Mathematics: From the Birth of Numbers by Jan Gullberg (PDF)

Description

A gently guided, profusely illustrated Grand Tour of the world of mathematics. 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. Over 1000 technical illustrations and cartoons and drawings

User’s Reviews

Editorial Reviews: Amazon.com Review What does mathematics mean? Is it numbers or arithmetic, proofs or equations? Jan Gullberg starts his massive historical overview with some insight into why human beings find it necessary to “reckon,” or count, and what math means to us. From there to the last chapter, on differential equations, is a very long, but surprisingly engrossing journey. Mathematics covers how symbolic logic fits into cultures around the world, and gives fascinating biographical tidbits on mathematicians from Archimedes to Wiles. It’s a big book, copiously illustrated with goofy little line drawings and cartoon reprints. But the real appeal (at least for math buffs) lies in the scads of problems–with solutions–illustrating the concepts. It really invites readers to sit down with a cup of tea, pencil and paper, and (ahem) a calculator and start solving. Remember the first time you “got it” in math class? With Mathematics you can recapture that bliss, and maybe learn something new, too. Everyone from schoolkids to professors (and maybe even die-hard mathphobes) can find something useful, informative, or entertaining here. –Therese Littleton From Scientific American The book is an enthusiastic and utterly amazing popularization that promises to be in print for decades…. It is an important reference and a book that is plain fun to dip into. If a family is to have only one mathematics book on the reference shelf, then this is the one. From Booklist A long book on mathematics? No need to brace yourself for tedium. Whether counting on an abacus or solving triple integrals, Gullberg explains his subject with an infectious zeal–and an unpredictable sense of humor. The basic formulas are all here, making this an ideal reference for readers who cannot quite remember what they once learned about trigonometric functions or vector algebra. But beware! Those looking for quick help with a problem may find themselves diverted for many hours by the wealth of historical anecdotes, literary quotations, artwork, light verse, and even cartoons sprinkled liberally through the pages. Perhaps because he is himself a well-practiced amateur in the field rather than a professional, Gullberg anticipates perfectly the perplexities of the average reader. Simplified derivations and numerous examples will clear up most of the hard points. But the point Gullberg makes clearest of all is that mathematics can be very exciting and thoroughly enjoyable. Bryce Christensen Review An enthusiastic and utterly amazing popularization….If a family is to have only one mathematics book on the reference shelf, then this is the one. — Scientific American From the Back Cover This gently guided, profusely illustrated Grand Tour of the world mathematics takes the reader on a long and fascinating journey – from the dual invention of numbers and language, through the primary realms of arithmetic, algebra, geometry, trigonometry, and calculus, to the final destination of differential equations, with excursions into symbolic logic, set theory, topology, fractals, probability, and assorted other mathematical byways. Mathematics: From the Birth of Numbers 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, and those with a sincere desire for more knowledge”, it links mathematics to the humanities, linguistics, the natural sciences, and technology. About the Author Jan Gullberg (1936―1998) was a practicing general surgeon. A native of Sweden, he was well known there for his writings on various scientific and medical topics.Peter Hilton was a British mathematician, noted for his contributions to homotopy theory and for code-breaking during the Second World War. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐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.

⭐This book is a wonderful supplement to the standard high school curriculum, beginning with algebra and extending through Euclidean geometry, analytic geometry, to differential and integral calculus, and including brief introductions to other “back of the book” topics like probability, determinants, and so on. It is full of hard-to-find details left behind by most texts, such as explicit solutions to third- and fourth- degree polynomials in one variable. It’s fun to browse this book in search of such tidbits to fill in your mathematical knowledge.”Mathematics…” is written at a level just right for someone who has progressed as far as calculus or college engineering math but no further. It is also nice that the myriad (albeit brief) historical references help connect the material with its initial development. Unfortunately, the lack of any contextual information (brief biographies would be welcome) make these references rather dry and unrevealing: authors, dates, and titles of publications is frequently all we get.I have to agree, too, with the Willingboro reviewer: although this text covers a wide variety of traditional high school and early college topics, at the same time it clearly exhausts its author’s knowledge of the subject and therefore cannot provide a foundation for proceeding further. It is akin to a travelogue that directs the reader along completed, well-worn paths, visiting all the conventional landmarks, without pointing out the existence of other paths, other points of interest, or taking the readers to lookout points and vistas suggesting territory remaining to be explored.Almost all the topics covered are ancient, rarely extending beyond what was known by the middle of the 19th century. (A chapter on fractals is the only exception.) Many important and modern subjects are barely mentioned and certainly not developed beyond the limited introduction available in most high school texts: graph theory, number theory, complex analysis, algebraic geometry, functional analysis, group theory, Galois theory, differential geometry, category theory, …, the list can go on and on. (For example, topology–a vast subject–gets less than three pages, whereas eight pages are devoted to illustrating the routine mechanics of solving euclidean triangles using trigonometry.) This is a shame, because the wealth of topics nevertheless discussed by this book provides an amazing foundation for introducing these modern ideas and pointing out their deeper implications and ramifications. As a result, mathematics comes out looking like a kind of beautiful fossil rather than an organic, evolving creature.

⭐This book is amazing for three reasons. First, it was not written by a mathematician yet it is a great, and in many places detailed, mathematics book. Second, it tackles very diverse topics. Third, it has really funny cartoons. You can read this book from cover to cover like I did, or pick out random chapters. There are chapters on logic, calculus, trigonometry, set theory, topology, geometry, number systems, fractals, complex numbers, and so much more. However, you must be warned that this is not a textbook. In many cases the author does not explain how he got a certain result. Instead. he just writes it down. Don’t pick up this book and complain that the chapter on integrals does not explain why certain methods are used. This is not the main idea behind the book. I think that as a reference this book is great. You can easily find whatever it is you are looking for and the material is presented with some humour.It has been said that if you are to own one math book, then this should be it. I think that this is true but not for all people. If you should own one reference book about material which is not very advanced, then yes, this is the book. However, if you want a book ABOUT math, then I think ‘The World of Mathematics’ by Newman is the one you should own. Personally, if I were to own just one math book it would definitely be Hardy’s ‘A course of pure mathematics’. But why own just one math book? Buy all of them!

⭐This is a truly outstanding work. Almost everything you can think of to do with maths, from the very beginning of counting and representing numbers, through equations, functions, geometry, calculus, limits, complex numbers; mathematicians, dates, history.. it’s all in here. It’s heavy duty, but with lots of examples, and a considerable amount of insight.

⭐The fact that Jan Gullberg is not a professional mathematician is precisely what makes this book so good.He demonstrates a rare depth of knowledge and understanding, yet at the same time, because his mind has not been “tram-lined” by the traditional approach to teaching mathematics, he is able to write in a light-hearted way using jokes and cartoons that looses nothing in terms of clarity of content. This stands in stark contrast to normal mathematical text books that present their topics in dry, sterile and frankly boring abstractions.His creative approach to explanation makes mathematics fun again because now he takes the reader on a voyage of discovery. Consequently, if you buy this book expecting the normal “text book approach” to delivery, you will be disappointed. But speaking for myself, it is precisely the traditional text book approach to mathematics that put me off in the first place. At school, I gave up on mathematics because the subject matter had been so highly abstracted away from every day life, that I was unable to place what I’d learnt into any category I could call “reality”. Upon leaving the classroom, I promptly forgot most of what I’d learnt.Fortunately, Mr Gullberg has changed all this.Well done, Sir!

⭐This is really well laid out. The history of numbers and maths and how we interpreted them across cultures and era’s. There’s so much information to read through, it’s nice to have on my shelf and im glad i have it now. I’d say its a bit like an encyclopedia but in a more fluid style of writing. There is a lot of info in here and you’ll probably enjoy havingvit too

⭐I don’t know anything about maths but my son is in his first year of Uni studying maths/ physics . I read the reviews on lots of the maths books and went for this one. I was so pleased when my son rang me up to tell me what a brilliant book it was. He said it covered all the maths he was doing at Uni and was interesting to read ( he has found lots of the course book dull)I can’t be precise about any of the maths content in this book but my son gives it top marks and I give myself top marks for being good at shopping ( no marks for maths though)

⭐A modern classic, now about 20 years old.Very helpful from high school thru early college – or for anyone with an interest in history of math, or how to actually solve various kinds of problem! Fun and informative, and very clearly written.

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