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Mathematics: A Very Short Introduction

3.86  ·  Rating details ·  1,501 ratings  ·  137 reviews
The aim of this book is to explain, carefully but not technically, the differences between advanced, research-level mathematics, and the sort of mathematics we learn at school. The most fundamental differences are philosophical, and readers of this book will emerge with a clearer understanding of paradoxical-sounding concepts such as infinity, curved space, and imaginary n ...more
Paperback, 160 pages
Published November 28th 2002 by Oxford University Press, USA (first published 2002)
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Average rating 3.86  · 
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 ·  1,501 ratings  ·  137 reviews

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Dec 02, 2015 rated it liked it
As the name suggests the book tries to tell a non-mathematician but interested person, what is Math about, what is it's goals, how mathematicians think and some techniques and results of modern and classical Math.
But for someone who is not very familiar with mathematics, it won't make any sense, for such a person this book can be hard, confusing and boring. Math was never an easy thing to understand.
Actually I think the book can be very enlightening for math undergraduate students, especially fo
Jan 24, 2017 rated it it was amazing
Absolutely great. Let me explain. Firstly about the level of the book. It is elementary but not basic. There are some concepts and especially some proofs that require some focus to grasp. The amount of equations is minimal, but still some maturity is required to fully appreciate the contents. I would say that the best audience of the book is a beginning undergrad in a stem program, a motivated and mature high school students with a keen interest on maths or a layman with some maturity of mathem ...more
Mar 18, 2007 rated it it was ok
Shelves: non-fiction
I generally find the "A Very Short Introduction" series to actually be quite good, with most of the volumes accomplishing exactly what they intend to by giving a good overall sense of a field of inquiry and its methods, or of the important elements of a given topic. Unfortunately, this volume did none of this very well. Many of the examples used to introduce to the reader to mathematical thinking are explained more clearly (and in a more engaging fashion) in Fermat's Enigma by Simon Singh. In ge ...more
Mirek Kukla
May 09, 2011 rated it it was ok
Shelves: math-logic
Long story short, I didn't really like this one. Gowers isn't a bad writer, but when all is said and done, this 'Introducution' is rather boring. It doesn't capture the imagination, and as far as math books are concerned, this quite simply isn't allowed. Don't bother with this one; if you want an engaging an accessible overview of mathematics, go pick up the far more interesting 'Language of Mathematics,' by Kieth Devlin. ...more
Oct 05, 2016 rated it it was amazing
I enjoyed this book so much, and because of its length, I finished it in one "seating" :-) The most important idea that I learned is to think about what a mathematical object DOES rather what it IS. This is the way mathematicians learn math, do math, and teach math. I plan to do the same in my mathematical endeavors. ...more
Dec 13, 2009 rated it did not like it
Surprisingly disappointing. I can't imagine who this book is written for. Nothing new to people who knew anything about math, and not terribly interesting to people trying to learn something about math. ...more
Bishnu Bhatta Buttowski
This book has vividly elaborated how the complex set of theorems or proofs arise from the basics axioms.

The writer starts from the evolution of number system and how the modelling and abstracting plays vital role in developing certain theorem.
Concepts of limits and infinity are great. The most impressive thing that the book tells you about is of the concept of infinity. Texts on these book would certainly clear up the concept of infinity in reader's mind. This approach is made by explaining the
Bijay Gurung
Mar 30, 2017 rated it liked it
Has the potential to change how we look at Mathematics, or at least us non-mathematicians, especially in regard to the use of the abstract method and fundamental concepts such as: "A mathematical object is what it does."

Wish I had read it sooner.
Nathan Ormond
Oct 29, 2020 rated it really liked it
Very good and cured me of some Platonist tendencies
Oct 13, 2015 rated it liked it
Good, not great. I had high hopes for Chapter 2 (on abstraction), but it is too difficult for me. I'm more interested in math than I was a student. I'll need to become a student again if I want to go any further in the subject. ...more
Mar 03, 2009 rated it really liked it
I like the Very Short Introductions, even though I knew most of this stuff anyway.
Tiago Faleiro
Dec 11, 2020 rated it it was ok
Shelves: unfinished, owned, science
I've always hated mathematics. I sucked at it in school, every single year. I always attributed it to being careless and not studying in the beginning, and having little to no foundations. And since mathematics always builds upon itself, I never managed to catch up. Luckily, I never needed mathematics ever again after school, and never touched on it again. However, I was listening to a podcast of a physicist that was really into mathematics and he was saying some interesting stuff and how mathem ...more
Sundararaman R
Dec 23, 2017 rated it really liked it
Pretty good considering the job it takes upon itself - to convey not the process of mathematical computation, but the mindset behind it and the type of thinking that goes into defining it. It answers several conceptual/philosophical questions I've had over the years, in trying to learn maths. This book can be a great aid to a student curious about the inner workings of maths, even if he/she might have to work on understanding it slowly over several weeks, chapter by chapter, even sentence by sen ...more
Jul 25, 2017 rated it really liked it
An excellent short tour of some key areas of math. This is not an "introduction" in terms of being a book for beginners but an introduction to a key component of the mindset of mathematics - the abstract method. Gowers leads the reader through several subtopics in math all with an eye to explaining the power of abstraction. The abstraction of math is covered in 3-key senses of the word "abstract." Firstly mathematical objects are abstract in that they are not physically observable. Secondly they ...more
Anton Mies
Jul 12, 2017 rated it really liked it
Red it and picked up a few things which I could reason with my "layman" math.

Another aspect, the author even if not intentionally passes on the beauty of the math or at least the perspective of mathematicians who are mesmerized by math's beauty. (Really discreet)

As previous reviews have described the book deals with the concepts and the reasoning of concepts and proof derivation. It is pretty scarce on equations rather full of well written but still hard to understand concepts, perhaps more nu
Shuby Deshpande
The book places a refreshing emphasis on abstraction in mathematics. As it would do injustice to cover a large array of mathematical topics within such a concise book, the author instead chooses to convey the basic principles of mathematical thought. This is done through techniques such as logically introducing Euclidean geometry axioms, and then logically deriving their subsequent falsification within the regimes of hyperbolic/spherical geometry (namely the axiom for parallel lines). This among ...more
May 22, 2017 rated it really liked it
The book provides a brisk sampling of few topics in math -- models, proofs, numbers/abstractions, limits/infinity, dimension, geometry, and approximation. I think the earlier chapters on models, proofs, and numbers as they are easy to grasp. Later chapters are interesting but more abstract as well; hence, they will need more effort to appreciate. All said, as the title says, the book provides a short introduction to Math. I think it is a perfect gift for high school students who are inclined tow ...more
Jun 21, 2017 rated it really liked it
This book is meant as an introduction to mathematics in the sense of what mathematical thinking is, what kinds of questions mathematics asks, and why they are motivated. The target audience seems to be laymen (e.g. if you want to convey to your family/friends what it is that you do). I think it does a good job at that, though it is hard to tell from the inside whether it succeeds. It has a number of fun examples of math problems that made it a reasonable read if one is looking for some nonrigoro ...more
Natasha Holme
Dec 27, 2017 rated it really liked it
Shelves: science, non-fiction
Impressively clear and enjoyable, given the potentially dry subject matter. Fourth science book I've read in this series, and this one stood out. The author has a passion for his subject and is able to educate, illuminate, and entertain effortlessly.

There were parts, naturally, that I did not understand. But the information was constructed in such a way that this did not ever hinder understanding of subsequent information.

I felt that the author cared about his remit, his subject, and his reader'
Mar 25, 2018 rated it it was amazing
This book was very different to a lot of mathematics books I’ve read in a positive way. Many maths books focus on the history of mathematics whereas this book focused on seemingly basic mathematical concepts in more depth. I can imagine the content of this book would be more useful in university interviews because it can be easily applied to various aspects of maths.

I’d definitely recommend this book as wider reading or if you’re generally interested in maths. Also, it is “short”, so it’s an ea
Steven Chew
Overall, it is acceptable. But it's probably too dry for like how the author would put it. Also makes me realise what i have missed as a young student. I was proud that i was good in math, not Einstein good but still.

Mathematics is a vast topics. This book in not about teaching you how to do maths but teach you how to look at things mathematically (which is not arithmetic and algebra).

The author tried hard to teach reader about thinking abstractly, but the language is not effective as i would
Joshua Snyder
Mar 15, 2019 rated it liked it
This was an interesting and concise introduction to mathematics, which would be accessible to a wide audience of readers. I found it interesting, but thought it could have gone into some more mathematical details, but I suppose this is to be expected of a very short introduction. Overall a good read, definitely worth it for a GCSE or A-Level student wanting to develop their interest in mathematics.
Lana Street
Jun 20, 2020 rated it really liked it
I had never read a book on mathematics before, however I have been studying it for a few years and so decided to read more into the philosophy behind mathematics. It was an amazing book to start with and once I had start it I couldn't put it down. A couple of the sections were a bit hard to wrap my head around and took me a bit longer to understand, however on the whole it was easy to understand and very easy and intriguing to read. ...more
Roberto Rigolin F Lopes
Oh, Mathematics! Your elegant but sometimes tricky curves looked very sexy to many smart people over the centuries. As a result, you are now a magnificent human endeavour with so many ramifications and still growing fast. Here we have a quick look at your foundations starting with models, passing through proofs and geometry, to end up on estimations/approximations. What a beauty.
Harriet M.
Feb 16, 2018 rated it really liked it
Shelves: misc-nonfiction
A book that pokes at the basic mathematical concepts most of us take for granted and looks at the assumptions behind them. I found most interesting -- and helpful -- the discussion of modeling and the case the author makes for abstract math. It merits reading slowly with time to digest, but it's engagingly written and very accessible to nonmathematicians. ...more
Sep 01, 2018 rated it it was amazing
This is a fast introduction to quite a broad range of topics in mathematics. I strongly recommend this for anyone who is interested in learning more about mathematics as a whole. It is not necessarily a book that's going to help you with your school or university-level work, but it could inspire you to study more. ...more
Apr 20, 2019 rated it it was ok
Shelves: maths
To be fair, it explicitly states that he assumes a certain level of Mathematical expertise. That and the first chapter was very useful in giving me an idea of what Maths is about--abstration ftw. That said, I should probably start with the 'for dummies' series.

Also, innumeracy cannot be THAT bad ):
M. Ashraf
Jul 23, 2019 rated it really liked it
Shelves: vsi
I think it is a very good book for Mathematics lover, though it is a very short introduction but it discussed principles and idea beyond introduction in a simple way and it is interesting answering questions, asking question and contain few brain teasers.
I enjoyed the book.
The chapters were great and the frequently asked questions at the end were great!

Apr 05, 2021 rated it it was ok
Shelves: stem
Uhhhhh I have NO idea what's going on.

T Vignesh Nayak
Apr 29, 2021 rated it it was amazing  ·  review of another edition
Well explained mathematics concept for beginners

This book is little bit technical for who doesn't has any idea of mathematics. But this books aims for Hilbert approach of mathematics and it shows power of abstraction. Major fields of mathematics are covered except probability, permutations and combinations.
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