Sunday, April 03, 2005

A Mathematician's Insight

G.H. Hardy (1877-1947) was, as Wikipedia says, "a prominent British mathematician, known for his achievements in number theory and mathematical analysis." Non-mathematicians (as I am) know him mainly for A Mathematician's Apology, "his essay from 1940 on the aesthetics of mathematics...with some personal content — which may be the layman's best insight into the mind of a working mathematician."

A Mathematician's Apology
is a fast and enriching read. I revisit it every few years. During my most recent visit, I was especially struck by this passage:
There are many highly respectable motives which may lead men to prosecute research, but three which are much more important than the rest. The first (without which the rest must come to nothing) is intellectual curiosity, desire to know the truth. Then, professional pride, anxiety to be satisfied with one's performance, the shame that overcomes any self-respecting craftsman when his work is unworthy of his talent. Finally, ambition, desire for reputation, and the position, even the power or the money, which it brings. It may be fine to feel, when you have done your work, that you have added to the happiness or alleviated the sufferings of others, but that will not be why you did it. So if a mathematician, or a chemist, or even a physiologist, were to tell me that the driving force in his work had been the desire to benefit humanity, then I should not believe him (nor should I think any better of him if I did). His dominant motives have been those which I have stated and in which, surely, there is nothing of which any decent man need be ashamed. [1979 edition, p. 79]
That's as incisive as anything Adam Smith had to say about self-interest being the engine of material progress.