2 of 2 people found the following review helpful
A good take on the subject,
This review is from: Mathematics: A Very Short Introduction (Very Short Introductions) (Paperback)
It's well known that some concepts in mathematics can be utterly mind-bending - concepts such as curved space, higher dimensional geometry, infinity, and more besides. To be able to work with any of these, you often need to let go of the urge to visualise something and instead settle for merely conceptualising it. You need, in other words, to feel comfortable thinking in a thoroughly abstract way. This book is an introduction to that way of thinking. It's not one of those books that joyously recaps all the rules and syntax you'd forgotten since leaving school. Rather, its aim is simply to give you the means to grapple with core aspects of advanced mathematics.
While this book doesn't overwhelm with technicalities (a British GCSE or equivalent in the subject should be sufficient prior knowledge for most readers), the rules and processes are not ignored, and there are brief introductions/reminders of topics such as Euclidean geometry, irrational numbers and so on. However the author's aims and emphasis are decidedly more psychological and philosophical. Why should we accept the axioms proposed by mathematicians? What exactly is a number? What does mathematical proof actually mean? These questions first need to be explored before embarking on the path to more esoteric concepts such as multi-dimensional geometry and manifolds (incidentally, useful for anyone interested in string theory).
The chapters are sensibly structured and Gowers's enthusiasm for the subject radiates from each page without ever sinking into that patronising "Hey kids, maths is fun!" style of writing. The last chapter contains a selection of genuinely interesting FAQs, including some good suggestions as to why so many people seem to strongly dislike mathematics, compared with say biology or English literature (about which the non-enthusiast may just feel indifferent). Overall I found this more interesting that expected; a useful take on the subject that lays the groundwork for some of the more advanced areas of mathematics.