One, Two, Three: Absolutely Elementary Mathematics by David Berlinski (PDF)

Description

From the acclaimed author of A Tour of the Calculus and The Advent of the Algorithm, here is a riveting look at mathematics that reveals a hidden world in some of its most fundamental concepts. In his latest foray into mathematics, David Berlinski takes on the simplest questions that can be asked: What is a number? How do addition, subtraction, multiplication, and division actually work? What are geometry and logic? As he delves into these subjects, he discovers and lucidly describes the beauty and complexity behind their seemingly simple exteriors, making clear how and why these mercurial, often slippery concepts are essential to who we are. Filled with illuminating historical anecdotes and asides on some of the most fascinating mathematicians through the ages, One, Two, Three is a captivating exploration of the foundation of mathematics: how it originated, who thought of it, and why it matters.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐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

⭐. 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. But there are some terse bits in the history of mathematics that tie everything together. It’s even possible to “do some forgetting” and see these discoveries afresh, and feel their attendant excitement. But also, revisiting the classroom scenes, Berlinski asks the questions students form but don’t put, and shows how to get to the answers teachers might not give. It’s truly exciting to see the relations between the various operations of addition, subtraction, multiplication and division, and the various proofs that work for some of these and not others, with Berlinski explaining and showing why this would be the case. Moreso, how this led to things before I only knew the names of: sets, and rings, and succession, and fields, and, in the tantalizing realm of physics, Planck’s length.I knew of the mysterious properties of zero from reading about binary, heretofore the most interesting and fruitful mathematical idea I had encountered, but Berlinski’s discussion of zero opens onto endless vistas. He brings up base 10 and the decimal system, but not in a discussion of bases (binary doesn’t figure in anywhere). rather, of exponents and logarithms. This last always seemed to me to be entirely arbitrary, but his brief once over clears it right up, and he doesn’t even delve into sines and cosines. That’s how absolutely elementary this mathematics is. Which makes for absolutely engaging reading.

⭐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.

⭐The 4 stars is a tip that the book may not please everyone as much as it did me–especially anyone who may mistakes 123 Absolutely Elementary Mathematics for a simple explanation of mathematic operations. The book is a 5-star meander back through the centuries of human endeavor. It is a tour in which Dr. Berlinski took me back to the beginning of arithmetic operations and made me experience that story as an unfolding perception of elementary mathematics developing through the centuries. We looked on as its progenitors engaged simple numbers and their properties and determinedly advanced understanding of mathematics to the achievement it is today. The tour revealed the touching history of men and women wrestling with abstruse implications and theories to bring forward to succeeding generations the well proven and elegant tool Dr. Berlinski calls Absolutely Elementary Mathematics–AEM for short. The professor surprised me with the vast subtlety of the natural numbers, and with the engaging humanity of the mathematicians who explored that arcane realm. I had needed this book as a summer reading assignment before entering junior high school–the mathematics taught in classrooms might have yielded something to me. But, it is still a helpful thing to have my understanding of numbers and math embellished now. Thanks, Professor Berlinski.

⭐A useful starter book for people who want to refresh their Mathematics skills and knowledge. The author has written some other books that are worth looking at.

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