### SUMMARY One Two Three

Hat 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 s what is primitive and thus given and what is civilized and thus made find one another in contentment

### DOWNLOAD ✓ SIGMAENCLOSURES.CO.UK Â David Berlinski

Lippery 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 matter This book made me think about how much we take for granted in basic mathematics What is the abstract concept of a number where did it come from Berlinski touches on some important developments of absolutely elementary mathematics and presents gobs of proofs of fundamental concepts I hadn’t seen before However this book was tedious in the detail and minutiae of proving every concept he presents It felt like a text book it this way but also the overly detailed stories of the mathematicians involved with the topics didn’t help the book flow much better I think this book could have been 50 75 pages shorter and spent less time spelling out all the details It’s great as a general overviewThe illustration of the number line folding on itself at zero so that the positive and negative number cancel each other out into nothingness and then unfold again to reveal creation excellent 1Q84 zero so that the positive and negative number cancel each other out into nothingness and then unfold again to reveal creation excellent

### David Berlinski Â 1 REVIEW

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 uestions that can be asked W Dr Berlinski's little book was a pleasure to read He managed to make book about elementary mathematics engaging and entertaining Highly recommended

Dr Berlinski's little book was a pleasure to read He managed to make book about elementary mathematics engaging and entertaining Highly recommended

In the end this book is about defining and proving elementary mathematics procedures Some of the proofs are elegant such as why two negatives eual a positive and the work with fractions However movement through the book is choppy and a background in math is necessary to enjoy this book's thesis

Somewhat Interesting but dry This book is the author's reflection on mathematics and consists of a historical overview the foundation of mathematics in commerce general observations and proofs Berlinski tries to make it interesting and winsome and sometimes succeeds but hardly enough to win me over I don't feel bettered by reading this and I felt it a mercy to finishOne word about the other reviewers who state that this work is just the author's opinions One wonders what universe these ignoramuses live in Presumably the same as me but they are oblivious to the fact One's banker might take issue with one's opinions but of the numbers there can be no doubt

The author a mathematics and philosophy professor writes about the basic concepts of simple arithmetic addition subtraction multiplication division starting with the premise that numbers exist outside of human endeavor then on to the definition of addition which is just adding by one lingering at the problem of zero then through some rather convoluted proofs of various theorems to stop at the abstract algebraic concepts of rings structures which include sets of integers and provide the definition of addition and multiplication and fields which define division through multiplicative inversesIf the summary above makes it seem as though this is a jaunt through the math you learned in elementary school think again “The recursion theorem justifies definitional descent by drawing a connection between the recipe or algorithm embodied in definitional descent and the existence of a uniue function the one that definitional descent has presumably defined” Berlinski is often this recursive; I often found myself wondering what was being proved or defined and what was being simply assumed But aside from tortuous mathematical definitions the book is written in an airy conversational sometimes jocular sometimes smug tone with many sentences given their own paragraphs in order to give them Weight Berlinski is even uite funny as when he discusses Guiseppe Peano whose axioms provide the groundwork for what Berlinksi attempts to show and his bizarre simplified Latin that no one used or understood or when he imagines early mathematicians’ dialogue when encountering the apparent absurdity that is negative numbers “Can I do that?” “Why not?” “I’m just asking” “What next? I mean besides giving up That always works” As a philosophical treatise on the concept of mathematics itself the book makes some trenchant points “across the vast range of arguments in psychology logic physics etc it is only within mathematics that arguments achieve the power to compel allegiance because they are seen to command assent” But as a tour of elementary abstract principles it’s a bit abstruse for the layman I enjoyed his insights on sets and some of the simpler chapters but finished the book feeling as though Berlinski was a bit too clever for his own good and yet not uite clever enough to make it all clear

Weird but enjoyable Literature plus mathematics I guess?But really isn’t this how we all are much impressed by things we do not understand and hoping that they represent something very wise and interesting?To get the number from the fraction it is necessary only to keep the fraction’s numerators while discarding its denominators the decimal point serving to separate the integer from the fraction that follows In place of 13141000—rather ungainly let us be honest—there is 1314 sleek as a seal and as easy to train; all that is needed to use it is a willingness to keep track of the decimal point and the places that it commandsMud we might leave to the philosophers They love the stuff

what is primitive and thus given and what is civilized and thus made find one another in contentment

An entertaining jaunt through some important points in the history and philosophy of the most basic foundations in mathematics

David Berlinksi is among the leaders of writing so called popular books about different aspects of math some that is highly advanced as in The Advent of the Algorithm and some that is very very basic as in 2011's One Two ThreeBerlinksi assigns the basic mathematical functions the group name AEM or Absolutely Elementary Mathematics The four major functions of addition subtraction multiplication and division are outlined as the building blocks of far complicated functions and euations Berlinksi also digs even deeper offering ways to think about even the idea of numberBerlinski holds doctorates in philosophy and mathematics so he is a good choice to explain math concepts in terms that don't lean too heavily on euations His purpose in One Two Three is to suggest answers for these simplest and most basic uestions about AEM and to show how such answers can be deduced via logic from some very simple assumptions One Two Three is both aided by and labors under Berlinksi's habit of breezy and almost flippant writing On the one hand he largely succeeds in getting complex ideas boiled down to terms that most people can understand and presents his arguments in ways that can be followed without specialized knowledge But on the other hand his tone sometimes crosses over into flippancy in ways that can slow readers down while they finish rolling their eyesHe too often sacrifices some clarity and direction in order to make a witty observation and in than one place sticks in some jokes for their own sake rather than explanatory value Whether or not Berlinksi is actually all that impressed with his own wit he gives a good enough imitation of being so to make several parts of One Two Three way annoying and way less useful than they could have beenOriginal available here

This book made me think about how much we take for granted in basic mathematics What is the abstract concept of a number where did it come from? Berlinski touches on some important developments of absolutely elementary mathematics and presents gobs of proofs of fundamental concepts I hadn’t seen before However this book was tedious in the detail and minutiae of proving every concept he presents It felt like a text book it this way but also the overly detailed stories of the mathematicians involved with the topics didn’t help the book flow much better I think this book could have been 50 75 pages shorter and spent less time spelling out all the details It’s great as a general overviewThe illustration of the number line folding on itself at zero so that the positive and negative number cancel each other out into nothingness and then unfold again to reveal creation excellent

Too wordy by the multiplicative inverse of one's successorBerlinski is far too enad by his own words to the point that even when he is making very simple arguments it becomes easy to lose track of where he is heading Don't get me wrong; I love math history anecdotes and analogies But when the telling is so ornate and circumlocutory it obscures than reveals As evidenced by those fake proofs of 12 which depend on the reader not noticing that one has sneaked a division by zero into a long set of euations mathematics is not well served by overcomplication for its own sake That is to say too wordy by half