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Mathematics From The Birth Of Numbers
This extraordinary work takes the reader on a long and fascinating journey--from the dual invention of numbers and language, through the major realms of arithmetic, algebra, geometry, trigonometry, and calculus, to the final destination of differential equations, with excursions into mathematical logic, set theory, topology, fractals, probability, and assorted other mathematical byways. The book is unique among popular books on mathematics in combining an engaging, easy-to-read history of the subject with a comprehensive mathematical survey text. Intended, in the author's words, "for the benefit of those who never studied the subject, those who think they have forgotten what they once learned, or those with a sincere desire for more knowledge," it links mathematics to the humanities, linguistics, the natural sciences, and technology.
Contains more than 1000 original technical illustrations, a multitude of reproductions from mathematical classics and other relevant works, and a generous sprinkling of humorous asides, ranging from limericks and tall stories to cartoons and decorative drawings.
Contains more than 1000 original technical illustrations, a multitude of reproductions from mathematical classics and other relevant works, and a generous sprinkling of humorous asides, ranging from limericks and tall stories to cartoons and decorative drawings.
1093 pages, Hardcover
First published January 1, 1997
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Displaying 1 - 29 of 29 reviews
June 24, 2021
Numeration
There is infinite beauty in mathematics and numbers!
Infinity in mathematics is catered for through recurring patterns and concepts, consider Pi and how it extends to infinite decimal places. When I say beauty, I think about how numbers can translate to graphical interpretation with multiple dimensions, each with unique relationships and transformations. Picture the very precise yet artistic language of symbols and formatting, especially the Greek alphabet and its evolution from the Phoenician alphabet.
I love traditional poetry where we marvel at the efficient and skilful formation of words to enchant our minds with glorious images. In terms of the ability to transform simple notation and symbols into multi-dimensional fractious patterns and images, mathematics is the ultimate poetic language.
Mathematics has a raw, honest and perfect beauty. Witness the power of the simple symbol =, which conveys balance, equilibrium and pure logic. How we strive for balance in our lives. The world exists with the reassurance and satisfaction that logic will prevail. There is a tendency to assume because mathematics is challenging and heavily utilised in science and technology, that we forget its impact on other aspects of nature, culture and history. Galileo Galilei stated, “Mathematics is the language with which God has written the universe.”
The book Mathematics from the Birth of Numbers, by Jan Gullberg, is a fascinating book that offers a different and informative look at mathematics. We have become fixated with learning how to deliver the usefulness that we no longer try to appreciate the true understanding and beauty. Jan Gullberg enables us to discover the cultural birth and evolution of numbering systems, and the almost mystical and mythical association with numbers such as seven as in the 7 arms of the Hebrew candelabra, the 7 wonders of the world, the 10 commandments, abstention for 40 days and nights during Lent, the 40 years the children of Israel wandered the desert, and Ali Baba and the 40 thieves. Numbers have a habit of repeating and appearing in very different circumstances.
This book covers notation and numbering systems from our ancient past. It reviews numeration from ancient languages dating back thousands of years BC to the most utilised numbering system in the world today – binary - as in computer code. The contents cover the history, background, definition and functionality for all mathematics from algebra to trigonometry, geometry, matrices, calculus, sequences & series, probability and statistics. It is not a how-to book for mathematical formula and methods, it is an evocative story of the birth, growth and maturity of numbers and mathematical techniques.
This is a history book dealing with the origins of numbers and mathematics. This is a mathematics book steeped in a wealth of history. A book that you will want to dip in and out of on a regular basis, it's probably not one you will read from cover to cover but it is a beautiful compendium of information and knowledge.
I would highly recommend this book, especially to those that love logic, history and mathematics.
There is infinite beauty in mathematics and numbers!
Infinity in mathematics is catered for through recurring patterns and concepts, consider Pi and how it extends to infinite decimal places. When I say beauty, I think about how numbers can translate to graphical interpretation with multiple dimensions, each with unique relationships and transformations. Picture the very precise yet artistic language of symbols and formatting, especially the Greek alphabet and its evolution from the Phoenician alphabet.
I love traditional poetry where we marvel at the efficient and skilful formation of words to enchant our minds with glorious images. In terms of the ability to transform simple notation and symbols into multi-dimensional fractious patterns and images, mathematics is the ultimate poetic language.
Mathematics has a raw, honest and perfect beauty. Witness the power of the simple symbol =, which conveys balance, equilibrium and pure logic. How we strive for balance in our lives. The world exists with the reassurance and satisfaction that logic will prevail. There is a tendency to assume because mathematics is challenging and heavily utilised in science and technology, that we forget its impact on other aspects of nature, culture and history. Galileo Galilei stated, “Mathematics is the language with which God has written the universe.”
The book Mathematics from the Birth of Numbers, by Jan Gullberg, is a fascinating book that offers a different and informative look at mathematics. We have become fixated with learning how to deliver the usefulness that we no longer try to appreciate the true understanding and beauty. Jan Gullberg enables us to discover the cultural birth and evolution of numbering systems, and the almost mystical and mythical association with numbers such as seven as in the 7 arms of the Hebrew candelabra, the 7 wonders of the world, the 10 commandments, abstention for 40 days and nights during Lent, the 40 years the children of Israel wandered the desert, and Ali Baba and the 40 thieves. Numbers have a habit of repeating and appearing in very different circumstances.
This book covers notation and numbering systems from our ancient past. It reviews numeration from ancient languages dating back thousands of years BC to the most utilised numbering system in the world today – binary - as in computer code. The contents cover the history, background, definition and functionality for all mathematics from algebra to trigonometry, geometry, matrices, calculus, sequences & series, probability and statistics. It is not a how-to book for mathematical formula and methods, it is an evocative story of the birth, growth and maturity of numbers and mathematical techniques.
This is a history book dealing with the origins of numbers and mathematics. This is a mathematics book steeped in a wealth of history. A book that you will want to dip in and out of on a regular basis, it's probably not one you will read from cover to cover but it is a beautiful compendium of information and knowledge.
I would highly recommend this book, especially to those that love logic, history and mathematics.
March 6, 2015
Not the book I was expecting. I assumed this would be a history of mathematics from the birth of numbers, organized chronologically and showing how concepts built over time worldwide. Instead it was organized by subject/field. This approach has its own virtues, as you have to know about algebra and geometry before moving on to integral calculus, for example, but it has the disadvantage of not showing how several branches of mathematics were developed at the same time then became integrated. I also don't feel it was always executed well. The book was at its best for the first 100-200 pages, which showed how mathematics developed simultaneously with language, explaining what a number is and the different types of numbers, how different cultures chose different bases and writing systems and what their advantages were, and expanding on the cornerstones of mathematics, all with interesting cartoons and illustrations. After the first 200 pages the book became more tedious. I became really frustrated by the 350 page point at the chapter about trigonometry, which rattled off a bunch of half-angle formulas and identities without exploring deeper into the why and engendering a greater appreciation of the subject. Most of the book was similarly frustrating. I ended up reading the more interesting chapters that explained why the subject was interesting such as the chapters on topology, fractals, motion, and probability, but I skimmed through the rest of the chapters except for the history sections. Speaking of the history sections, all of them were disappointingly short, some at only 1-3 pages, which doesn't make sense in a book about mathematics over a thousand pages long. I was really interested to read how and why different fields were developed in more depth. All this being said, the book is incredibly useful as an encyclopedia or reference material, as it concentrates so many formulas and strategies from so many branches into one book, but as a book about the history of mathematics it's disappointing.
November 28, 2007
This is how math should be taught. A top down approach as opposed to rote, with a lot of interesting history and random information to keep it interesting.. it's "why is this interesting / worthwhile and how does it fit in" vs "memorize this or fail."
If you've ever wanted to get further into the math world for its own sake but find it difficult to get going, this is a great place to start.
If you've ever wanted to get further into the math world for its own sake but find it difficult to get going, this is a great place to start.
January 7, 2008
It took me the better part of a year to read Mathematics: From the Birth of Numbers, and at times I found it rather challenging. I suspect that I have greater than average interest in mathematics, and I did manage to make it at least through college calculus, but that didn’t always help me much. Part of my problem may have been that, for every concept, Gullberg presents the most general and abstract case, so even things I thought I understood were confusing. I started out with a pencil and paper to work out every proof and every example, but I gave it up well before page 200 (out of 1,040). Many people will find this book highly valuable, but it is not for the mathematical tourist.
June 14, 2019
This is truly an ambitious book. To discuss "Mathematics From the Birth of Numbers" in a single volume when entire textbooks--entire libraries, even--have been devoted to topics covered in but one chapter of this book seems like an impossible challenge. To some extent it is, and to some extent, the author succeeded admirably. It depends on what one means by the discussion of mathematics. This book spans many of those different endeavors.
First, it is partly a history of mathematics. Beginning with the first chapter, the author discusses the origin of numbers themselves (albeit briefly) and guides the reader through an increasingly well-developed mathematical landscape culminating with a treatment of differential equations. Is it a complete history? Not at all. It is developed well enough to give the reader a taste of how mathematics occurred throughout the past centuries, but it would not serve as a primary text for a course in the history of mathematics. What it lacks in depth, however--as I'll say repeatedly--it makes up for in breadth. Few textbooks on the history of mathematics could cover as many subjects as are handled by this book, making it a perfect supplementary text.
Second, it is partly a course in mathematics. Again, the breadth requires a certain lack of depth. Ostensibly the reader without much mathematical experience *could* learn mathematics from this book. However, the development of ideas is more rapid than most students would be able to keep up with. Readers wishing to actually learn mathematics would be better served buying several textbooks: one or two each on their topics of interest. However, it again makes a wonderful supplementary text because it collects the bare bones of all of those sub-disciplines between the same two covers. Additionally, it provides the beginning student of mathematics with a truly marvelous and extensive survey of the field. The student who doesn't know whether s/he wants to read a book next on probability theory, combinatorics, or differential equations would be extraordinarily well-served by this book's tantalizing overviews.
Third, it is a remarkable reference. Once more, while such a broad book cannot be encyclopedic on any one topic, it does make for a good book to keep on hand whenever one needs to refresh one's memory of the basics of any number of mathematical topics. Because it's both a course and a history, furthermore, I found it contained some information that most other books on mathematics omit. When I (yes, even in the twenty-first century) wanted to learn how to perform more advanced operations than mere counting on my abacus, this book was my first reference. Similarly, students who grew up in the age of computers might be interested, if for no other reason than historical curiosity, to read the section explaining the correct operation of a slide rule. Regarding the use of this book as a reference, the reader should be aware that, while the vast majority of the notation is fairly standard, I did notice a few instances in which the author uses different notation from that to which I'm accustomed from my own mathematical education.
Mostly, we can consider this book a single portrait of what one might consider to be elementary (meaning high-school and early undergraduate) mathematics. No, it doesn't contain as many proofs as I would like and no, it doesn't have the exercises that would make it a more effective (if twice as long) pedagogical tool. But it is still a remarkable book because it manages to collect all of that content into a *single* portrait. In so doing, the author helps the reader to observe the connections between the various disciplines of mathematics and for that reason, this book deserves our attention and respect.
The reader with absolutely no mathematical experience will probably find this to be a difficult read, but if you have even a little bit of background in mathematics, I think you will (as I did) find it to be a delightful and entertaining book well worth keeping in your personal or professional library.
First, it is partly a history of mathematics. Beginning with the first chapter, the author discusses the origin of numbers themselves (albeit briefly) and guides the reader through an increasingly well-developed mathematical landscape culminating with a treatment of differential equations. Is it a complete history? Not at all. It is developed well enough to give the reader a taste of how mathematics occurred throughout the past centuries, but it would not serve as a primary text for a course in the history of mathematics. What it lacks in depth, however--as I'll say repeatedly--it makes up for in breadth. Few textbooks on the history of mathematics could cover as many subjects as are handled by this book, making it a perfect supplementary text.
Second, it is partly a course in mathematics. Again, the breadth requires a certain lack of depth. Ostensibly the reader without much mathematical experience *could* learn mathematics from this book. However, the development of ideas is more rapid than most students would be able to keep up with. Readers wishing to actually learn mathematics would be better served buying several textbooks: one or two each on their topics of interest. However, it again makes a wonderful supplementary text because it collects the bare bones of all of those sub-disciplines between the same two covers. Additionally, it provides the beginning student of mathematics with a truly marvelous and extensive survey of the field. The student who doesn't know whether s/he wants to read a book next on probability theory, combinatorics, or differential equations would be extraordinarily well-served by this book's tantalizing overviews.
Third, it is a remarkable reference. Once more, while such a broad book cannot be encyclopedic on any one topic, it does make for a good book to keep on hand whenever one needs to refresh one's memory of the basics of any number of mathematical topics. Because it's both a course and a history, furthermore, I found it contained some information that most other books on mathematics omit. When I (yes, even in the twenty-first century) wanted to learn how to perform more advanced operations than mere counting on my abacus, this book was my first reference. Similarly, students who grew up in the age of computers might be interested, if for no other reason than historical curiosity, to read the section explaining the correct operation of a slide rule. Regarding the use of this book as a reference, the reader should be aware that, while the vast majority of the notation is fairly standard, I did notice a few instances in which the author uses different notation from that to which I'm accustomed from my own mathematical education.
Mostly, we can consider this book a single portrait of what one might consider to be elementary (meaning high-school and early undergraduate) mathematics. No, it doesn't contain as many proofs as I would like and no, it doesn't have the exercises that would make it a more effective (if twice as long) pedagogical tool. But it is still a remarkable book because it manages to collect all of that content into a *single* portrait. In so doing, the author helps the reader to observe the connections between the various disciplines of mathematics and for that reason, this book deserves our attention and respect.
The reader with absolutely no mathematical experience will probably find this to be a difficult read, but if you have even a little bit of background in mathematics, I think you will (as I did) find it to be a delightful and entertaining book well worth keeping in your personal or professional library.
December 6, 2010
One would never completely finish such a volume; rather, (s)he would peruse the pages carefully and quietly, with a pencil in the hand, getting lost in the glimpse of the huge discipline of mathematics that the author has so generously bestowed.
It is also quite amazing that the author's occupation was a practitioner of surgery.
It is also quite amazing that the author's occupation was a practitioner of surgery.
February 19, 2012
I bought this on a whim at Bookbuyers in Mountain View and only read a few parts of it. I'm marking it as read since I gave it to my daughter's math teacher to help her class with their projects on math in ancient civilizations.
This is a very quirky and personal book on math written by a doctor (I think) who has always been interested in mathematics. It's part history, part reference, part cartoons.
Every time I cracked the book open, there was something interesting, whether it was the history of estimates of pi or a primer on Taylor expansions and trigonometric functions.
The layout reminds me of early LaTeX-formatted handouts I used to get in college with all the equations and that strange Bookman kind of font. I wouldn't be surprised if this book is self-published, which in no way detracts from its awesomeness.
This is a very quirky and personal book on math written by a doctor (I think) who has always been interested in mathematics. It's part history, part reference, part cartoons.
Every time I cracked the book open, there was something interesting, whether it was the history of estimates of pi or a primer on Taylor expansions and trigonometric functions.
The layout reminds me of early LaTeX-formatted handouts I used to get in college with all the equations and that strange Bookman kind of font. I wouldn't be surprised if this book is self-published, which in no way detracts from its awesomeness.
May 20, 2018
I enjoyed it however, I think that I would prefer something that prioritizes conceptual progression a bit more over temporal progression. Understanding the latter is extremely useful but, right now I'm seeking the former.
March 28, 2008
A compendium of mathematical ideas, stories and history. A great book for those interested in recreational mathematics, basic facts about a wide range of concepts in math or inveterate browsers.
January 8, 2018
Some interesting historical information and math categories. Perhaps useful as a reference work.
August 18, 2019
Disarming, unpretentious, funny, deep.
December 10, 2018
I'm giving the book 4 stars because it was so comprehensive and well written. However, bear in mind that I am not proficient in mathematics at all; as a result most of the book was beyond me. Nonetheless I plowed through a few pages each day gleaning what I could. The first half of the book was understandable to me and I enjoyed not only the math but the history too.
February 1, 2019
This book was awesome! Though I admit some (ok, a lot) ended up being over my head, and I did skim a lot, I still learned a lot. The material was presented in an interesting and logical way, and was in no way dry!
May 22, 2022
Probably one of the best books on Mathematics.
November 1, 2014
Excellent tome on general mathematics from counting all the way to differential equations. Contains examples galore. If you aren't satisfied after all of this, it contains an extensive bibliography for further reading. The book also contains an index to help find things in the text.
Along with the mathematics, it covers some history of the particular subject being done, with the important people who brought forth the developments necessary and the important works that they were covered in.
For instance, in the section on Trigonometry it explains that the word Trigonometry is not actually a native Greek word and that the term was invented by a German mathematician and astronomer named Bartholomaeus Pitiscus back in 1595. It goes on to cover important developments, how they used it and relevant problems. This book is a wonderful addition to a library if you can afford it. Though it is more of a reference guide really, it does contain a good deal of history.
Along with the mathematics, it covers some history of the particular subject being done, with the important people who brought forth the developments necessary and the important works that they were covered in.
For instance, in the section on Trigonometry it explains that the word Trigonometry is not actually a native Greek word and that the term was invented by a German mathematician and astronomer named Bartholomaeus Pitiscus back in 1595. It goes on to cover important developments, how they used it and relevant problems. This book is a wonderful addition to a library if you can afford it. Though it is more of a reference guide really, it does contain a good deal of history.
May 5, 2014
I forget where I learned of this book but I thought it would be interesting and probably challenging to see how much of my math I remembered. I didn't find the history portion of the book to be of much interest but the explanation of each concept was thorough and well explained. As I searched and read certain topics I realized I have forgotten much. As I struggled to remember things I received an email from the Kahn Academy with some refresher problems for the SAT test. I could complete those so my mathematical mind is some place beyond high school but not through college. Not only would people with an interest in math enjoy this book but probably those interested in history would find some portions enlightening.
September 19, 2020
This is a "Moby dick" book, but worth seeking, both as reference and as passtime: like the labyrinth which opens the text, this book invites contemplative engagement. It proceeds by steps, and Gullberg establishes the historical development of concepts and tools as they combine to assemble the intimidating landscape which is "Mathematics." Gullberg includes witty asides and cartoons, and has a deep fondness for the material which is obvious. This book is a path--not a royal road! A treasure beyond price. It is also quite rigorous; be prepared to cogitate and computate
The only better guide to math I am aware of is the Princeton Companion. It is more comprehensive, but less quirky and personal.
The only better guide to math I am aware of is the Princeton Companion. It is more comprehensive, but less quirky and personal.
January 7, 2016
Bought an almost brand new copy of this book spontenously in early 2014 and then forgot about it(probably because the cover looked nice).Only rediscovered it again a few days ago whilst tidying up my book collection and the joy!!
This is a rich source of mathematical history and formulas for both maths and non maths enthusiasts alike.
Based on other reviews I would have to agree it serves very well as a good reference point as it can take time to digest some of the contents.
Highly recommended!
This is a rich source of mathematical history and formulas for both maths and non maths enthusiasts alike.
Based on other reviews I would have to agree it serves very well as a good reference point as it can take time to digest some of the contents.
Highly recommended!
February 1, 2009
Looooong. 1000 pages. Didn't get to the end before library wanted it back. Mostly an attempt to explain math (ALL of math) to a layman. Some good things in it, but a little dated, and waaaaay too much. Not much attempt to go beyond the basics, but that's OK.
February 20, 2020
Excellent book on what mathematical areas there are and explains them clearly. Historical perspectives. Arm chair or bathroom reading. Great in soft cover. Good value since out if print. Highly recommend.
Read
September 18, 2012Read bits and parts of this book over a period of a few years. Can't really read it from cover to cover.
January 17, 2011
If you ever want a better relationship with Math, here is the ultimate guide.
October 19, 2012
I've marked this book as read though the truth is that it is an ongoing read which will take years. I think it is a great encyclopedia like book on maths.
July 30, 2012
One of the best references I have found.
June 9, 2013
For someone who loves stories, this is an excellent (and thorough) introduction to mathematics and the stories behind its creation. Reading it re-ignited my interest in math.
July 5, 2017
Difficult, and fast.
September 15, 2014
Great history of how numbers, math and different cultures grew together.
Read
July 31, 2013An awesome resource.
Read
May 27, 2019Mathematics: From the Birth of Numbers
Jan Gullberg
Jan Gullberg expertly provides an immersion into various mathematical topics in her non-fiction novel Mathematics: From the Birth of Numbers. Featuring chapters describing topics from advanced algebra, trigonometry, and analytic geometry to set theory to even single variable and multivariable differential calculus, Gullberg elucidates many mathematical disciplines that some would regard as “difficult” or even “impossible” (which I found myself to be thinking beginning around the chapter on harmonic analysis and Fourier Series).
Having been fortunate enough to have already taken the first year of calculus as a junior, I was able to follow along with most topics of Gullberg’s novel, especially being interested in the history of mathematics itself.
Interested in pursuing mathematics myself, I especially appreciated Gullberg’s section on applications of mathematics to probabilistic and statistical scenarios. Combinatorics is a field in which I was interested before reading the novel. Mathematics: From the Birth of Numbers not only provided me with enough basic information on the section of combinatorial mathematics but also -- most notably through the detailed technical drawings and diagrams within -- assisted me with furthering my interest in the field.
Gullberg’s research novel may not carry the aura of a coveted fiction novel; however, for someone interested in mathematics, I would certainly recommend Gullberg’s work as a foremost introductory novel to various field of mathematical thought.
-- Submitted to Goodreads in partial fulfillment of the final assignment for AP English Language and Composition.
Jan Gullberg
Jan Gullberg expertly provides an immersion into various mathematical topics in her non-fiction novel Mathematics: From the Birth of Numbers. Featuring chapters describing topics from advanced algebra, trigonometry, and analytic geometry to set theory to even single variable and multivariable differential calculus, Gullberg elucidates many mathematical disciplines that some would regard as “difficult” or even “impossible” (which I found myself to be thinking beginning around the chapter on harmonic analysis and Fourier Series).
Having been fortunate enough to have already taken the first year of calculus as a junior, I was able to follow along with most topics of Gullberg’s novel, especially being interested in the history of mathematics itself.
Interested in pursuing mathematics myself, I especially appreciated Gullberg’s section on applications of mathematics to probabilistic and statistical scenarios. Combinatorics is a field in which I was interested before reading the novel. Mathematics: From the Birth of Numbers not only provided me with enough basic information on the section of combinatorial mathematics but also -- most notably through the detailed technical drawings and diagrams within -- assisted me with furthering my interest in the field.
Gullberg’s research novel may not carry the aura of a coveted fiction novel; however, for someone interested in mathematics, I would certainly recommend Gullberg’s work as a foremost introductory novel to various field of mathematical thought.
-- Submitted to Goodreads in partial fulfillment of the final assignment for AP English Language and Composition.
This entire review has been hidden because of spoilers.
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