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I enjoyed getting the survey of math. I've been kind of trying to get a better understanding of how different branches of math fit together and I think walking through the history of the development of math was helpful. I know other people have noted that the book is a little western-centric in their reviews but I mean it's written by some old white man in the 60's. I would just take everything he says, especially about the history of math, with a grain of salt. I wonder if there's some updated I enjoyed getting the survey of math. I've been kind of trying to get a better understanding of how different branches of math fit together and I think walking through the history of the development of math was helpful. I know other people have noted that the book is a little western-centric in their reviews but I mean it's written by some old white man in the 60's. I would just take everything he says, especially about the history of math, with a grain of salt. I wonder if there's some updated book I could read on math that surveys math and the different branches. I feel like a lot of what was covered in the book was stuff I learned already in school, especially high school. I do think it's worth a read for people who don't know much math and I think the exercises are pretty basic/accessible. Math really doesn't change much especially something like Euclidean Geometry. A 3.5 stars from me. ...more

Sep 02, 2014 Roy Lotz rated it it was amazing

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

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 Muslims destroying the Library of Alexandria, 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 involved, 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 to map the skies. We encounter Newton measuring the refraction of light, and Galileo plotting the course of cannonballs. We learn how sinusoidal motion allows us to quantify 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 curiosity.

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Oct 27, 2016 Ali rated it really liked it

My first review in English and I'm sure it's full of errors!

There are two main flaws in this book. History of mathematics and philosophy of mathematics. Other reviewers have correctly mentioned Kline's unfair views on history. Throughout the book it was clear that Kline considers mathematics merely a mental construction. Although I don't find it plausible, but it's acceptable that a mathematician have such approach towards ontological issue since (at least as far as I understand) the topic is very well open. So far I was OK, but in last chapter while discussing the structure of mathematics he limits realism in ontology to ancient Greeks and only adds: "This view of mathematics was undoubtedly the dominant one until well into the eighteenth century and is held by some even today". Then he starts defending his view that mathematics is "entirely a human creation" and he concludes: "Only the relatively universal acceptance of mathematics [...] may lure us into getting that subject an objective existence". I find it totally unacceptable how he covers this topic of high importance and complexity especially in a book that has been written to non mathematicians. His inaccuracy and unfairness on history is evident even if reader knows nothing of mathematics' history but the flaw on philosophic issue is very well hidden!

Beyond these flaws, it's really a good book for someone who has been away from mathematics after high school or college. Concepts are beautifully explained with historic approach and it gives a clear picture of how mathematics has developed.

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Dec 17, 2008 Jake rated it did not like it

Mr. Kline and his book are a remnant of a happily bygone era. I can only assume that the good people at Dover books who consent to repackage and sell this chauvinistic relic from 1967 must be equally unenlightened, and greedy into the mix.

I gave up on this thing after the 'historical overview' bit (chapters 1-4). I'm just not content with a history of numbers that spends 20 pages on the drama of the Pythagoreans and irrational numbers, and then gives us this on the invention of negative numbers

"Perhaps because the Hindus were in debt more often than not, it occurred to them that it would also be useful to have numbers which represent the amount of money one owes."

I mean, come on. Up yours, Morris.

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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 civili 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. ...more

Mar 31, 2011 Kevin rated it it was amazing

Someone asked me to compile a list of the 10 most influential books I had ever read. This ranked near the top. I read it for the first time in my early twenties and it (among other things) began the process of turning my life around after half a decade of stupid choices.

Stated quickly: There is more to mathematics than the memorization of arithmetic and the mechanical transformations of algebra. They are to real math what pronunciation and grammar are to rhetoric, composition, and poetry (That i

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Oct 12, 2012 Carlos rated it it was amazing

This book isn't just about mathematics. It's about history, science, philosophy, the arts, and astronomy. One of my best reads ever. Reread many times. This book isn't just about mathematics. It's about history, science, philosophy, the arts, and astronomy. One of my best reads ever. Reread many times. ...more

Fairly nice popular tour of some of the more famous concepts of mathematics I read this as a physics student in the late 1990s. Good stuff from what I recall.

Dec 31, 2014 Dustin Burt rated it it was amazing

Many years ago, I hated math. Let be clear: this was a thorough loathing of the subject. Also many years ago, at one particular crossroads in my academic and professional paths, I realized I needed to get back into mathematics--and move well into calculus (at least). I walked into my local bookstore and saw this book. I bought it, and within minutes of having purchased it, I found I couldn't stop reading it.

I walked the entire way home from the bookstore (never mind I had driven to get there), r

I walked the entire way home from the bookstore (never mind I had driven to get there), reading this book the whole way home. Since that time, I have read this book no fewer than a dozen times, and my first copy remains my most treasured book of all. I have bought subsequent copies to lend and gift to others who don't care for math, but find themselves needing more strength in it.

The hook for me is the (surprisingly) engaging history of mathematics and of the (unsurprising) wonderfully odd people who contributed so much to both the art and science of mathematics. There is no question that the book is densely packed with a good deal of math (my paperback copy has around 550 pages of it), but the writing style is clear and non-technical, and the graphs and figures are very helpful and informative.

As I write this review, I'm thinking it may just be time for another read through.

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Mar 08, 2007 Kamili rated it it was amazing

So you really want to feel stupid? Read this and have all the memories of 8th grade geometry come back to you. Why is it that I can remember every detail of Josh Engels' hair, but I can't remember how to do a proof? The mind reels. So you really want to feel stupid? Read this and have all the memories of 8th grade geometry come back to you. Why is it that I can remember every detail of Josh Engels' hair, but I can't remember how to do a proof? The mind reels. ...more

Nov 23, 2017 Nicolas rated it it was amazing

As noted in a lot of comments, the first few chapters vary between heavily biased or outright blatantly Eurocentric. Watching Marcus Du Sautoy's The Story of Math series will be far more effective in getting a sense of the history of Mathematics.

That said. This is a wonderful work, Kline's explanation of very abstract concepts in a very clear way makes it well worth reading. His anticipation of questions that might arise when encountering a new subject in Mathematics is always on target. Much of what is infuriatingly missing in classic college textbooks is addressed here. Who came up with this concept, why is it important, how does it relate to other fields, how does it relate to the real world?

Kline walk as perfect line between just enough complexity and details about a subject to keep the reader engaged, while adding in a concrete example just at the right time. He balances the theoretical and practical almost effortlessly.
He focuses on the understanding of mathematics, not just the functional aspect of carrying out.

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Oct 23, 2007 Russell rated it it was amazing

My math skills are underdeveloped. I'll freely admit that. I am seeking to remedy that as quickly as I can.
To that end, this book was a fantastic help for me. It really should be a standard text in at least college, if not in high school. The fun part of this wasn't just having math explained clearly, but also the history of the math. Kline has
brief biographies of the major players behind the ideas, where the ideas came from, where they led, and different aspects of the whys and wherefores.

It's

It's a math book that is also a history of math.

It is a very accessible book, Kline presents the math clearly and neatly, with plenty of practice problems to reinforce the principles (answers are in the back of the book, thankfully!).

If you are looking to brush up on rusty math skills, or have a strange yearning to get a quick overview of math history, this book is a great choice.

I loved it, but I know that there is something wrong with me ;)

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May 23, 2008 Ron Moreland rated it liked it

Recommends it for: anyone wanting to look at math in simplified terms

This book simplifies complex mathematical topics. This is precisely what a good math teacher will do for their students. This book gives an overview regarding where some of the math which has been studied comes from. It also explores subjects ranging from basic math to Calculus and gives problems and solutions in a simple, easy to understand, practical way.

Dec 14, 2007 Jean-Luc rated it really liked it

Wish I had read this in grade school. It was *that* easy to understand...

Feb 22, 2008 J. rated it really liked it

Interesting insight into the history of math.

A good, if dated (and very euro-centric) history of mathematics. Can be read relatively easily without knowing too much mathematics in advance -- by a late high-school or college level reader.

Oct 17, 2008 Damien marked it as to-read

I've been reading this book on and off for years. This books contains things that I have never been exposed to, and it contains things which I, sadly, did not retain from any of my schooling. I've been reading this book on and off for years. This books contains things that I have never been exposed to, and it contains things which I, sadly, did not retain from any of my schooling. ...more

Starting my business school pre-work. I'm enjoying so far that this provides a history of mathemtics and is written for a liberal arts major. Starting my business school pre-work. I'm enjoying so far that this provides a history of mathemtics and is written for a liberal arts major. ...more

While mathematics has recently risen to prominence as the "M" in STEM, mathematical literacy has often been neglected in education and society at large. Too often, people are introduced to mathematics via dry technical books with a positivist focus on numerical operations. They gain little context for quantitative reasoning and the transformative, civilizing force that mathematics has been throughout the centuries. Consequently, a majority of people--myself included--finish their formal educatio While mathematics has recently risen to prominence as the "M" in STEM, mathematical literacy has often been neglected in education and society at large. Too often, people are introduced to mathematics via dry technical books with a positivist focus on numerical operations. They gain little context for quantitative reasoning and the transformative, civilizing force that mathematics has been throughout the centuries. Consequently, a majority of people--myself included--finish their formal education with little appreciation of the subject, its significance, its power, and its allure. If our education system did a better job telling the (hi)story of math, we'd have a society more equipped and enthusiastic for reason, problem solving, and critical thinking.

Kline provides the missing context to math that I wish I'd had growing up. Like Bertrand Russell's eminently readable History of Western Philosophy, Kline shows the human side of his subject, recounting the mathematical problems societies have struggled with over the centuries and the ingenious ways these problems have been solved. We see mathematics as part of the revolutionary rational search for truth in ancient Greece; math's instrumentality to profound questions in cosmology in Hellenistic Greece, the Renaissance, and beyond; how mathematical laws of nature helped to usher in the scientific revolution; and how math opened the door to the study of social sciences with statistics and probability. Maybe the most interesting section is the discussion of non-Euclidean geometry, its discovery, and its implications for society and truth.

Along the way, Kline introduces the many fascinating personalities behind the ingenious mathematics ideas: Galileo, Descartes, Newton, Cardan, Pascal, Fermat, Gauss, and many more.

The book never gets bogged down in technicalities, though for the non-mathematician, the math at times gets complicated very fast. This wasn't at all an impediment to my overall enjoyment of the book.

Kline is an expert teacher with a comprehensive grasp of and contagious enthusiasm for his subject. I've added a few more of his books to my list.

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I got this book after reading some good reviews. But it delivers what it promises: it's a practical approach to maths for those who have not studied this science much but have an interest in it. I have a degree in mathematics and I'm a math teacher ata a high school, and in this book I have not learned anything nor have I come across any interesting approach or explanation. My fault, I guess.

Nevertheless, the book it's OK, and it could be recommended for people with a lower background in mathema

Nevertheless, the book it's OK, and it could be recommended for people with a lower background in mathematics, looking for a complete but not very deep guide to enter the most important branches of mathematics.

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Mayyyyybe a better title could be, Mathematics for the Nonmathematician Who Is Reasonably Comfortable With Mathematics.

Doubles almost as a history of mathematics, up to the end of the 18th century, with extra material on statistics and probability. Kline's approach, which I approve of, is always to try to combine the actual math with its development and the problems that people were trying to solve at the time.

Mayyyyybe a better title could be, Mathematics for the Nonmathematician Who Is Reasonably Comfortable With Mathematics.

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This book is well written, and clearly well-intentioned towards a public not coming from a mathematical background, however, I did not find it very intuitive for a beginner of math studies such as me. I did not read all the chapters and will get back to it in a later moment when more ready to tackle it.

Sep 11, 2020 Lin rated it really liked it

A competently written popular math book, there are better ones out there with more modern branches of mathematics covered like Kasner's book, but I still liked this one a lot. It was partially what inspired me to want to do mathematics, so I've got to give it credit there. A competently written popular math book, there are better ones out there with more modern branches of mathematics covered like Kasner's book, but I still liked this one a lot. It was partially what inspired me to want to do mathematics, so I've got to give it credit there. ...more

Nov 24, 2020 Giang Le rated it it was amazing

One of my recent favorite reads! This book gives me the high-level overview of math history that I wish I had when I approached math for the first time as a kid.

Far too many words and incessantly gendered. Ended up skipping a lot of the history parts. Bits about the actual math were interesting enough.

Jan 10, 2016 Alex Lee rated it it was amazing

For such a far reaching and difficult subject matter, Kline does quite a good job at summarizing and exploring for us mathematics as a method in exploring and understanding relationships in this world. Ultimately what makes math interesting, is of course, its application.

Kline takes a definite position on mathematics as something to be admired and understood. His writing is quite clear as it is clear he is interested in clarity of thought. Yet Kline ends with an understanding of the limits of this method. He would, in the beginning, question the veracity of philosophy and other speculative endeavors but he ends with a deeper understanding of math, one in which math itself is understood as merely relations on relations, not actually explanations of any sort.

One should also question the extent to which mathematics really represents the physical world. The discipline has been effective in treating some abstractions: space, time, mass, velocity, weight, force, the frequency of light and sound, and other concepts. It treats those physical concepts which can be represented by numbers or geometrical figures. But physical objects posses other properties as well. We do not usually think of human beings as being chunks of matter moving in space and time. Nor would a poet or an artist be content to say that the mathematical laws of planetary motion represent the essence of the planets. We have become so accustomed to the analysis of the physical world in terms of space, time, form, mass and the like, that we tend to overlook the fact that these concepts represent just some properties and narrow ones at that. They cause us to look at the world with blinders. The mathematical approach may not be the deepest possible or the most illuminating; it certainly does not answer the question of whether the solar system is designed for any special ends. Scientists may say that this question does not fall within the province of science, but it is nevertheless a question which human beings would like to see answered. The refusal of scientists to consider it does not wipe out the question, but only reveals a limitation of the mathematical approach.

With this capstone, we see the end of Kline's book in which he sets out to explore mathematical concepts, demonstrating their usefulness and their reality for us. In some ways this is not the most exciting book, since these "question[s] [that] human being[s] would like to see answered" are what drive us in a big way to explore and learn, but Kline sets out to write a fairly comprehensive book for nonmathematicians about math and he does this with a disciplined approach that leaves very little to be desired. Bravo.

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This is a re-release of the textbook originally titled Mathematics for Liberal Arts. The text offers a high level overview of the most important branches of mathematics, while discussing its historical development and its tight relationship with empirical science.

It is unfortunate that the title of the book has been changed, since the target audience is less clear now. The book probably succeeds admirably at delivering a captivating account of mathematics to a reader completely, or at least largely, unfamiliar with the topic - and I am going to rate it highly for that. Only a word of warning, take good heed of the target audience, if you have not slept through your high school mathematics lessons, there is nothing new for you in this book mathematics-wise (save perhaps for the chapter on non-Euclidead geometries), and at best, the only new thing you will end up learning will be the historical background - but there are much better resources for that.

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Morris Kline was a Professor of Mathematics, a writer on the history, philosophy, and teaching of mathematics, and also a popularizer of mathematical subjects.

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"All mathematical proofs must be deductive. Each proof is a chain of deductive arguments, each of which has its premises and conclusion." — 4 likes

"The feeling that one must be an authority in a subject to say anything about it is unfounded. We are all laymen outside the field of our own specialty," — 2 likes

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