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Number: The Language of Science

4.10  ·  Rating details ·  470 ratings  ·  43 reviews
Number is an eloquent, accessible tour de force that reveals how the concept of number evolved from prehistoric times through the twentieth century. Tobias Dantzig shows that the development of math—from the invention of counting to the discovery of infinity—is a profoundly human story that progressed by “trying and erring, by groping and stumbling.” He shows how commerce, ...more
Paperback, 416 pages
Published January 30th 2007 by Plume (first published 1930)
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4.10  · 
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 ·  470 ratings  ·  43 reviews

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Jul 16, 2018 rated it it was amazing
Literate Mathematics

A classic in every sense: a model of style and erudition to rank with Oscar Wilde, as inspiring as Zadie Smith, as concise as a page from George Orwell, and as timeless as any of Dickens’s tales. If you have an interest in mathematics, or if you have been scarred by the imposition of tedious calculating techniques in your school days, or if you simply want to understand an enormous part of intellectual history, this is the single most important book you could have at hand.

Jul 24, 2019 rated it it was amazing
Shelves: nonfiction
This book may be old, but its a classic. The book was written in the 30s, author made his last edits in the 50s and my edition is from the 90s. This might tell you that the book is still quite relevant and a landmark for the history of the number from the humble integer to the mind boggling infinities and with it a short history of mathematics, phylosophy and science. If you are researching these topics this is where you start.

Considering that this book mostly deals with the history of the conce
Mar 25, 2010 rated it really liked it
On the cover is an interesting mini-review: "This is beyond doubt the most interesting book on the evolution of mathematics which has ever fallen into my hands." -- Albert Einstein.

With an endorsement like that, what more needs to be said? Indeed, this is a very interesting and very informative book, scarcely dimmed by the passage of years -- it was first published in 1930! In the interim, much has changed; one amusing example is the following statement on page 121: "Today [1930:] over 700 corre
Jun 24, 2016 rated it liked it
The anthropological survey about number systems in the first few chapters was pretty interesting, but the dryness of the writing really came into the forefront when the later chapters turned to increasingly technical mathematics. While I appreciate the rigor, it ended up feeling like I was reading a math textbook, which is not my jam right now.
Nov 10, 2011 rated it really liked it
Loved this (near) closing line - The reality of today was but an illusion yesterday.
Dennis Littrell
Apr 07, 2018 rated it it was amazing
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 a
Apr 15, 2009 rated it it was amazing
Shelves: philosophy-read
This is another one I pick up a lot. There is some really dense math that is really outside my understanding, but also some incredibly lucid analysis of the development of mathematics and how it has effected the way we perceive and cognate. Tremendous stuff, and humbling!
Sep 01, 2018 rated it it was amazing
The most amazing thing about numbers is they don’t actually exist. It is all our imagination. Mathematics is high art as it creates a whole new world like number system. In this book author changes your perception about numbers. The book goes from the history of creation of numbers in different societies to real, trancedental and complex numbers.
Its a must read for anyone who is atall interested in mathematics.
Jul 03, 2011 rated it it was ok
The first couple of chapters were interesting--about the evolution of counting and the development of language to describe abstract concepts like "how many", but after that, the book got extremely tedious and boring. Not one of my favorites on math.
Stephen Armstrong
Aug 04, 2013 rated it it was amazing
Number theory clearly explained in this classic. Beautifully written. 2007 publication date, original was in 1930. What book on number theory survives 77 years, unless it is extraordinary?
Anthony Tenaglier
Oct 23, 2012 rated it liked it
"Though the source be obscure, still the stream flows on"
Joseph Schrock
Oct 07, 2018 rated it really liked it  ·  review of another edition
This book was quite interesting to me; however, the latter portions were more technical than I could well tackle, given my limited mathematical expertise.

I did not agree with the author's nominalist views on the ultimate nature of mathematics. My views are more "Platonist", given that I am convinced that mathematics has some form of objective existence, and in view of my belief that mathematics is discovered rather than created or invented. Tobias Dantzig believed that logic is a branch of math
Panagiotis Jones
Nov 03, 2018 rated it really liked it
I am not well-versed in the history of mathematics, so my opinion of this book comes from my exclusive experience with it, rather than a comparison with its kind.
It has enough detail to satisfy you, while keeping away from excessiveness. It is brilliantly written and with a touch of philosophy. I have learned a great deal about the history of mathematics, and have come to realize and understand many fundamental ideas--how they came to be, why they came to be, and what they led to. I am glad to a
Munthir Mahir
Apr 15, 2018 rated it did not like it
Have to give it to the author for apparently trying to make the topic accessible to the general reader. It is certainly not written for the serious mathematicians (maybe for the aspiring mathematician). It, also, contains equations in detailed explanation which I find unnecessary. A lot of the discussion, although fits to the subject of number evolution, is dry and involves mathematical proofs. This book is definitely not accessible.
Apr 23, 2018 rated it really liked it
Loved the chapter: The Anatomy of the Infinite.
Maggie Wesolowska
Mar 20, 2018 rated it really liked it
Great book, profound but easy to understand, substantial but light. Mr Dantzig writes:
“Our intuition permits us, by an act of the mind, to sever all time into the two classes, the past and the future, which are mutually exclusive and yet together comprise all of time, eternity.
The now is the partition which separates all the past from all the future; any instant of the past was once a now, any instant of the future will be a now anon, and so any instant may itself act as such a partition.
To be
Brett Bavar
May 31, 2010 rated it really liked it  ·  review of another edition
Shelves: nonfiction
A fascinating account of the history of mathematics, from the innate number sense of humans and other animals to the bewildering abstract concept of infinity.

I love to get glimpses of the way that knowledge and science have developed through the incremental contributions of real individuals. This book gave me a bit of that insight into the development of mathematics. In fact, I think a quote from chapter 10 sums this up quite nicely...

". . . [There is a:] widespread opinion that mathematics has
Greg Talbot
Dec 16, 2013 rated it really liked it

It's a lot to ask of a book to give a portrayal of what it means to be human.Near impossible to find so much reflected humanity in a book on mathematical principles. Tobias Dantzig gives us an elegant history of the discovery of mathematical principles. This discoveries are products of imagination, abstract reasoning, and the outposts
of thought were erected before it's territory was marginally searched.

From finger counting, to abacuses, to expanding the domain of's a slow road. One
Francisco Rodríguez
Oct 01, 2014 rated it liked it
Shelves: mathematics
I was fascinated by the fact that the act of counting and the concept of number is not a self-evident truth inherent in human beings, but something that had to be learnt.

Realizing that a pair of horses and the passage of two days are two different instances of the same concept of the number "two" required thousands of years. Proof of this, given in the book, is that some primitive tribes have different names for the numbers when referring to people, days, objects, places, etc.

The book is full of
Daniel Toker
Jul 13, 2010 rated it really liked it
This was recommended to me by someone of much higher intelligence and more knowledge than I. He called it an "easy" book on the history, philosophy, and central concepts of mathematics. Well, I understood the history easily enough, and the philosophy was at times challenging but I think I understood it. The math, though, was simply beyond me. I think I should revisit this once I've studied set theory....

My mathematical ineptitude aside, I highly recommend this book to anyone interested in the to
Jun 21, 2016 rated it it was amazing
The first two chapters are slow, but after that it speeds up quickly. Tells the history of mathematics (up to set theory) as a story of uncovering/intuiting new types of numbers and the process of proving that these new (and increasingly abstract) entities do follow the central axioms that numbers follow, and can be used as such. It's a history of mathematics that I've never come across before. I thought it was fucking brilliant.
Jan 17, 2015 rated it really liked it
This is a rather old book (originally published in 1930's) and so the language is slightly dated and some of the concepts are explained rather confusingly. But it does give a great explanation of some basic facts about Number theory came to be. The book does not not shy away from Math when appropriate but most of denser math is in the appendices. But overall this is a good read for anyone interested in the history of Math.
Amanda Pearl
Apr 10, 2011 rated it it was amazing
Shelves: in-my-bookcase
An incredibly dense, but thoroughly engaging, look at the history of mathematics. Admittedly, it took me a while to get into the groove of the book but once I did I found it difficult to put down. I'd recommend this for any current, former or aspiring mathematician and number lovers; but the insights into the philosophy and history of numbers and differing branches of mathematics over the ages would be interesting to anyone with a basic high school background in the subject.

Seoul Rationalthinkers
Oct 30, 2011 rated it really liked it
"The evolution of mathematical thought from the earliest times to the latest constructions is presented here with admirable consistency and originality and in a wonderful and lively style." - Albert Einstein

A layman's book that turned around my attitude towards math. (The actual math in it is very minimal and described in such a way that the reader feels smart. All math courses should begin with this...)
May 26, 2007 rated it it was amazing  ·  review of another edition
Recommends it for: Everybody
I found this book in the attic. It's about the history of the concept of numbers in the early civilization, and the development of mathematics. The history is told in an easy to understand and entertaining language. It evokes interest each time I open a new page. How I was really happy when this book was re-released in 2005!
Dan Carey
Jan 02, 2011 rated it it was ok
Interesting though some of the material was, it just didn't hold my interest. (I also hadn't realized when I bought the book that it had originally been written in the 1930s. But when the author referred to the Australian Aborigines as "barbarians", that sentiment seemed so out of place with modern thinking that I checked the copyright information.)
Aug 21, 2008 rated it liked it
This was the last book I read for Smith College--for a math class, actually. It's about the evolution of number and how integral number is to life. Not really up my alley, but fascinating. I ended up writing a paper on how the evolution of number correlates with the evolution of American literature. Pretty snazzy.
Jun 20, 2008 rated it really liked it
Recommends it for: people who like math
Very informative book about number theory. At some points it is a bit technical, which can't be avoided, but if you are literate in advanced mathematics there should be no problem. If you are not, it is still a great read.
Aug 14, 2012 rated it it was amazing
Simply an awesome account. Skipped the first three Appendices, but will revisit soon. Had problem trying to fathom some of the more recent concepts, especially those involving set theories, but will revisit. Overall, excellent read.
May 29, 2013 rated it it was amazing
A number: Like, what's the big deal? Everybody knows what numbers are, right? Actually, maybe not. The concept of "number" is a lot more complicated than that. From this book, I went on to do post grad work in mathematics; I'd like to do much more.
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BOOK ONE: Chapters 9 & 10 1 1 Aug 31, 2019 05:46PM  

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Tobias Dantzig (February 19, 1884 – August 9, 1956) was a mathematician of Baltic German and Russian American heritage, the father of George Dantzig, and the author of Number: The Language of Science (A critical survey written for the cultured non-mathematician) (1930) and Aspects of Science (New York, Macmillan, 1937).
“In the history of culture the discovery of zero will always stand out as one of the greatest single achievements of the human race.” 2 likes
“It is not a story of brilliant achievement, heroic deeds, or noble sacrifice. It is a story of blind stumbling and chance discovery, of groping in the dark and refusing to admit the light. It is a story replete with obscurantism and prejudice, of sound judgement often eclipsed by loyalty to tradition, and of reason long held subservient to custom. In short, it is a human story” 2 likes
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