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Mathematics and the Imagination (Dover Books on Mathematics) Paperback – March 28, 2001

by Edward Kasner (Author), James Newman (Author)

22 customer reviews

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Anyone who gambles, plays cards, loves puzzles, or simply seeks an intellectual challenge will love this amusing and thought-provoking book. With wit and clarity, the authors deftly progress from simple arithmetic to calculus and non-Euclidean geometry. "Charming and exciting." — Saturday Review of Literature. Includes 169 figures.

Mathematics and the Imagination (Dover Books on Mathematics)

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Product Details

Series: Dover Books on Mathematics
Paperback: 400 pages
Publisher: Dover Publications (March 28, 2001)
Language: English
ISBN-10: 0486417034
ISBN-13: 978-0486417035
Product Dimensions: 0.8 x 5.5 x 8.5 inches
Shipping Weight: 15.2 ounces (View shipping rates and policies)
Average Customer Review: 4.5 out of 5 stars See all reviews (22 customer reviews)
Amazon Best Sellers Rank: #369,908 in Books (See Top 100 in Books)
- #15 in Books > Science & Math > Mathematics > Geometry & Topology > Non-Euclidean Geometries
- #124 in Books > Science & Math > Mathematics > Pure Mathematics > Logic
- #149 in Books > Humor & Entertainment > Puzzles & Games > Math Games

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Customer Reviews

4.5 out of 5 stars

5 star		64%
4 star		27%
3 star		5%
2 star		4%
1 star		0%

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Most Helpful Customer Reviews

40 of 40 people found the following review helpful

Somewhat dated but still well worth reading

By Charles Ashbacher HALL OF FAMETOP 500 REVIEWERVINE VOICE on June 12, 2001

Format: Paperback

Originally published in 1940, the material in this book is beginning to show a little age. However, the quality of the writing renders those defects to near irrelevancy. Popular descriptions of mathematics are differentiated by the quality of the writing rather than the distinctiveness of the mathematics, and this one shines.
I like this book, starting with the title. It takes an enormous amount of imagination to do mathematics, something unappreciated by the public. It is easy to understand the use of linear segments to approximate the length of a curve. However, it requires an enormous leap of abstraction to believe that if they are made of zero length and then summed up, the result is the true length. Calculus students dutifully record and apply this, but in most cases don't appreciate the significance of the idea. In nearly all cases of major mathematical advancement, a fundamental change in thought processes was necessary. Those changes require imagination and the advances explained in this book are well documented and described.
Mathematicians are containers of some of the greatest concentrations of imagination that humans possess. Their leaps of abstraction often include descriptions of objects that cannot be visualized. Kasner and Newman capture this essential ingredient, serving it up in palatable portions.

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28 of 28 people found the following review helpful

Oldie but Goodie

By Skip on April 12, 2000

Format: Paperback

Having had this book around the house for ages, I picked it up and to my surprise within a few minutes really understood (not just enough to use, but actually understood) what logarithms really are, where they come from. The chapter on e, pi, and i is another great one to get the story behind the story, as it were. For me the book could better have continued in this vein of explaining concepts we've seen before but never really grasped intuitively, and perhaps because I'm not terribly interested in mathematical games I found that segment less fun. But in fairness, they've done a good job getting away from textbook math and into some interesting themes. I don't know if it's all still valid, as it is so old--references to Fermat's last theorem are at least outdated!

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18 of 18 people found the following review helpful

Mathematics and the Imagination

By Hugo Campanelli on June 10, 2001

Format: Paperback

This book came to me by chance.Instantly got my attention.It is written in such a way,that makes interesant to travel through different chapters.In each one you have the mathematical theme mixed with stories , mathematicians histories and puzzles.You learn about people with the greatest imagination.Their personality and a lot of other things,that make you enjoy the reading,no matter if you love mathematics or you have hated it all the time.I've enjoyed specially the chapter about Mathematical Analysis,with the story about rivalry between the egocentric Newton and the humble Leibnitz. This book is the opportunity to learn that mathematics are not the boring thing we have learned at school.

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23 of 25 people found the following review helpful

Indulge your enjoyment of mathematics and expand your mind

By A Customer on November 4, 2001

Format: Paperback

My school teacher gave me this book to read when I was 13 years old, based on the interest I showed in Mathematics that went beyond the curriculum at school. In many ways it was way beyond my comprehension at the time, but little did I know that it would have such a lasting effect on me. Reading about concepts of infinity, that you could only describe to a fellow teenager as "different sizes of infinity", I realized that there really is a philosophy of mathematics that transcends all other subjects and that there is also an art to working with the subject. I can't recommend this book enough, and I never did give it back to my teacher!

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10 of 10 people found the following review helpful

Entertaining and educational for the few

By Sympa on November 12, 2009

Format: Paperback

This book is for very few as it is not for the following group of readers:
a) only peripherally interested in math;
b) interested in math but wanting to learn more in a concise manner and readily bored with exhaustive math history and early 20th century verbosity;
c) mathematicians who already know that stuff;
d) interested in math but requiring well organized and structured material.

If you do not belong to any of the above four groups of readers, you probably will like this book. You may even love it. To improve the probability you will like it you should not read chapters sequentially. This will bore you. Instead jump in directly to the mathematics domains you are familiar with and you like best. For instance, chapter VII covers Probability and chapter IX covers Calculus. If you like Geometry, you are in luck as the authors dedicate two chapters to it (IV and VIII).

The chapter on calculus covers a lot of grounds including not only derivatives but also definite and indefinite integrals, calculus and the laws of motions, and trigonometry. Your head may spin after this broad and deep excursion into calculus. And, this may be one of the authors' most successful chapters.

The authors divulge a lot of fascinating information even though the latter is not always easily extractable. This includes very intuitive explanations of the discovery and calculations of Pi, e, i, and logarithms. They explain how mathematicians leveraged those discoveries. The numbers Pi and e have so many applications that they suggest our civilization in terms of mathematical understanding and its practical application would be truly primitive if not for them (Pi, e).Read more ›

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Most Recent Customer Reviews

Three Stars

Has nice examples, but the author's clever little remarks made it irritating.

Published 16 days ago by Pdecordoba

I read it when I was 12, then again ...

I read it when I was 12, then again at 35, and now at 70 years old. I have revisited it throughout my life and I am most grateful for all it has given me.

Published 8 months ago by RichB

Two Stars

Wasn't what I had thought. Not very interesting I thought

Published 8 months ago by tainan

This book explains the differences between infinity and very large...

I first read this book in 1956 and was amazed at its clarity. When my granddaughter had trouble understanding the concept that a series with an infinite number of terms could... Read more

Published 21 months ago by Dave

Nothing short of a fun read

I gained quite a few good concepts relating to the philosophies behind mathematics along with good mathematic examples that anyone with basic algebra skills would yield some... Read more

Published 21 months ago by JUSTIN PLEWS

Best math intro out there

I read this for the first time in 1971, when I was in high school. It was a good layman's introduction to many of the fields of mathematics then, and it still is. Read more

Published 22 months ago by rokpyle

Mathematics review.

I found the book to be very interesting. There were parts that were beyond my knowledge or interest. I would buy again and recommend to others.

Published on December 2, 2013 by Wm A. Hendrickson

Great intro to thinking like a mathematician

About 50 years ago, my plane geometry teacher recognized I might have some math ability, if properly nurtured, and gave me a copy of this book. Read more

Published on August 25, 2012 by GWT

Wonderful Service!

Wonderful Service! Your customer service is very much appreciated ... from the description of the condition to the packaging of the product ... all very top shelf!

Published on October 14, 2011 by Ray Weigand

Proud owner of my Granddad's copy

My Granddad was a great engineer, and loved puzzles and games. After his funeral I was looking through his books and found this one, the original edition! Read more

Published on January 29, 2011 by RobotMan

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