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Mathematics in Western Culture

by Morris Kline (Author)
4.7 4.7 out of 5 stars 34 ratings
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This book gives a remarkably fine account of the influences mathematics has exerted on the development of philosophy, the physical sciences, religion, and the arts in Western life.
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  1. ISBN-10
    019500714X
  2. ISBN-13
    978-0195007145
  3. Publisher
    Oxford University Press
  4. Publication date
    December 31, 1964
  5. Language
    English
  6. Dimensions
    8.5 x 1.19 x 5.57 inches
  7. Print length
    512 pages
  8. See all details
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Editorial Reviews

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"[Kline] is unfalteringly clear in explaining mathematical ideas; he is learned but not pedantic; he has historical discernment, a sympathetic social outlook and a nice sense of fun and irony.... The beauty and fascination and rare excellence of mathematics emerge from his story. It is an exciting, provocative book."--Scientific American"Still the best textbook for the history and philosophy of mathematics for undergraduate liberal arts students. Especially good for the age of the Scientific Revulution."--Janet A. Fitzgerald, Molloy College, NY

About the Author

Morris Kline is Professor Emeritus at the Courant Institute of Mathematical Sciences, New York University.

Product details

  • Publisher ‏ : ‎ Oxford University Press (December 31, 1964)
  • Language ‏ : ‎ English
  • Paperback ‏ : ‎ 512 pages
  • ISBN-10 ‏ : ‎ 019500714X
  • ISBN-13 ‏ : ‎ 978-0195007145
  • Item Weight ‏ : ‎ 15 ounces
  • Dimensions ‏ : ‎ 8.5 x 1.19 x 5.57 inches
  • Customer Reviews:
    4.7 4.7 out of 5 stars 34 ratings

About the author

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Morris Kline

Morris Kline

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Morris Kline (May 1, 1908 – June 10, 1992) was a Professor of Mathematics, a writer on the history, philosophy, and teaching of mathematics, and also a popularizer of mathematical subjects.

Bio from Wikipedia, the free encyclopedia.

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4.7 out of 5 stars
4.7 out of 5
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34 global ratings

Top reviews from the United States

jdee28
5.0 out of 5 stars One of the great books
Reviewed in the United States on February 2, 2024
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Clarifies science, math, philosophy. Makes Western culture so much more understandable.
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Gbnet
5.0 out of 5 stars Simply, don't miss it
Reviewed in the United States on May 9, 2012
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I graduated in physics several years ago. It happens in life that you first do things and later you understand what you have done. With this book it happened to me to understand most of what I have studied after I have read it. It was a turning point in my life and in my career too. This doesn't mean it will be the same for everybody but surely that was my experience. Since I have read it, I have never forgot the following paragraph.

When earth was put apart

Granted that it was the superior mathematics of the new theory which inspired Copernicus and Kepler, and later Galileo, to repudiate religious convictions, scientific arguments, common sense, and well-entrenched habits of thought, how did the theory help to shape modern times?

First, Copernican theory has done more to determine the content of modern science than is generally recognized. The most powerful and most useful single law of science is Newton's law of gravitation. Without anticipating here the discussion reserved for a more appropriate place in this book we can say that the best experimental evidence for this law, the evidence which established it, depends entirely on the heliocentric theory.

Second, this theory is responsible for a new trend in science and human thought, barely perceptible, at the time but all-important today. Since our eyes do not see, nor our bodies feel, the rotation and revolution of the Earth, the new theory rejected the evidence of the senses- Things were not what they seemed to be. Sense data could be misleading and reason was the reliable guide. Copernicus and Kepler thereby set the precedent that guides modern science, namely, that reason and mathematics are more important in understanding and interpreting the universe than the evidence of the senses. Vast portions of electrical and atomic theory and the whole theory of relativity would never have been conceived if scientists had not come to accept the reliance upon reason first exemplified by Copernican theory. In this very significant sense Copernicus and Kepler began the Age of Reason, in addition to fulfilling the cardinal function of scientists and mathematicians, that is, to provide a rational comprehension of the universe.

By deflating the stock of Homo sapiens, Copernican theory reopened questions that the guardians of Western civilization had been answering dogmatically upon the basis of Christian theology. Once there had been only one answer; now there are ten or twenty to such basic questions as: Why does man desire to live and for what purpose? Why should he be moral and principled? Why seek to preserve the race? It is one thing for man to answer such questions in the belief that he is the child and ward of a generous, powerful and provident God. It is another to answer them knowing that he is a speck of dust in a cyclone.

Mathematics in Western culture, Morris Kline, 1953
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Janice A
5.0 out of 5 stars Great Book
Reviewed in the United States on September 22, 2021
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A must read for every scholar!
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Thomas Levenson
5.0 out of 5 stars Five Stars
Reviewed in the United States on May 23, 2015
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Just a great introduction to mathematics as a science.
3 people found this helpful
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george mchugh
5.0 out of 5 stars Highly recommended for a novice like myself
Reviewed in the United States on August 5, 2014
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Highly recommended for a novice like myself. Gives the reader much needed perspective in the history of ideas in an unthreatening and engaging way. Great read.
2 people found this helpful
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TRIP
5.0 out of 5 stars Love his writing style and presentation
Reviewed in the United States on February 14, 2017
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If you are a Morris Kline fan, this is a must have. Love his writing style and presentation.
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John P. Jones III
5.0 out of 5 stars More than a sack of bones...
Reviewed in the United States on July 5, 2013
Professor Morris Kline wrote this book in 1953. He started out strong, from the first page of his preface, and kept going from there: "...educated people almost universally reject mathematics as an intellectual interest. This attitude toward the subject is, in a sense, justified. School course and books have presented `mathematics' as a series of apparently meaningless technical procedures. Such material is as representative of the subject as an account of the name, position, and function of every bone in the human skeleton is representative of the living, thinking, and emotional being called man." (As for the quaint last word, please recall the year it was written.) Kline supports his assertion with a like one, which serves as the book's epigraph, from René Descartes, a portion of which reads: "...the earliest pioneers of Philosophy in bygone ages refused to admit to the study of wisdom anyone who was not versed in Mathematics..."

Kline's work is a tour-de-force of Western scientific achievement, and its impact on the culture and lives of its citizens. Most fundamentally, science requires a solid mathematical basis. He is never heavy-handed in his assertions, but he demonstrates the numerous times that the religious establishment is opposed to the scientific method. The High Priests of Ancient Egypt knew that the solar year was 365 and a quarter days long, but hide this knowledge in order to retain their power over the people by predicting the annual flooding of the Nile. He quotes St. Augustine: "The good Christian should beware of mathematicians and all those who make empty prophecies. The danger already exists that the mathematicians have made a covenant with the devil to darken the spirit and to confine man in the bonds of Hell." And Kline also details the efforts of the Catholic Church against Galileo in order to retain an earth-centered universe, just like the Bible proclaimed.

It really all did start in Greece, with Pythagoras, Euclid, and several others whose mathematical concepts still shape the world in which we live. As the author points out, it was Alexander who was so instrumental in spreading these concepts throughout a large swath of the inhabited world. He moved the center of the world's learning to a town named after himself in Egypt. Upon the burning of the library there, in the 600's, there was an "interlude," as the author puts it, and others have referred to as a "dark age." The light would shine again, numerous centuries later, as Kline says: "The Polish Copernicus, the German Kepler, the Italian Galileo, the French Descartes and the English Newton received light and warmth from the sun of Greece."

As the title suggests, Kline includes several chapters that demonstrate the impact of mathematics in the cultural arenas. There is one devoted to the development of perspective in painting, and the author dedicates three chapters dedicated to Newton's impact on religion, literature and aesthetics, and philosophy. There is also a chapter dedicated to the influence of mathematics on music.

In terms of scientific developments, Kline provides a lucid explanation of the development of calculus, "grasping the fleeting instant" as he say. He highly praises the work of James Clerk Maxwell in developing electromagnetic theory. Maxwell's broad theory specifically predicted radio waves, and Kline emphasizes that it was Maxwell's insistence on EXACT reasoning that was the cause. Rather drolly, he entitles the development of statistics as the "mathematical theory of ignorance." He concludes with three strong chapters on the paradoxes of the infinite, non- Euclidian geometry and the theory of relativity.

Kline does use equations and drawing throughout the book, which should enhance and not detract from the reading experience. None from Maxwell though, which can be a bit difficult. Concerning the role of mathematics, the author concludes with the following: "It is the distillation of highest purity that exact thought has extracted from man's efforts to understand nature, to impart order to the confusion of events occurring in the physical world, to create beauty, and to satisfy the natural proclivity of the healthy brain to exercise itself." An excellent one volume study of the impact of mathematics on western culture. 5-stars, plus.
6 people found this helpful
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gg
1.0 out of 5 stars Kline says on page 9 that math contains no truths ...
Reviewed in the United States on August 28, 2016
Kline says on page 9 that math contains no truths. I guess 2 + 2 is not always 4, and 2 x 2 is not always 4.

I guess next time you take a math test, if your teacher marks a wrong answer, you can say "Well, don't you know that there are no truths in math?"
2 people found this helpful
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Top reviews from other countries

Roger Cockrell
5.0 out of 5 stars See my review below
Reviewed in the United Kingdom on September 12, 2022
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This is a brilliantly written book, which helps me to understand many mathematical topics that hitherto have been a bit of a blur. Highly recommended.
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MathEnthusiast
5.0 out of 5 stars Satisfied costumer
Reviewed in Canada on September 11, 2016
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Excellent service and a very nice and clean copy of the book.
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Star
5.0 out of 5 stars Five Stars
Reviewed in the United Kingdom on March 13, 2015
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A lot of information
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M. F. Cayley
4.0 out of 5 stars A good overview, comprehensible to the non-mathematician
Reviewed in the United Kingdom on July 11, 2010
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This is a well-written overview of the role of maths in western culture. It is comprehensible to the layman - no deep mathematical knowledge is required. My only criticism is that I would have preferred greater recognition of the extent to which western maths has drawn on developments made by other cultures, particularly in India and the Middle East.
2 people found this helpful
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