Mathematics: A Very Short IntroductionThe aim of this book is to explain, carefully but not technically, the differences between advanced, researchlevel 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 paradoxicalsounding concepts such as infinity, curved space, and imaginary numbers. The first few chapters are about general aspects of mathematical thought. These are followed by discussions of more specific topics, and the book closes with a chapter answering common sociological questions about the mathematical community (such as "Is it true that mathematicians burn out at the age of 25?") ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocketsized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable. 
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Excellent introduction to the world of mathematics.  Goodreads
... style of writing.  Goodreads
This book is an introduction to that way of thinking.  Goodreads
Review: Mathematics: A Very Short Introduction (Very Short Introductions)
User Review  Can Arel  GoodreadsI wish more people wrote books in this style. The author is not only a great mathematician but he can also explain his thought process. I got many aha moments while reading and they will definitely ... Read full review
Review: Mathematics: A Very Short Introduction (Very Short Introductions)
User Review  Daniel Wright  GoodreadsRemember: do not ask of a mathematical concept what it is; ask what it does. This is perhaps the most important thing Professor Gowers explains in this absolute joy of a book. He writes with a ... Read full review
Contents
Numbers and abstraction  17 
Proofs  35 
Limits and infinity  56 
Dimension  70 
Geometry  86 
Estimates and approximations  112 
o Some frequently asked questions  126 
Common terms and phrases
180 degrees abstract method angles answer approximate argument axioms becomes calculations Chapter chess circle complicated concept cube curved defined definition dimensional distance divided edges equation Euclid's exactly example fact Figure follows fourdimensional fourdimensional sphere give given golden ratio graph grid hyperbolic geometry idea infinite decimal infinity Koch snowflake large number line segment logarithm manifold mathematical proof mathematicians mathematics means molecules multiply natural logarithm negative numbers number of digits number of regions number system objects obvious parallel postulate pentagons philosophical polygon possible prime number prime number theorem problem proof properties prove Pythagoras question real numbers rectangle result roughly rules sequence shape side lengths simple smaller sort space speed sphere spherical geometry square root statement straight line surface tells theory three dimensions threedimensional Timothy Gowers trefoil knot triangle twodimensional understand vertices visualize whole number words