{"product_id":"one-two-three-isbn-9781400079100","title":"One, Two, Three","description":"\u003cp\u003eThe acclaimed author of \u003ci\u003eA Tour of the Calculus \u003c\/i\u003eand \u003ci\u003eThe Infinite Ascent\u003c\/i\u003e offers an enlightening and enthralling tour of the basics of mathematics, and reveals a world of fascination in fundamental mathematical ideas.\u003cbr\u003e \u003cbr\u003e\u003ci\u003eOne, Two, Three\u003c\/i\u003e is David Berlinski’s captivating exploration of the foundation of mathematics, its fundamental ideas, and why they matter. By unraveling the complex answers to these most elementary questions—What is a number? How do addition, subtraction, and other functions actually work? What are geometry and logic?—Berlinski reveals the intricacy behind their seemingly simple exteriors. Peppered with enlightening historical anecdotes and asides on some of history’s most fascinating mathematicians, \u003ci\u003eOne, Two, Three, \u003c\/i\u003erevels in the beauty of numbers as Berlinski shows us how and why these often slippery concepts are as essential to the field of mathematics as to who we are.\u003c\/p\u003e“It is candy for the intellectually curious.”\u003cbr\u003e     —Leonard Mlodinow, bestselling author of \u003ci\u003eThe Drunkard’s Walk\u003cbr\u003e\u003cbr\u003e\u003c\/i\u003e“David Berlinski plus any topic equals an extraordinary book. . . . Making simple and accessible that which had previously been murky and intimidating is Berlinski’s specialty.”\u003cbr\u003e\u003ci\u003e     —Chicago Tribune\u003cbr\u003e\u003cbr\u003e\u003c\/i\u003e“A writer who takes immense pleasure in [his subject] and tries to create it in others.”\u003cbr\u003e\u003ci\u003e    —The New York Times Book Review\u003cbr\u003e\u003cbr\u003e\u003c\/i\u003e“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!” \u003cbr\u003e    —Gregory Chaitin, author of \u003ci\u003eMeta Math!\u003c\/i\u003e\u003cbr\u003e \u003cbr\u003e“He is both poet and genius. And he’s funny . . . The writing is clean and powerful . . . Go, Berlinski, go.”\u003cbr\u003e    —\u003ci\u003eSan Francisco Chronicle\u003c\/i\u003e\u003cbr\u003e \u003cbr\u003e“Remarkable. . . . Using simple speech—and a flare for literary wordplay—Berlinski spells out historically necessary numerical notions for the public.”\u003cbr\u003e    —\u003ci\u003eSacramento Book Review\u003c\/i\u003e\u003cbr\u003e \u003cbr\u003e“Berlinski releases math from its textbook script and restores its majestic drama.”\u003cbr\u003e    —\u003ci\u003eBooklist\u003c\/i\u003e\u003cbr\u003e \u003cbr\u003e“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.”\u003cbr\u003e     —\u003ci\u003eKirkus Reviews\u003c\/i\u003e\u003cbr\u003e\u003ci\u003e \u003c\/i\u003e\u003cbr\u003e“A logician, professor, novelist, and accomplished writer, Berlinski revels in riffs, employing a jazzy style.”\u003cbr\u003e     —\u003ci\u003eNational Review\u003c\/i\u003e\u003cbr\u003e \u003cbr\u003e“With wit and philosophy, with the clash of symbols and history, Berlinski displays the inner soul of simple arithmetic.”\u003cbr\u003e     —Philip J. Davis, professor emeritus of applied mathematics, Brown University\u003cbr\u003e \u003cbr\u003e“For mathematically challenged folk like me, David Berlinski . . . renders mathematics not easy, but accessible and absorbing. . . . You’ll enjoy yourself.”\u003cbr\u003e     –Paul McHugh, Distinguished Service Professor of Psychiatry, Johns Hopkins University\u003cp\u003e\u003cb\u003eDavid Berlinski\u003c\/b\u003e received a B.A. from Columbia University and a Ph.D. from Princeton University. He has taught mathematics and philosophy at universities in the United States and France, and currently lives in Paris.\u003c\/p\u003e\u003cp\u003e\u003cb\u003eIntroduction\u003c\/b\u003e\u003cbr\u003e\u003cb\u003e \u003c\/b\u003e\u003cbr\u003eThis is a little book about absolutely elementary mathematics (\u003cb\u003eAEM\u003c\/b\u003e); and so a book about the natural numbers, zero, the negative numbers, and the fractions. It is neither a textbook, a treatise, nor a trot. I should like to think that this book acts as an anchor to my other books about mathematics.\u003cbr\u003e \u003cbr\u003eMathematicians have always imagined that mathematics is rather like a city, one whose skyline is dominated by three great towers, the state ministries of a powerful intellectual culture—our own, as it happens. They are, these great buildings, devoted to Geometry, Analysis, and Algebra: the study of space, the study of time, and the study of symbols and structures.\u003cbr\u003e \u003cbr\u003eImposing as Babylonian ziggurats, these buildings convey a sacred air.\u003cbr\u003e \u003cbr\u003eThe common ground on which they rest is sacred too, made sacred by the scuffle of human feet.\u003cbr\u003e \u003cbr\u003eThis is the domain of absolutely elementary mathematics.\u003cbr\u003e \u003cbr\u003eMany parts of mathematics glitter alluringly. They are exotic. Elementary mathematics, on the other hand, evokes the very stuff of life: paying bills, marking birthdays, dividing debts, cutting bread, and measuring distances. It is earthy. Were textbooks to disappear tomorrow, and with them the treasures that they contain, it would take centuries to rediscover the calculus, but only days to recover our debts, and with our debts, the numbers that express them.\u003cbr\u003eElementary mathematics as it is often taught and sometimes used requires an immersion into messiness. Patience is demanded, pleasure deferred. Decimal points seem to wander, negative numbers become positive, and fractions stand suddenly on their heads. \u003cbr\u003e \u003cbr\u003eAnd what \u003ci\u003eis \u003c\/i\u003ethree-fourths divided by seven-eights? \u003cbr\u003e \u003cbr\u003eThe electronic calculator has allowed almost everyone to treat questions such as this with an insouciant indifference. Quick, accurate, and cheap, it does better what one hundred years ago men and women struggled to do well. The sense that in elementary mathematics things are familiar—half remembered, even if half forgotten—is comforting, and so are the calculator and the computer, faithful almost to a fault, but the imperatives of memory and technology do prompt an obvious question: why bother to learn what we already know or at least thought we knew? \u003cbr\u003e \u003cbr\u003eThe question embodies a confusion. The techniques of elementary mathematics are one thing, but their \u003ci\u003eexplanations \u003c\/i\u003eare quite another. Everyone can add two simple natural numbers together—two and two, for instance. It is much harder to say what addition means and why it is justified. Mathematics explains the meaning and provides the justification. The theories that result demand the same combination of art and sophistication that is characteristic of any great intellectual endeavor. \u003cbr\u003e \u003cbr\u003eIt could so easily have been otherwise. Elementary mathematics, although pressing in its urgency, might have refused to cohere in its theory, so that, when laid out, it resembled a map in which roads diverged for no good reason or ended in a hopeless jumble. But the theory by which elementary mathematics is explained and its techniques are justified is intellectually coherent. It is powerful. It makes sense. It is never counter-intuitive. And so it is appropriate to its subject. If when it comes to the simplest of mathematical operations—addition again—there remains something that we do not understand, that is only because there is nothing in nature (or in life) that we understand as completely as we might wish. \u003cbr\u003e \u003cbr\u003eNonetheless, the theory that results is radical. Do not doubt it. The staples of childhood education are gone in the night. One idea is left, and so one idea predominates: \u003ci\u003ethat the calculations and concepts of absolutely elementary mathematics are controlled by the single act of counting by one. \u003c\/i\u003eThere is in this analysis an economy of effect, and a reduction of experience to its essentials, as dramatic as anything found in the physical sciences. \u003cbr\u003e \u003cbr\u003eUntil the end of the nineteenth century, this was not understood. A century later, it is still not \u003ci\u003ewidely \u003c\/i\u003eunderstood. School instruction is of little help. “Please forget what you have learned in school,” the German mathematician Edmund Landau wrote in his book \u003ci\u003eFoundations of Analysis; \u003c\/i\u003e“you haven’t learned it.” \u003cbr\u003e \u003cbr\u003eFrom time to time, I am going to ask that readers do some forgetting all their own. \u003cbr\u003e \u003cbr\u003e \u003cbr\u003eA secret must now be imparted. It is one familiar to anyone writing about (or teaching) mathematics: no one very much likes the subject. It is best to say this at once. Like chess, mathematics has the power to command obsession but not often affection. \u003cbr\u003e \u003cbr\u003eWhy should this be—the distaste for mathematics, I mean? \u003cbr\u003e \u003cbr\u003eThere are two obvious reasons. Mathematics confronts the beginner with an aura of strangeness, one roughly in proportion to its use of arcane symbols. There is something about mathematical symbolism, a kind of peevishness, that while it demands patience, seems hardly to promise pleasure. \u003cbr\u003e \u003cbr\u003e\u003ci\u003eWhy bother? \u003c\/i\u003e\u003cbr\u003e\u003ci\u003e \u003c\/i\u003e\u003cbr\u003eIf the symbolic apparatus of mathematics is one impediment to its appreciation, the arguments that it makes are another. Mathematics is a matter of proof, or it is nothing. But certainty does not come cheap. There is often a remarkable level of detail in even a simple mathematical argument, and, what is worse, a maddening difference between the complicated structure of a proof and the simple and obvious thing it is intended to demonstrate. There is no natural number standing between zero and one. Who would doubt it? Yet it must be shown, and shown step by step. Diffi cult ideas are required. \u003cbr\u003e \u003cbr\u003e\u003ci\u003eWhy bother? \u003c\/i\u003e\u003cbr\u003e\u003ci\u003e \u003c\/i\u003e\u003cbr\u003eA tricky bargain is inevitably involved. In mathematics, something must be invested before anything is gained, and what is gained is never quite so palpable as what has been invested. It is a bargain that many men and women reject. \u003cbr\u003e \u003cbr\u003e\u003ci\u003eWhy bother indeed? \u003c\/i\u003e\u003cbr\u003e\u003ci\u003e \u003c\/i\u003e\u003cbr\u003eThe question is not ignominious. It merits an answer. \u003cbr\u003e \u003cbr\u003eIn the case of many parts of mathematics, answers are obvious. Geometry is the study of space, the mysterious stuff between points. To be indifferent to geometry is to be indifferent to the physical world. This is one reason that high-school students have traditionally accepted Euclid with the grudging sense that they were being forced to learn something that they needed to know. \u003cbr\u003e \u003cbr\u003eAnd algebra? The repugnance (in high school) that this subject evokes has always been balanced by the sense that its symbols have a magical power to control the flux and fleen of things. Farmers and fertilizers were the staple of ancient textbooks. But energy and mass figure in those that are modern. Einstein required \u003ci\u003eonly \u003c\/i\u003ehigh-school algebra in creating his theory of special relativity, but he required high-school \u003ci\u003ealgebra, \u003c\/i\u003eand he would have been lost without it. \u003cbr\u003e \u003cbr\u003eMathematical analysis came to the mature attention of European mathematicians in the form of the calculus. They understood almost at once that they had been vouchsafed the first and in some respects the greatest of scientific theories. To wonder at the importance of analysis, or to scoff at its claims, is to ignore the richest and most intensely developed body of knowledge acquired by the human race. \u003cbr\u003e \u003cbr\u003eYes, yes. This is all very uplifting, but absolutely elementary mathematics? Not very long ago, the French mathematician Alain Connes invented the term \u003ci\u003earchaic mathematics \u003c\/i\u003eto describe the place where ideas are primeval and where they have not yet separated themselves into disciplines. It is an elegant phrase, an apt description. And it indicates just why elementary mathematics, when seen properly, has the grandeur of what is absolute. It is fundamental, and so, like language, an instinctive gesture of the human race. \u003cbr\u003e \u003cbr\u003eA \u003ci\u003etheory \u003c\/i\u003eof absolutely elementary mathematics is an account in modern terms of something deep in the imagination; its development over the centuries represents an extraordinary exercise in self-consciousness. \u003cbr\u003e \u003cbr\u003eThis is what justifies the bothering, the sense that, by seeing an old, familiar place through the mathematician’s eyes, we can gain the power to see it for the first time. \u003cbr\u003e \u003cbr\u003eThis is no little thing.\u003c\/p\u003e","brand":"Vintage","offers":[{"title":"Default Title","offer_id":46301990977765,"sku":"NP9781400079100","price":18.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781400079100.jpg?v=1767734207","url":"https:\/\/k12savings.com\/es\/products\/one-two-three-isbn-9781400079100","provider":"K12savings","version":"1.0","type":"link"}