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One, Two, Three: Absolutely Elementary Mathematics Hardcover – May 10, 2011

3.7 out of 5 stars 16 customer reviews

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Leonard Mlodinow Reviews One, Two, Three

Leonard Mlodinow is a physicist at Caltech and the bestselling author of The Drunkard’s Walk: How Randomness Rules our Lives and Euclid’s Window: The Story of Geometry from Parallel Lines to Hyperspace. He also wrote for Star Trek: The Next Generation. He lives in South Pasadena, California. Read his review of One, Two, Three:

Fifteen years ago, if publishers were sure of anything, it was that (1) calculus is not funny, and (1+1) no one wants to go to lie in bed clutching a book about the concept and history of integral and differential operators. Then along came the always audacious David Berlinski (his bio described him as “having a tendency to lose academic positions with what he himself describes as an embarrassing urgency”). A mathematician who is by trade a purveyor of proofs, Berlinski wrote A Tour of the Calculus, proving the skeptics wrong on both counts. With One, Two, Three: Absolutely Elementary Mathematics, Berlinski has now applied his vast knowledge, wit, and inimitable trademark writing style to tackle another subject about as sexy as American cheese: arithmetic. But don’t worry, you won’t find any multiplication tables here--this is a book about what it means to multiply (and add, subtract, and divide). Berlinski challenges us to see these as deeper issues, a level of mathematical thinking that most people never consider, but which forms the very logical foundation upon which rest ideas as vital as one plus one equals two.

Is there more to arithmetic than its application through our rote rules of calculation? Berlinski describes how, beginning in the late nineteenth century, mathematicians got around to questioning the meaning of arithmetic, and searching for axioms upon which that structure might be placed. Then he guides us through their reasoning.

Numbers form the foundation of our universe, yet most of us never puzzle over what they mean. We take for granted our numbers, the operations we perform on them, and the rules, such as commutivity, that those operations follow. It all seems to work when we buy our cappuccino and croissant, so why question it, unless you get shortchanged? The truth is, we don’t question arithmetic because we are in that famous and unenviable position of not knowing the extent of what we do not know. But Berlinski educates us, and shows that the logical basis of arithmetic is worth knowing, and worth appreciating, for it is both beautiful and profound, and represents a grand feat of human imagination. It is the revelation of a world of ideas upon which the simplest counting and calculating--acts without which no planning or transactions, from engineering to commerce, could exist--is predicated. That is David Berlinski’s gift to the reader. It is candy for the intellectually curious.

(photo: Marcio Fernandes)


"Berlinski here discusses the ‘commons’ of mathematics: natural numbers, zero, negative numbers, and fractions…. The seamless integration of broader contextual ideas brings his writing to life." —Library Journal

“[A] tour de force by a mathematician who wants the intellectually curious and logically minded . . . to understand the foundations and beauty of one of the major branches of mathematics.”
Kirkus Reviews
“With broad culture and wry humor, Berlinski takes a look at some basic concepts in math and the people who worried about them. A treat!”
—Gregory Chaitin, author of Meta Math!
“With wit and philosophy, with the clash of symbols and history, Berlinski displays the inner soul of simple arithmetic.”
—Philip J. Davis, professor emeritus of applied mathematics, Brown University

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Product Details

  • Hardcover: 224 pages
  • Publisher: Pantheon; 1St Edition edition (May 10, 2011)
  • Language: English
  • ISBN-10: 0375423338
  • ISBN-13: 978-0375423338
  • Product Dimensions: 5.8 x 0.9 x 8.5 inches
  • Shipping Weight: 9.6 ounces
  • Average Customer Review: 3.7 out of 5 stars  See all reviews (16 customer reviews)
  • Amazon Best Sellers Rank: #604,025 in Books (See Top 100 in Books)

Customer Reviews

Top Customer Reviews

Format: Hardcover
I stumbled across this book while searching for other related pop books about math. I am very pleased that I took the chance to order and read it. It is entertaining, and informative on the history of math. The most intriguing portion to me was how Berlinski explained the origin of the negative numbers, the mysterious digit zero, why multiplication is different than addition, why a base number taken to the zeroth power equals one and why division by one equals the number, as these were all areas where many math textbooks and teachers have never explained why to suit my curiosity. I encourage the curious reader to get this must read book!
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Format: Hardcover
If you are bright and verbal and curious, but somehow got turned off from math early in life, I would suggest that Dr. Berlinski can help. Mathematics, at its origin, was not based on the rote following of formulas, but on the solving of complex mental puzzles. Once you see that, you can become a math person. Berlinski has finally written the book with which to start. Please ignore the noisy minority of one star granters to Berlinski's work which has nothing to do his mathematical quality and everything to do with angry atheists lashing out at a man who dares to question their particular brand of jihad.
I've had the pleasure of interviewing David on the radio and it was a real treat.

Review by Jerry Bowyer.
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Format: Hardcover Verified Purchase
Numerous students, I'm convinced, have a mental block against either English or math. Mine is the latter, which is why I'm not a physicist, despite being attracted to physics. I did first pick up "A Tour of the Calculus" hoping to at some point along the way unravel the mystery of it's subject A Tour of the Calculus. But this book I picked up purely from my English major desire to read more Berlinski. Odd as it sounds, I simply put up with all the math in this book in order to read the writing, which is erudite and lyrical. Along the way, however, the author started getting around my defenses, and I started following the formulas. Why is a whole 'nother paragraph.

Berlinski anticipates, and voices, the reader's (or at least this reader's) questions and objections along the way. Yes, I learned the number line. But why is there a number line? And, if it comes to that, why read about it? Because it's an amazing invention, DB made me see, and like a truly top notch teacher, he related it to counting, which has forever taken on a sort of golden glow for this reader, and showed how it can even handle the negative numbers, themselves an amazing invention. That would have been enough, but there's more. And it's even more elementary or primal. "The calculations and concepts of absolutely elementary mathematics are controlled by the single act of counting by one." You're kidding! I'm hooked, and that's only page five.

There aren't many of the long, lyrical portraits that seem drawn from forgotten novels that are so prevalent in "Calculus", although they start sprouting in the second half of the book.
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Format: Paperback
I stole my review title from a quote about the book on the back cover, but it is an accurate description.

I found this book through a long series of events. First I found Berlinski from a guest spot he did on Ben Stein's movie 'Expelled: No Intelligence Allowed.' Then as my personal research in the sciences continued I found him in various guest spots and interviews including an interview on his position of dissent on Darwinian Evolution. It was an interview about his book 'The Devil's Delusion.' I had seen countless videos and speeches by Berlinkski. I admire his vast knowledge, vocabulary, word choice, and understanding. He has a true passion for his subjects and a desire for all his readers to take it with them. I am far from passionate about mathematics but I am passionate about truth.

Berlinksi is a brilliant teacher unlike most of our high school math teachers in this way; he not only is brilliant enough to understand his own subject within himself but to be able to present it in the most basic way possible to the least naturally intellectually gifted (Me). He is an intellectual that is able to present himself as an everyman. I cannot stress this point enough. How many books have you read the back of when the subject matter alone makes you cringe? It is not that you aren't interested in the subject matter. This is generally because we tend to feel that we will be inadequate to understand not necessarily the material presented, but how it is presented and by whom. Berlinski has the amazing ability to hold your hand as you walk through what seemed before to be dangerous ground.

I recommend not only this book but Berlinski as a man. He is a powerful mind that I am glad to have encountered in this life.
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Format: Hardcover Verified Purchase
This book is for people who are interested in fundamental math and love poetry and the ways it can weave words to create images and feelings that are new to the reader. New experiences not just new concepts! Some people will always find fault with those whose thought processes are different than theirs. This book is very irritating to those who resent "fancy language" and feel that words they personally do not already know are more words than the English language really needs.
Berlinski is a genius who can conjure up (for he is a magician with metaphors) new insights, moods and nuances using words as precisely as razor sharp mathematical concepts. Prosaic souls require that the meaning of a Berlinski sentence unfold itself in their minds instantaneously - or else the fault is Berlinski's. They accuse him of ostentation when he displays greater mastery of the English language than they possess. Criticism of “mystical-type statements…which did not say anything extraordinary” reveals the intellectual poverty of the critic, not any failing of the poet. They resent the effort required to think a new thought forged in a new form, not noticing the enormous intellectual content whose essence could never be reduced to computer input. A strictly either/or mind, a digital consciousness, cannot abide ambiguity. For example, if someone criticizes Darwin then he must be a “creationist,” a most damning epithet in the mind of a “modern” critic. Such an accusation is absurd given Berlinski’s intellectual biography and self-described agnosticism.
Berlinski is basically a poet who loves mathematics and science. This is a great book that will be in print for decades because it brings more than mere concepts; it brings us new experiences by means of words.
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