s book, you find these metaphors juxtaposed. Readers become the traveling companions of someone part geek and part Indiana Jones; it is an enjoyable trip.”
“This charming book radiates love of mathematics... and of life. Mazur (mathematics, Marlboro College) weaves elementary explanations of a wide range of essential mathematical ideas into narratives of his far-ranging travels. Trekking into the rainforest of Venezuela, conversing in a café (cafe) in Paris, touring the Greek islands on a luxury yacht, and other adventures--they all serve as backdrops to careful treatments of the Pythagorean theorem, Boolean algebra, non-Euclidean geometry, Zeno's paradox, the Law of Large Numbers, the Continuum Hypothesis, etc. Along the way Mazur explains topics such as the difference between mathematical and scientific induction and others of metamathematical nature. The chapter subtitled ‘The Role of Intuition and Belief in Mathematics’ illustrates his approach to mathematics as more than formulas and theorems by relating the human side of Jordan's travails when proving his Curve Theorem. Another example is his historical account of the quest to prove the Parallel Axiom.
The value of the extensive bibliography is greatly enhanced by guiding comments. The index is unusually complete. This book is a treasure of human experience and intellectual excitement. One wonders how many of today's students can appreciate its value. Summing Up: Highly recommended. All levels.”
From The Mathematical Inteligencer
“Joseph Mazur does readers the great service of setting the arcane ideas and procedures of mathematics back in the world where they belong, the market-place, the smoky café, the classroom, the laboratory, the sidewalk, the sailboat, the rainforest. He reminds us how beautiful they are, how compelling, without letting us forget that they have their tragic moments as well as various lead and walk-on roles in the human comedy.”
From The Editors of Barnes and Noble
“Joe Mazur holds an MIT doctorate in mathematics, but his history of the search for universal truths in logic and math has a narrative charm that will make it appealing even to the average educated reader. Euclid in the Rainforest paints a sweeping history that identifies three central ideas of logic that have guided Western thought for the past 2,500 years. By situating his theories in stories set first in the rainforests of Venezuela and then on the Mediterranean coastline, Mazur draws us into explorations that might otherwise seem hopelessly obtuse or irrelevant.”
"How does one summarize a book that is about rainforest adventures, probability, the Cafe Luxembourg, Euclid and prime numbers? This is an absolutely delightful book, full of insight, suffused with gentle humor--a picaresque novel of mathematics. What do we mean by proof and persuasion in the most symbolic of fields, Mazur asks, and responds with stories that effortlessly guide us to the heartland of reason. This is a fabulous book, in all senses, from beginning to end."
“My chief regret after more than 40 years of trying to teach concepts in mathematics and statistics to biology students is that I did not have Mazur's book avaliable. It should be assigned reading for all undergraduates interested in science.”
“Euclid in the Rainforest is beautifully written and packed with insights into how mathematicians convince themselves they are right. Joe Mazur is a talented teacher who knows his subject inside out, and his delightful stories take his readers effortlessly to the heart of mathematics--logic and proof. This original and charming book is accessible to anyone, and deserves major success.”
"Mazur has a wonderfully engaging writing style, and a marvelous feel for the interface between the physical world as we experience it every day and the mathematical one. The book is a pleasure to read."
"Joe Mazur's Euclid in the Rainforest is written with warmth and a lifetime's attachment to the things of this world and the forms of the world it manifests. Here are the pleasures of sitting with the author, as a young man, learning his craft in a Greenwich Village cafe from an old professor; and much later on, teaching the craft in turn to an eight-year-old. Inspiring stuff. By overhearing such conversations as these, the reader too is led to savor the beauties of mathematics.”
“Mazur is an excellent storyteller. Euclid in the Rainforest is a warm and creative masterpiece that reveals the spirit of mathematics.”
Ever since the appearance of Lancelot Hogben’s Mathematics for the Million and Courant & Robbins’ What is Mathematics, mathematicians who believe not only in the practical importance but also the aesthetic beauty of the subject, and who have the gift of good expression, have written books accessible to the layman. The book under review is one such work....
A beginning student reader of this book will find that he is learning mathematics painlessly as if he is reading a book of stories....
The book deserves to be assigned as supplemental reading to all undergraduates taking science classes.
Reviews for The Motion Paradox
From The New Scientist
"THIS is one of the most fascinating science books I have ever read. It tells the story of the 2500-year quest to gain an understanding of the slippery concept of motion. Beginning with the Greek paradoxes that showed that motion is utterly impossible, the book progresses through Galilean relativity, Einsteinian relativity and superstring theory, finally coming up to date with the still unresolved question of whether space and time are continuous or grainy. Joseph Mazur has succeeded in telling a fresh and untold story with clarity and style."
From Publisher's Weekly
"The Greek philosopher Zeno sought to reveal that motion and speed were logical impossibilities; one of his famous four paradoxes argued that a moving object can never reach its destination, because it must first travel half the distance, then half the remaining distance, and so on. In this entertaining, informative diversion, Mazur (Euclid in the Rainforest) spins out the discoveries of the mathematicians and scientists who have grappled with the riddles of time and space over the last two millennia, from Aristotle up to Heisenberg and contemporary string theorists. Yet for all their answers, the fundamental premise that motion is an illusion created by consciousness still remains. Many elements of the story, such as the astronomical breakthroughs of Galileo and Tycho, or the simultaneous development of calculus by Leibniz and Newton, have been discussed in greater detail in other recent books. But Mazur spins a good yarn, and his conversational tone holds readers' attention even as the mathematical formulae pile up in later chapters." Copyright © Reed Business Information, a division of Reed Elsevier Inc. All rights reserved.
"Zeno's four paradoxes have bamboozled the greatest mathematical minds, for he purported to prove that motion is impossible, a conclusion somewhat at variance with experience. In this history of puzzlement over the paradoxes, mathematician Mazur begins by imagining Zeno stumping the entire ancient-Greek brain trust except for Aristotle, who offered refutations of Zeno. With Aristotle's own notions of motion refuted by Kepler, Galileo, and Newton, Zeno enjoyed a brief renaissance but seemed tamed once more by calculus and its mathematical tool kit. Motion and time again were continuous, not infinitely divisible, which is the underlying assertion that lets Zeno claim that fleet-footed Achilles can never catch up to a tortoise that has a head start. Then, as Mazur relates, Planck's discovery of the quantum, and Einstein's of relativity, restored Zeno's paradoxes to philosophical relevance. Entrained with some requisite algebra, Mazur's account achieves an entrancing verbal clarity in its discussion of the success and limits of mathematically modeling motion, and itself is a fine example of popularizing a famous philosophical mind-bender." Copyright © American Library Association. All rights reserved
This book is on the Library Journal's list of the best Sci-Tech books of 2006.