You might be thinking of: "One rather curious conclusion emerges, that pure mathematics is on the whole distinctly more useful than applied." I wonder what he w

You might be thinking of: "One rather curious conclusion emerges, that pure mathematics is on the whole distinctly more useful than applied." I wonder what he would think if he could see the ways in which number theory, once often regarded as the purest of the branches of math, is now used in things like cryptography. "Apology" is definitely worth reading. Some of his opinions can seem rather elitist: "Statesmen, despise publicits, painters despise art-critics, and physiologists, physicists, or mathematicians usually have similar feelings; there is no scorn more profound, or on the whole more justifiable, than that of the men who make for the men who explain. Exposition, criticism, appreciation is work for second-rate minds." At the same time, he is very honest about himself - in fact, he seems to have been suffering from depression over what he perceived as a decline in his ability to do math at the level he was accustomed to: "If then I find myself writing, not mathematics but 'about' mathematics, it is a confession of weakness, for which I may rightly be scorned or pitied by younger and more vigorous mathematicians. I write about mathematics because, like any other mathematician who has passed sixty, I have no longer the freshness of mind, the energy, or the patience to carry on effectively with my proper job." Or: "A mathematician may still be competent enough at sixty, but it is useless to expect him to have original ideas." Or more sadly, but with some serenity: "It is plain now that my life, for what it is worth, is finished, and that nothing I can do can perceptibly increase or diminish its value. It is very diffciult to be dispassionate, but I count it a 'success'; I have had more reward and not less than was due to a man of my particular grade of ability." "If I had been offered a life neither better nor worse when I was twenty, I would have accepted without hesitation." The personal reflections bookend a central portion where he illustrates with several examples (e.g. Euclid's proof of the infinitude of the primes) his feelings about the "importance" of math, its "usefulness", and the distinction between pure and applied math. It's interesting to compare "Apology" to "Littlewood's Miscellany" (I recommend the Cambridge University Press version, which contains the essay "The Mathematician's Art of Work" - ISBN 0-521-33702-X). There is more math than in "Apology" and many anecdotes. J. E. Littlewood was Hardy's long-time collaborator.