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Number: The Language of Science Paperback – January 30, 2007

4.5 out of 5 stars 30 customer reviews

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Editorial Reviews

Review

Anyone interested in the history of numbers and mathematics should read this book. (Mario Livio, author of The Golden Ratio)

A classic . . . it deserves a place on the bookshelf of anyone interested in the history of thought. (Charles Seife, author of Zero and Decoding the Universe)

Beyond doubt the most interesting book on the evolution of mathematics which has ever fallen into my hands. (Albert Einstein)

From the Back Cover

"It is the aim of this book to...present the evolution of number as the profoundly human story which it is."

—Tobias Dantzig

"This is beyond doubt the most interesting book on the evolution of mathematics which has ever fallen into my hands. If people know how to treasure the truly good, this book will attain a lasting place in the literature of the world. The evolution of mathematical thought from the earliest times to the latest constructions is presented here with admirable consistency and originality and in a wonderfully lively style."

—Albert Einstein

"Tobias Dantzig's Number: The Language of Science is one of the truly great classics of mathematical exposition, perhaps the most lucid history of the number concept ever written. Its republication should be a cause for celebration by every scientifically minded person, regardless of his or her mathematical background."

—Eli Maor, author of e: The Story of a Number and To Infinity and Beyond

"Tobias Dantzig's Number is a classic. A fascinating account of the evolution of mathematics, it deserves a place on the bookshelf of anyone who is interested in the history of thought."

—Charles Seife, author of Zero and Alpha and Omega

"A classic! Anyone interested in the history of numbers and mathematics should read this book."

—Mario Livio, author of The Golden Ratio

From the rudimentary mathematical abilities of prehistoric man to the counterintuitive and bizarre ideas at the edges of modern math, this masterpiece of science writing tells the story of mathematics through the history of its most central concept: number.

Dantzig succeeds in his aim to reveal a human story, and in making that story accessible to the non-expert. In his friendly and welcoming style, he shows how math developed from basic faculties present in us all, beginning with our "number sense"—the ability to discern that an object has been added to or removed from a small collection of objects without counting. The subsequent evolution of the concept of number is inextricably linked with the history of human culture, as Dantzig demonstrates. He shows how advances in math were spurred by the demands of growing commerce in the ancient world; how the pure speculation of philosophers and religious mystics contributed to our understanding of numbers; how the exchange of ideas between cultures in times of war and imperial conquest fueled advances in knowledge; and, ultimately, how the forces of history combine with human intuition to trigger revolutions in thought.

Sweeping in scope, Number is an open doorway into the world of math. Dantzig explains the foundations of mathematics with ease, and eloquently explores deeper philosophical questions that arise along the way. He describes the properties of all kinds of numbers—integers, primes, irrationals, transcendentals, and more. He explains the significance of zero, and shows that its invention had revolutionary consequences for arithmetic. He shows how the invention of symbols for use in algebra—a radical departure from tradition at the time—ushered in a new era of math; how arithmetic and geometry reflect each other; and how calculus uses infinity to model the continuity of space and time.

With a new afterword, notes section, and bibliography written by math professor and author Joseph Mazur, and a new foreword by mathematician Barry Mazur, the Masterpiece Science edition of Number—which was first published in 1930—is the first update of Dantzig's classic work in over fifty years. It is a story that ranges from the dawn of man to the genius of history's greatest mathematicians, vividly revealing how the pursuit of knowledge transcends the rise and fall of civilizations.


© Copyright Pearson Education. All rights reserved.

--This text refers to an out of print or unavailable edition of this title.
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Product Details

  • Paperback: 416 pages
  • Publisher: Plume (January 30, 2007)
  • Language: English
  • ISBN-10: 0452288118
  • ISBN-13: 978-0452288119
  • Product Dimensions: 5.3 x 0.8 x 8 inches
  • Shipping Weight: 6.4 ounces (View shipping rates and policies)
  • Average Customer Review: 4.5 out of 5 stars  See all reviews (30 customer reviews)
  • Amazon Best Sellers Rank: #72,513 in Books (See Top 100 in Books)

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Customer Reviews

Top Customer Reviews

Format: Paperback
This is a book hardly read in our times of "modern math" (we are living in a museum of great innovations!) and that shows the theory of numbers as a human activity, stressing the fundamental role of the intuition in the construction of the mathematics. It seems to me that the gradual forgetfulness of this kind of book is one of the important causes for the continuous decline in the number of interested (and interesting!) people in the field of mathematics. I recommend this reading. You'll find a lot of fun!
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Format: Hardcover
Einstein called this "the most interesting book on the evolution of mathematics which has ever fallen into my hands."

Number was first published in 1930 with the fourth edition coming out in 1954. This is a republication of that fourth edition (Dantzig died in 1956) edited by Joseph Mazur with a foreword by Barry Mazur. It is an eminently readable book like something from the pages of that fascinating four-volume work The World of Mathematics (1956) edited by James R. Newman in that it is aimed at mathematicians and the educated lay public alike.

Part history, part mathematics and part philosophy, Number is the story of how we humans got from "one, two...many" to various levels of infinity. Strange to say it is also about reality. Here is Dantzig's concluding statement from page 341 in Appendix D: "...modern science differs from its classical predecessor: it has recognized the anthropomorphic origin and nature of human knowledge. Be it determinism or rationality, empiricism or the mathematical method, it has recognized that man is the measure of all things, and that there is no other measure."

Or more pointedly from a couple of pages earlier: "Man's confident belief in the absolute validity of the two methods [mathematics and experiment] has been found to be of an anthropomorphic origin; both have been found to rest on articles of faith."

These are inescapably the statements of a postmodernist.
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Format: Hardcover
The striking facts about Danzig's book are :

1. It does not claim to be a 'popular' science book. At the outset, he warns the reader ".. it is not written for those who are afflicted with an incurable horror of the symbol". In doing so, I think he has gained more readership, simply because noone likes to be patronised, and most 'popular' science books are extremely patronising.

2. He makes it a point to explain to the reader that mathematics is not something that was made by the Hand of God. He clearly explains the mistakes made by some of the most eminent mathematicians, and thus brings out the 'human' element in the evolution of mathematics very beautifully.

3. He interweaves his philosophy with that of the history of math, and thus makes it eminently readable.
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Format: Paperback
This is a reprint of the author's 1954 fourth edition sandwiched between a new Foreword and Afterword. Neither the editor (Joseph Mazur) nor his brother (Barry Mazur, who wrote the Foreword) nor either of the advertised reviewers (Mario Livio or Charles Seife) apparently actually proofread the text as there are a distressing number of readily apparent typographic errors in the printing, both in the text and figures.
For a volume trumpeted on its title page as "The MASTERPIECE SCIENCE Edition" the many errors belie that mantle. In addition, the Afterword, which attempts to bring the reader up to date on relevant mathematical developments that occured after the fourth edition, fails to mention "undecidability" and the immense impact it has had on the issues discussed in the chapter entitled "The Anatomy of the Infinite."

Dantzig's Number continues to be accessible and generally insightful, but it is a shame that no one at Plume Books took due care and responsibility for its production.
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Format: Paperback
I am a mathematics teacher and have used this book as either a required reading or suggested supplement for a variety of courses, including math history for liberal arts students, number theory for mathematics majors, etc.

The book (4th edition) is divided into Part I and Part II -- the latter comprising only the last 4th of the book. Any successful college student will find Part I informative, and at times wonderfully enlightening about the development of the concepts of number and measurement. This book was written for the armchair reader, so expect a reader-friendly style of writing. However, I have found that Part II can be quite challenging for liberal arts students -- and quite stimulating to those whose studies included a more rigorous tour of mathematics. Do not let this bother you! I think Part I is worth the price of the book on its own.

If you wish to learn more about the history of mathematics and mathematicians, you might wish to examine Notable Mathematicians: From Ancient Times to the Present edited by Robyn V. Young and Zoran Minderovic.
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