Thursday, November 12, 2009

Mathematician's Apology

Hardy's Mathematician's apology figures among the must read for any Math major. The book was written when Hardy was over 60 and passed his prime. The book is a fast read and is divided into 29 sections . It begins with a lengthy forward by Snow detailing his accquaintance with Hardy and tidbits about the book. From the beginning Hardy is candid that it is his personal opinion and inspite of inputs from his reviewers remains firm in the stance he has chosen. Numerous books have been written since Hardy about what constitutes a beautiful mathematics. Hardy bites more than he can chew when he says applied mathematics is elementary and real mathematics is not. But then it was before the development of Nuclear bomb and advent of computer sciences. Hardy acknowledges that its not easy to keep defending his assertion he made in 1920s about real and applied mathematics.
He excoriates both Alfred Northwood and Hogben the other defenders of mathematics. He is especially critical of Hogben and I am sure most Mathematicians will readily identify with Hardy here.
It is hard to defend ones choice without defending oneself. Hardy comes out both proud and humble in this book. Its not a motivational book that would propel you into plunging heads down into mathematical water. He reminices about his collaboration with Littlewood and Ramanujam. His continued lamentation about getting old is unsettling when people like Avraham Trahtman continue to do ground breaking mathematics in their 60s. Hardy's disdain about expository mathematics appears sophomoric especially if you have read Paul Halmos "I want to be a Mathematician". Its one thing to come up with something and its other to make it accessible and provide insight into it. A great mathematical exposition kindles the interest of many otherwise many results gather dust.
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