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The Mathematical Experience (Penguin Press Science) [Paperback]

Philip J. Davis , Reuben Hersh
5.0 out of 5 stars  See all reviews (4 customer reviews)

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Book Description

27 Sep 1990 Penguin Press Science
This is a revised edition of a monograph describing what mathematics is about and what mathematicians do. It is also a text aimed at non-mathematics majors. It contains exercises and is accompanied by an instructor's guide.
--This text refers to an out of print or unavailable edition of this title.


Product details

  • Paperback: 464 pages
  • Publisher: Penguin Books Ltd; New edition edition (27 Sep 1990)
  • Language: English
  • ISBN-10: 0140134743
  • ISBN-13: 978-0140134742
  • Product Dimensions: 23.6 x 16.3 x 2.8 cm
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (4 customer reviews)
  • Amazon Bestsellers Rank: 336,262 in Books (See Top 100 in Books)
  • See Complete Table of Contents

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Review

"This beautifully written book can be recommended to any cultivated person with a certain sophistication of thought, and also to the practicing mathematician who will find here a vantage point from which to make a tour d'horizon of his science." --Publ. Math. Debrecen "This is an unusual book, being more a book about mathematics than a mathematics book. It includes mathematical issues, but also questions from the philosophy of mathematics, the psychology of mathematical discovery, the history of mathematics, and biographies of mathematicians, in short, a book about the mathematical experience broadly considered… The book found its way into "Much for liberal arts students" courses and into education courses directed at future teachers. Term paper topics, essay assignments, problems, computer applications, and suggested readings are included. This new material should greatly enhance the usefulness of this very creative book. The range of topics covered is immense and the contents cannot easily be summarized. The book makes excellent casual reading, would make a good textbook, or could easily be used as a supplement to nearly any course concerned with mathematics." -Zentralblatt Math "This is a people-centered book about mathematics, and as such it provides an opportunity to explore fundamental issues that are typically absent from the experience of most college and university students (as well as their teachers). This new edition provides an excellent initiation of students into some of the more challenging aspects of mathematics…The study edition of The Mathematical Experience will help its readers acquire a real understanding of mathematics." -Notices of the AMS "Two distinguished mathematicians...have written a perfectly marvelous book about the Queen of Sciences, from which one will get a real feeling for what mathematicians do and who they are. The exposition is clear and full of wit and humor..." --The New Yorker (1984 American Book Award Edition) --This text refers to an out of print or unavailable edition of this title.

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Most Helpful Customer Reviews
8 of 8 people found the following review helpful
Format:Paperback
Back in the early 90's when I was an almost-penniless mathematics student I was standing in front of a bookshelf in my local bookstore and had to choose between this and Gödel, Escher, Bach. I chose this book and I still don't regret it. [I have also subsequently bought GEB :-)]
Driven by their obvious love of the subject, the authors do a credible job of tackling just what it is about mathematics that makes mathematicians love it so much, often to the bafflement of the rest of the world. A particular personal favourite is the series of four conversations between an "ideal mathematician" and, respectively, a University Public Information Officer, a philosophy student, a positive philosopher and a sceptical classicist.
I would recommend this book to students of mathematics at any level beyond the elementary, especially those with an interest in the foundations of their subject. The authors do however acknowledge that some parts of the book will seem alien to the layman.
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2 of 2 people found the following review helpful
5.0 out of 5 stars Thought Provoking 6 Jun 2010
By B
Format:Paperback|Verified Purchase
If you are the kind of person who enjoys Horizon and other science programs but wishes they were less stripped of technicalities and more in depth: if you are very curious about physics and mathematics, you may find this a very stimulating read. After all you don't need to be a good comedian to enjoy watching comedy, so with little mathematical knowledge you can enjoy this very wide ranging discussion of many exotic fields of maths and gain a sense of the range and significance and methodologies of this field at the outer limits of human abstract thought. This very readable, demanding, though provoking book that can occupy you for weeks and sustain several re-readings.
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2 of 2 people found the following review helpful
5.0 out of 5 stars A Must Read for the Curious 21 Oct 2009
Format:Paperback
Around my early to mid teens, finding the mathematics I was being taught easy but also puzzling I started to have philosophical questions that were just not properly addressed. I later hoped (naively I now know) my Science/Engineering degree would answer those questions. It didn't. I had wanted to dig deeper into what mathematics is but instead was taught increasingly obscure and complex "results" that were useful to my discipline. Had I known it at the time this book would have answered my questions (often answering them with more questions, true). It appears to give an excellent framework to the consideration of any uneasiness you might feel with mathematics especially if you find/found school levels maths easy.

If after reading this you still feel uneasy then you know you need to proceed further into philosophy.

A great book.
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5.0 out of 5 stars Classic 25 April 2010
Format:Paperback
This book is a c;assic work on the subject of wnat mathematics is all about. No one interested in maths should be without it.
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Most Helpful Customer Reviews on Amazon.com (beta)
Amazon.com: 4.7 out of 5 stars  22 reviews
61 of 69 people found the following review helpful
5.0 out of 5 stars A survey on exactly that. 23 Jan 2000
By Yoon Ha Lee - Published on Amazon.com
Format:Hardcover
Along with Ivars Peterson's books on math, I suppose this has changed my life, too.
I was going to study history. Math? Who cared about math? Math was for those science-types. I had an image of mathematicians as bespectacled, socially-inept, hunch-shouldered gnomes who lived in universities and ventured out of their burrows for--well, maybe they didn't venture out at all.
The joke's on me. I'm a math major now. This book is one of the reasons.
I've always loved history: the march of events, the ebb and flow of cause and effect and unexpected accident. I didn't realize that math, too, had a history, an ebb and flow. If I'd ever thought about it, I would have realized that an angel didn't come down from the heavens bearing The Big Book of Math, complete with proofs. But that's what it seemed like, until I read about the almost architectural building of theorem upon theorem, idea upon idea. Math wasn't a Big Book; it evolved and grew. Grows still, I should say.
Did numbers exist? Well, of course they existed. Wait a second. What *is* a number anyway? How *does* one exist? Would they exist if there were no people?
And so I learned that math, too, has its philosophies.
Most of all, I learned that mathematicians were and are people, not gnomes in burrows who have nothing to do with the rest of the world. That math is important for more than the homework assignments that plagued my high school evening hours. That math is worth studying.
If you could convey this to heaven knows how many disgruntled and frustrated math students around the world, I wonder if they might like the subject better.
I sure did.
33 of 36 people found the following review helpful
5.0 out of 5 stars One of the best books about math. 1 Dec 2000
By Shard - Published on Amazon.com
Format:Paperback
Some books are of such depth that it is impossible to completely digest all that they contain even after multiple re-readings. Many achieve this through their level of technicality, or through sheer obscurity. The true gems are those that achieve it through clear intelligible discussion of deep concepts. Books like this point outside of themselves, leading one to whole new conceptual worlds. They force new connections to be made in the reader's brain. I reserve my highest recommendation for books of this type, and "The Mathematical Experience" is certainly one of them.
Popular books such as Ivars Peterson's "Mathematical Mystery Tour" and Keith Devlin's "Mathematics: The Science of Patterns" excel at giving the non-mathematician a glimpse into the world of modern mathematics, and an appreciation of the beauty and interest found therein. Depending on the level of sophistication of the reader, some popular math books are more appealing than others, in as much as they convey more or less actual mathematical knowledge. However I would venture to guess that these works hold little interest for real mathematicians, being much too shallow in their description of modern problems, even outside the specialized field of the reader.
Davis and Hersch on the other hand should strike a chord with most practicing professionals, as well as with the lay audience. As the authors state in the introduction, the layman reader may at times "feel like a guest who has been invited to a family dinner. After polite general conversation, the family turns to narrow family concerns, its delights and its worries, and the guest is left up in the air, but fascinated."
We receive the same service of exposure to intriguing mathematical ideas as in other popular books, but we also get healthy doses of philosophy and history. We get glimpses of truly mind-boggling (or mind-expanding ... the authors would perhaps say that bogglification is a primary path to expansion), mathematical concepts such as the Frechet ultrafilter, the truly huge integer known as a moser, or Weiss's restatement of the Chinese Remainder Theorem which is so abstract and generalized as to defy the understanding of all but a handful of practicing mathematicians.
The book tackles problems of mathematical experience which are tough because they fall into the realm of philosophy: the meaning of proof, the goal of abstraction and generalization, the existence of mathematical objects and structures, and the necessary interplay between natural and formal language, or between algorithmic and dialectic processes. What is amazing is that Davis and Hersch make these ideas not only accessible to an intelligent layman, but also interesting and vital, without (I presume), losing the interest of real mathematicians.
Rather than a zoo of mathematical curiosities, the book is an anthology of essays about the practice of mathematics, with illustrations ranging from the elementary to the extraordinarily deep. I suspect that the questions "What is mathematics?" and "What does a mathematician actually do?" are rather off-putting to the majority of professionals in the field. But "The Mathematical Experience" asks these questions, and rather than giving a terse answer, takes them very seriously and fearlessly analyses them from a variety of stances. Of course, the authors don't presume to give definitive answers. They do, however, provide much food for thought ... so much that the reader is likely to come away from the book transformed.
If you are not a mathematician, but a curious layman, "The Mathematical Experience" is the best place to go after you've read William Dunham, Ivars Peterson, Keith Devlin, Ian Stewart, or others like them. If you are a student of mathematics, or a student or practitioner of any other science, you'll do yourself a great favor by reading this book. If you are a mathematician who generally dislikes and avoids pop-math writing, give this a try. You may be very pleasantly surprised.
20 of 22 people found the following review helpful
5.0 out of 5 stars Excellent dialog on the development of mathematics.. 12 Feb 2001
By Kersi Von Zerububbel - Published on Amazon.com
Format:Paperback
This book was a sheer joy to read and digest. The authors skilfully comingle history, mathematics, philosophy, and biography. The result is a truly fantastic voyage into the meaning and gist of discovery and conjecture. In chapter after chapter important ideas like Fourier analysis, Non-Cantorian Set Theory, and Objects and Structures are scrutinized in a very interesting manner.
The deeper you go into the book the more will you revel in the sheer majesty and scope of the topics. I had to read the chapter on Inner Issues twice to really get everything out of the text. Topics such as Teaching and Learning are very insightful and full of little hidden gems.
If you are prepared to expend some effort and if you wish to know what mathematics "really is like", grab this book. I am sure this will become a permanent treasure in your library and you will peruse it often long into the night.
14 of 15 people found the following review helpful
5.0 out of 5 stars Philosophy, History and Myths of Mathematics 20 Nov 2003
By Jim Morrison - Published on Amazon.com
Format:Paperback
The Mathematical Experience by Philip J. Davis and Reuben Hersh
1981 Houghton Mifflin Company, Boston
Is all of pure mathematics a meaningless game? What are the contradictions that upset the very foundations of mathematics? If a can of tuna cost $1.05 how much does two cans of tuna cost (Pg. 71)? If you think you know the answer, don't be so sure. How old are the oldest mathematical tables? What is mathematics anyway, and why does it work? Can anyone prove that 1 + 1 = 2?
This is a book about the history and philosophy of mathematics. I'm certainly not a mathematician, and there are parts of the book I will never understand, yet the balance of it made the experience well worth while. The authors presented the material so that it is interesting and (mostly) easily understood. They have a creative way of making a difficult subject exciting. They do this by giving us insights into how mathematicians work and create. They live up to the title making mathematics a human experience by adding fascinating history. Frankly I was shocked when they pointing out how even mathematicians have made questionable assumptions and taken some basic "truths" on faith. They show the beauty of math in the "Aesthetic Component" chapter. Ultimately the question that comes up again and again is the question of whether or not we can really know anything about time and space independent of our own experience to make an adequate foundation for a complete system in mathematics. If you have ever wondered about the world of mathematics and the personalities involved you might consider this book. If you are a mathematics teacher you should read this book. If you are a mathematician you could find it quite unsettling.
It contains eight chapters, each one broken up into many subtitles so if you do get bogged down in the mathematics it isn't for long. There are 440 pages. I'd like to see a much more complete glossary for people like me who need it.
12 of 13 people found the following review helpful
5.0 out of 5 stars rare. 26 Aug 2000
By Jihwan Myung - Published on Amazon.com
Format:Paperback
It was about five years ago. Physics suddenly seemed fascinating but I was struggling with math. My tutor suggested two books for me. One of them was this book. I cannot say this book was particularly helpful but it gave me a good sense of what mathematics is: its people, culture, history, and philosophy. Quite unlike E.T. Bell's Men of Mathematics, this book does not contain romantically presented stories of some math heros. And unlike some popular math books by Ian Stewart, it does not attempt to explain (rather unsuccessfully) some esoteric theories. It is just as the title suggest--what a mathematical experience can be. A book of this kind is rare.
P.S. Now, some five years later, I am not sure if mathematical knowledge maintains a separte existence as Plato had thought, and as the authors believe. (Ref. Plato, Phaedo)
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