![[cover]](../covers/0521427061.gif)
by G. H. Hardy
isbn: 0521427061
subject: Nonfiction,
Mathematics
finished: 4/20/2001
It is sometimes said that those who cannot do, teach. This is almost always a useless, stupid thing to say. Still, whatever grain of truth may lie behind it is at the core of A Mathematician's Apology, which was written late in Hardy's life. His capability for generating original mathematics had faded but he retained a sharp, insightful mind and a desire to explain what is beautiful and eternal about mathematics to general readers.
As a pure mathematician, Hardy had a pronounced disdain for "useful" mathematics, saying
...our general conclusion must be that such mathematics is useful as is wanted by a superior engineer or a moderate physicist; and that is roughly the same thing as to say, such mathematics as has no particular aesthetic merit.The thesis of the book, then, is that pure mathematics is nothing more or less than art, and it should be evaluated as such. If it isn't useful, then at least it isn't harmful in that it doesn't contribute to modern warfare.
It is interesting that time and time again, Hardy uses number theory as an example of a beautiful but impractical branch of mathematics -- he surely would have been surprised by its usefulness towards the end of the twentieth century. Has this increase in utility decreased its beauty? One would like to have had the chance to ask Hardy this question. Ironically, since he was writing in 1940, Hardy also believed that relativity and quantum mechanics were useless branches of mathematics.
A Mathematician's Apology is a wonderful book; it explains in a clear way what I dimly (having only a mathematics degree and being far from a practicing mathematician) understand to be the aesthetic sense behind good mathematics. It is also a sad book; the center of Hardy's life, the creation of original mathematics, was no longer available to him. And finally, it's motivating and can be read as a case for finding the single thing that one can do really well, and doing it. Hardy says:
I still say to myself when I am depressed, and find myself forced to listen to pompous and tiresome people, "Well, I have done one thing you could never have done, and that is to have collaborated with both Littlewood and Ramanujan on something like equal terms."
The introduction (of the "Canto" imprint of the Cambridge University Press) weighs in at one-third of the length of the book; it turns out to be an affectionate biographical sketch of Hardy by a non-mathematician. It's fairly interesting and helps put Hardy's life and circumstances into perspective.