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Number: The Language of Science Paperback – January 30, 2007
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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."
"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."
"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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Top Customer Reviews
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.Read more ›
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.
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.
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.
Most Recent Customer Reviews
Who could have thought a college text would be so interesting? This book provided hours of entertainment as I was studying, not to mention the paper and binding id also amazing. Read morePublished 1 month ago by James L.
This is a classic, and highly recommended to anyone who considers themselves a "math geek"Published 8 months ago by Mark
Finally got a chance to read this classic book. Not impressed. I was hoping for a chronological history of mathematics, but what I got was a dispersive, hard-to-follow, account of... Read morePublished 15 months ago by Mike Jahan
Good book. A little hard to read. I didn't realize that this is a really old book with a new cover. The forward is by Einstein. Read morePublished 19 months ago by Helen Carlile
This book is every bit as good, entertaining and satisfying as Einstein said it was. It is packed with information and insights. Top tier book in every way.Published 20 months ago by Bill Clack