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"Mathematics and the Physical World" by Morris Kline

Excellent title introducing the reader to the spatial discipline on mathematics including its physical properties.

You landed on a review of a book written by one of my personal favorite authors in the subject of Math: Morris Kline. To the unsuspecting or the curious one wanting to fully understand and rid the confusions about the rigorous, yet beautiful, subject of Math, let me tell you: Author Kline is quite possibly one of the most keen writers in talking about Math, whether it's about the history or the function/philosophy of the science. If anything, Kline is the "John Gribbin" of Mathematics, in terms of writing. I wish I knew about Kline during my early school years, then Math would've been so much easier to the point where I'd likely outwit my own teachers (yeah, I'm one of those people).

With a gentle introduction and the beauty of the discipline, author Kline neatly explains and reasons of the why and the what of Math in its role of defining its very own beauty, and of Nature entirely. Kline discreetly discusses how Math is essential in the physical realm of the planet in which we live, yet take for granted, all without making the reader eye-crossed enough to fall asleep. Saying that tells a lot, because I'm certain not very many writers can make a tough subject sound so simple to explain. That's right, ladies and gentlemen: Kline introduces you into a world only a chunk of people are able to master, and that is both Mathematics and Physics. And don't you dare close your browser, after I said those.

After, Kline, from the beginning to a bit passed the middle parts of the book, gives the reader a truly amazing account in how huge Math plays in Physics—Math is the batteries needed to rev up Physics. What's nice is the author talks about the various studies of Physics, currently taught in many schools today, from the physics of music to gravity. Along with those are some Astrophysics, a brief emphasis on Quantum Mechanics/Physics, Fluid Mechanics Theory of Light (Optics) and some Geometry and Trigonometry stuff. Throughout these chapters, Kline gives simple scenarios and mathematically breaks them down arriving to answers that calculate distances, like how far is the Moon from the Earth and how, and why, projectiles eventually follow a perpendicular curve against the floor and not completely horizontal (due to gravitational pull, which you also learn as well). All of these early on in the book will make you want to pursue a serious curiosity in anything Physics—something I guarantee you should check out. (Even those current students of Physics, this book will serve as a huge inspiration to get you excited about the subject again.)

Near the end of the book is something that fascinated me and I feel is my favorite: Calculus and [Non-Euclidean] Geometry! I have a confession to make: From high school to college, I have never taken a course in Calculus (I will soon though!), though I have taken Statistics and (Symbolic) Logic. As I started reading from Differential Calculus to Integral Calculus, and its serious usage in Physics, my heart skipped a beat. Kline really explained Calculus in such a clean, non-technical fashion that I wonder why people/students complain why it's too hard. It's just a study of the rate of change, with applications learned from Algebra, Geometry and Trigonometry (areas in Math I have studied, additionally). As for Integral Calculus, I always wondered about that fancy symbol you'd find on violins and cellos, but all it is symbolizing is the summation—a "fancy" letter S denoted as . Paired with the Calculus stuff, Kline talks about Differential Equations and Derivatives. Speaking of Derivatives, in comparison to online tutorials and written in some books, lots of teachers and authors use Gottfried Leibniz's notation of derivatives which is:



Because, especially when talking about Calculus and Physics, Isaac Newton gets lots of recognition and respect but almost never uses his notation which is:

Nevertheless, those chapters, especially if you've never taken a course in Calculus, makes it super easy to understand its discipline and its application to Physics.

There were a few misspelled words in the entire book but we can let that slide, since the gentle writing all throughout makes up for it. Once again, never has a book talking about both Math and Physics could ever been written in such clear, understandable fashion, and written enough to get you very curious in extending your learning of Physics and of majority of science in general. This book is the hidden gold nugget many people struggling with Math and Physics may be looking for this entire time. Since it was reproduced by my ultimate favorite publication company Dover Publications, the price of this book isn't wallet ailing.

Now, since this is a reprint of the original 1959 edition, you'll notice how old time was back then. Kline mentioned how there were 2 billion people on the planet that time! Yeah, lots has changed over the years, and here we are in 2017. Besides old, growing facts like those, the Math and Physical talks still apply today.

It is of my honor to praise the late, great Morris Kline for this book of his. Excellent work, Mr. Kline, and if you're spiritually reading this, along with your family and friends, this book review is for you! I STRONGLY recommend this book!

(NOTE: if you were a colleague of Morris Kline, or if you are one of Kline's children, we would like to interview you here on THE SEEDS OF BOOKS! Use the Contact Form using the subject line "Media" on the email form. We look forward to talking with you, for all our fans to see!)





  • Wonderful writing accessible to everyone interested in the physical sciences, mathematically.
  • Gently explained without pushing out all the advanced mathematics.
  • Great book for those wanting to venture into Pure Mathematics and/or Physics.
  • None.
100% (A+)
Fan Rating
Title Mathematics and the Physical World
Author(s) Morris Kline
Description Since the major branches of mathematics grew and expanded in conjunction with science, the most effective way to appreciate and understand mathematics is in terms of the study of nature. Unfortunately, the relationship of mathematics to the study of nature is neglected in dry, technique-oriented textbooks, and it has remained for Professor Morris Kline to describe the simultaneous growth of mathematics and the physical sciences in this remarkable book.

In a manner that reflects both erudition and enthusiasm, the author provides a stimulating account of the development of basic mathematics from arithmetic, algebra, geometry, and trigonometry, to calculus, differential equations, and the non-Euclidean geometries. At the same time, Dr. Kline shows how mathematics is used in optics, astronomy, motion under the law of gravitation, acoustics, electromagnetism, and other phenomena. Historical and biographical materials are also included, while mathematical notation has been kept to a minimum.

This is an excellent presentation of mathematical ideas from the time of the Greeks to the modern era. It will be of great interest to the mathematically inclined high school and college student, as well as to any reader who wants to understand—perhaps for the first time—the true greatness of mathematical achievements.
Dedication "TO Douglas Mann Kline"
ISBN 0-486-24104-1
Book Dimensions Width: 5.75″ (5 6/8″)
Height: 8.25″ (8 1/4″)
Depth: 0.94″ (15/16;″)
Page Count 512
Contents 1: The Why and Wherefore, 2: Discovery and Proof, 3: The Science of Arithmetic, 4: The Deeper Waters of Arithmetic, 5: Numbers, Known and Unknown, 6: The Laws of Space and Forms, 7: The Dimensions of the Heavenly Spheres, 8: The Revolutions of the Heavenly Spheres, 9: The Scientific Revolution, 10: The Wedding of Curve and Equation, 11: Explanation Versus Description, 12: Vertical Motion, 13: Motion on an Inclined Plane, 14: The Motion of Projectiles, 15: From Projectile to Planet and Satellite, 16: Deductions from the Law of Gravitation, 17: More Light on Light, 18: The Mathematics of Oscillatory Motion, 19: Oscillations of the Air, 20: Old Foes with New Faces, 21: Mathematical Oscillations of the Ether, 22: The Differential Calculus, 23: The Integral Calculus, 24: Differential Equations—The Heart of Analysis, 25: From Calculus to Cosmic Planning, 26: Non-Euclidean Geometries, 27: Mathematics and Nature, Index
Author Photograph --
Cover Design Paul E. Kennedy
Published March 1, 1981
Publisher Dover Publications (www.doverpublications.com). Published in Canada by General Publishing Company, Ltd., 30 Lesmill Road, Don Mills, Toronto, Ontario. Published in the United Kingdom by Constable and Company, Ltd.
Manufactured in United States of America. Dover Publications, Inc. 180 Varick Street New York, N.Y. 10014
Copyright © 1959 by Morris Kline. All Rights Reserved under Pan American and International Copyright Conventions.
Book Format Kindle, Hardcover, eBook
Quoted Reviews "Kline is a first-class teacher and an able writer. . . . This is an enlarging and brilliant book. . . ." — Scientific American.

"Dr. Morris Kline has succeeded brilliantly in explaining the nature of much that is basic in math, and how it is used in science. . . ." — San Francisco Chronicle
Best Seller's List --
About The Author DR. MORRIS KLINE is a prominent teacher, research mathematician, and writer. He has taught mathematics at the undergraduate and graduate levels since 1930 and has been a guest lecturer at a number of universities in the United States and Europe. He is currently Professor of Mathematics at New York University. His research career was effectively launched during two years as a research assistant at the Institute for Advanced Study of Princeton.

A good deal of Dr. Kline's time is still devoted to the direction of the Division of Electromagnetic Research of New York University. During the year 1958-59 he was a John Simon Guggenheim Memorial Fellow and a Fullbright lecturer at the Technical University in Aachen, Germany.

Dr. Kline is married and has three children; the Klines live in Brooklyn, New York.
Other Dover republication of the edition originally published by Henry Holt & Co., New York, 1911.
Library of Congress Cataloging-in-Publication Data ????
CIP Number 80-83667
LC Control Number ????
LC Call Number ????
DDC Call Number ????


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