A nice workout typically jolts you out of bad day and makes you alive. For me,a good book does the same when I have no energy to step out of home. Last few days I have not been keeping well and this book has kept my mind active despite the dullness around. In this delightful little book, Timothy Gowers delves in to the philosophical differences between people who are happy with the notions of infinity, curved spaces, square-root of –1, N dimensional spaces, etc, from those who find them disturbingly paradoxical.

Inequalities are a boon to various derivative valuation problems that arise in real life. One can use inequalities to get around problems for which closed form solutions are difficult. The other day I was struggling with an inequality . So, took my friend’s help who worked on it in a jiffy and produced a bound. He also happened to suggest this book to me so that , I can quickly refresh basic inequalities and probably stop bothering him with trivial questions –:) .

“ We write to know about that which we know.” - Grace Paley( on composition)

Instead of approaching “Metric spaces” from a real analysis perspective, this book tries to use an application to motivate the reader. The application is based on “contraction mapping theorem” which is used in solving a single equation / simultaneous equations. In its most simple form, let’s say there is an equation of the type x = f(x) which needs to be solved. One of the ways to solve this type of equation is as follows: