Mathematics for the Nonmathematician

For a long time, I've been searching for a book exactly like this one. Somewhat embarrassed by my ignorance of math, I wanted to relearn what I had forgotten in college, and perhaps go further. But I didn't want to simply learn math; I wanted to learn its history, how it shaped and was shaped by the cultures in which it grew. This is a tall order, requiring both historical and mathematical understanding; but Kline is equal (or, perhaps, almost equal) to the task. Before I get into the positive qualities of this book, I should note its flaws. As another reviewer pointed out, Kline's beginning chapter on history is inept, even offensive. He heaps praise upon praise when describing the accomplishments of the Greeks, and dismisses the contributions of the Arabs, Babylonians, Egyptians, and Indians with a wave of the hand. He even relays the story of the Arabs destroying the library, which historians have seen fit to doubt as far back as Edward Gibbon. For Kline, mathematics made a brilliant beginning with the Greeks, and then stayed more or less the same until the Enlightenment. The extent to which that is true, I know not; but it at least seems unlikely to me. Thankfully, the book gets markedly better after that. (One shouldn't judge a book by the cover, or even the first chapter, apparently.) For, whatever Kline lacks as a historian, he makes up as a pedagogue. Kline doesn't simply move from arithmetic to geometry to algebra to trigonometry, but instead situates every subject within a specific historical period and practical problem. For example, he teaches trigonometry by using the kind of problems that the Alexandrian Greeks, such as Ptolemy and Eratosthenes, were tackling: the distance from the earth to the moon, the radius of the earth, the establishment of longitude and latitude. Every chapter comes with biographical sketches of the major thinkers involves, as well as some practical problem that the mathematical theory would solve. Following this procedure, Kline manages to take the most abstract of all abstract subjects, and to make it exquisitely human. In school, we are taught trigonometry by showing us how to plug numbers into a calculator. Kline shows us that trigonometry allows us to chart the earth, and measure the heavens. We encounter Newton measuring the refraction of light, and Galileo plotting the course of cannonballs. We learn how sinusoidal motion allows us to measure time, and how the Renaissance painters invented projective geometry in their attempt to create realistic perspective. In sum, Kline shows mathematics for what it is: a tremendously exciting intellectual endeavor--one that has expanded our knowledge of the universe immeasurably. Math is not born of the dreams of philosophers (at least, not exclusively), but has been, and continues to be, integral to the solution of everyday problems. It's curious that something only accessible to the mind allows us to make sense of our senses. In short, Kline has given me the greatest gift a teacher can give--not knowledge, but wonder.

Wow. I am definitely a non-mathematician. This is the book I sincerely wish had vbeen made available to me as a young person. It explains the WHY of mathematics better than most of my teachers and explains what the point of the equations were that were like Greek, Chinese and pictographs to me as a young student. A bargain for this price point and interesting to read. Don't let the age of the book fool you, it is a classic volume and well worth buying for yourself or for a intellectually curious HS age student struggling with these concepts. Recommended. And actually somewhat fin to read through and engage with the exercises in the back. At least this time I don't have grades depending on this stuff!

Am gifting this book to a young person not drawn to mathematics but who is finding a grounding in mathematics essential. This book provides that access and will be well-received.

A spectrum exists in the books written by or about mathematicians and mathematics, and this spectrum is heavily weighted at the extremes. At one end, we have books purely verbal, descriptive and, more often than not, hagiographic in their descriptions of great mathematicians and their discoveries. - I suppose one could denominate these as mathematics groupie books. At the other end of the spectrum, we have straightforward mathematics textbooks, rather dry and boring, which roll off the presses with the regularity of the academic terms. To split the difference, to write a literate, narrative book on mathematics, is to attempt something akin to the labours of Hercules and, in the end, impossible to do perfectly, rather like trisecting an angle. Kline, however, does a bang-up job here, and approaches the limit - so to speak - of what is possible. Good show, Morris! But, as many other reviewers have made clear, this book should have printed across its cover the words above the entrance to Plato's Academy: "Let no man ignorant of mathematics enter here." It is a bit of a catch-22 for someone who wants to learn mathematics but is put off by textbooks; you really have to already possess a fluency in the mathematical tongue, to possess a flair for the subject, in order to appreciate the sweep of this really quite grand book. Some pages of the book are simply equation followed by equation leading to a satisfying simplification or representing a derivation. If you can't follow these steps - sometimes quite involved - then you simply won't arrive at the "Aha!" moments which are the chief delight of this book. To quote Kline, "In his wisdom, Thales perceived what we shall perceive as we follow the story of mathematics, that the obvious is far more suspect than the abstruse." The abstruse insights in which this book abounds can only be reached by a competent grasp of mathematical methodology. That being said, Kline is a whimsical and almost lyrical writer - a bit of a shocker for a book on mathematics! He has a wry wit which he gives full rein to herein. In describing the Greeks and their obsession with astronomy, he observes, "The problem of finding the design of planetary motions continued to engage the minds of the Greeks, possibly because they were not distracted by the `heavenly' stars of stage, screen, and radio with whom many modern minds seem preoccupied." His prose is rich in such quips. The book is actually a lark to read at points. But the heart of the book is unvarnished mathematics - with which I have a slight problem. He covers the derivation of trigonometric functions splendidly, as well as their uses, as well as the kinetics, or mathematics of motion. But his account of the calculus is rather sparse for my taste. Any treatment of derivatives and integrals without mention, account or derivation of the fundamental theorem is, to my mind, lacking. Further, his derivation of the quadratic formula is absurdly complex and takes pages. It is true, as one reviewer noted, that most students are only presented with the equation and not given its derivation. But the derivation is - comparatively - simple. I worked it out on my own when I was in school, and it need only cover one page, at maximum. The book is really quite an achievement. But I'm only giving it four stars because it is extremely uneven: No fundamental theorem of the calculus but reams about projectile motion etc. As a bonus, I'll tack on as a comment, once the review is posted, Kline's mischievous proof that 2=1 for the prospective reader to see if he can suss out the flaw in it. If the mathematics leaves you stymied this is not the book for you. On the other hand, if you follow the mathematics quite easily, but are left baffled and staring at the page, determined to suss out the mathematical solecism embedded in it, then you poseess just the sort of questing mind that will delight in this tome!

I purchased the book because of the reviews--throughout the years--here and other places. I thought it was worth a try, and after 20 minutes of reading the book, I felt I should share it with my wife--who is an engineer, but is not a lover of mathematics. She appreciates math and appreciates the opportunities math has provided her, but she (and I) do not enjoy the archaic learning methods--taught throughout the U.S. I thought to myself, she'll likely say that's nice, but pass on the opportunity to read the book; the truth is she did pass on the chance to read the book. However, the reason she chose to pass on reading my book, which I saw as our book (if she was interested in the book), was such, that she wanted her own book--to mark up, dog-ear, and make her very own. I cannot stress to everyone how surprised I was to find her interested in Mathematics for the Nonmathematician! My wife has read more of the book than I have, and she does so very regularly. My wife has even gone so far that, she asks me to go to bed an hour early, so that we may discuss the book before going to sleep! The bottom line is this, my wife requested her own book after 30 minutes of reading; and she is so fascinated by the history and principles of mathematics, that she regularly requests an hour to discuss what she read. This book is AWESOME! FANTASTIC! and SIMPLISTIC! (Don't take my word for it, spend the few dollars to read it yourself...)

I bought the book for two reasons. One, at $3.99 it's low risk, and two, I like the author's perspective that mathematics is rooted in human experience and should be taught that way. I am also reading Morris Kline's calculus text and it works much better than going through abstract proofs and derivations. These can and should be tackled once you understand and can work with the concepts. That's the good news. The bad news is that, while there are interesting takes on how math came about, the writing is pompous and wordy. Full of phrases like "it is not unreasonable to make the statement that..." It it a perfect example of what Aldous Huxley considers bad writing (which is very entertaining, check it out). Kline's book reflects the prejudices of the 50's and 60's, that mathematics reflects the progress of "man",Western civilization was created by great "men", Women are only mentioned in the context of caring about their appearance or buying dresses. Made me cringe. We are told that pure math flourished in ancient Greece and not in the rest of Europe because the rest of Europe was populated by "barbarians". That's it. Case closed. This book might be useful as recommended extra reading for a high school or first year junior college 'Western Civilization" type course by an instructor who is not overly concerned about exposing students to poor writing.

I used to tutor high school kids in math. Man I wish I could have given this book out like candy. I wish every single person on the planet would read this book. It puts math in what most math classes lack; context. If I could sum up why this book is awesome in one word, that would be it. Context. But that's not all; it's very readable, it gives you a very good grasp of mathematics that you're likely to come across in high school, and it's just plain enjoyable. This book will change the way you saw math in high school.

We are in 1967, Kline is trying to thrill us, nonmathematicians, with mathematics. Bravo! He dares to go through the centuries explaining how the foundations of mathematics have been evolving. Of course, his accounts on history and philosophy throughout this book are naturally biased because he is madly in love with mathematics. However, he makes mathematics very interesting. By showing it as a growing body of knowledge defining, in precise terms, the chain of ideas that have been pushing civilization forward. Incredible. Here goes my favorite example. Non-Euclidean geometry set mathematicians FREER because it showed that mathematics is NOT a body of truths. It is a body of consistent reasoning being slowly developed within the rise and fall of civilizations. And the main source of mathematical ideas is nature herself.

some of the concepts of mathematics are explained so beautifully that would force you to pick up your mathematics book

Es un excelente libro para reaprender conceptos matemáticos básicos, pero se necesita dedicarle mucho tiempo. No promete que será fácil y rápido, el fuerte de este libro es el enfoque diferente de Morris Kline en cuanto a lo que es importante aprender y como aprenderlo. Por el estilo anticuado de la edición, estar cargado con mucha historia y capítulos que el mismo autor menciona como opcionales, solo lo recomendaría a alguien que sea paciente para aprender.

One of my all time favourite books. It's huge and packs so much information - but doesn't just spoon feed, there are exercises at the end of each section as well as a very comprehensive reference list for further reading on all the topics covered. The book is not a maths text book, it covers how mathematics evolved and provides interesting and in depth details about both ancient and modern mathematical origins. I am definitely not a mathematician but enjoyed this book immensely (maybe I'm just a total geek?). Will definitely revisit this book for years to come.

I throughly enjoyed this book, as someone who is trying to brush up and improve my understanding of mathematics, the best aspect of this book is the historical and chronological direction it takes, starting from the ancients greeks ending with modern day mathematical concepts such as non-euclidean geometry; but, more importantly, expressing why the fields of mathematics developed into what they are today by highlighting the problems they were trying to solve in their respective time periods, with mathematical examples present in most chapters. I do want to stress two predominant points: the first being, that this book does go into some depth of the topics it covers, but approaches topics in a more encompassing manner, in other words, if you are looking for very in depth content about a specific subject, then this book IS NOT for you. The second point being, a fair amount of the book deals with the history of mathematics, which is refreshing and insightful, but it is just a heads up.

Das Buch versucht Mathematik verständlich zu erklären und das schaft es auch ohne Probleme. Dazu ist zu sagen, das buch enthält zwar übungsaufgaben, dennoch ist es kein richtiges Lehrbuch. Dieses Buch sollte man wie einen Roman lesen, es gibt einen Verständlichen überblick, über (fast) alle Themen der Mathematik. Ich studiere Physik und das Buch war dennoch interresant, denn es gibt einem nicht nur stuhr Axiome, sonder erläutert auch den historischen kontext und welches Problem mit den Rechnungen versucht wurde zu lösen. Daher kann ich das Buch uneingeschränkt empfehlen. Aber wie schon gesagt, es ist kein richtiges Lehrbuch, es ist eher eine Einführung in die Konzepte der Mathematik, doch am ende jedes Kapitel stehen Listen mit Büchern die Empfohlen werden um sich mit Spezielem Thema tiefergehend zu befassen. Also wer ein Buch sucht welches ihn in die Welt der Mthematik einführt ist am Ziel.