The G. H. Hardy Reader

I’m afraid I don’t remember when I first read G. H. Hardy’s A Mathematician’s Apology. In any case it was a very long time ago, perhaps even before my sophomore year at the university when I took a course in number theory in which my professor, the late E. G. Straus, used the classic book, An Introduction to the Theory of Numbers, by Hardy and E. M. Wright, as his primary reference: it was required for the course, but, true to form, Straus largely developed the various themes independently. I also recall, from those days, now over forty years ago, getting my hands on a copy of Hardy’s A Course of Pure Mathematics and being amazed by its style and concision, as well as its sweep — indeed, from my early university days on, Hardy figured in one way or another in my reading and my musing about mathematics, mathematicians, and the prospect of becoming one.

It was also very evocative to discover the very British milieu Hardy occupied, with the full trappings of Cambridge and Oxford in the early days of the last century, replete with real tennis, cricket, High Table, pipes, and tweed jackets covered by academic gowns. What a marvelous image it was (and still is) to consider Hardy and Littlewood holding forth in that environment. Surely the most irresistible tale from those chapters of relatively modern mathematical history is that of the appearance of Ramanujan on the scene like a bolt from the blue. This is of course a major episode in itself, and while I did first discover Ramanujan in the pages of A Mathematician’s Apology, the definitive source on his life is surely Robert Kanigel’s The Man Who Knew Infinity. Still, Hardy’s own writings about Ramanujan are telling in a special way, in that they reveal a lot about Hardy and the ultimately tragic orbit of his life: his description of his relationship and work with Ramanujan is poignant and touching and contrasts sharply with the tone of much of Hardy’s other autobiographical writing.

Indeed, Hardy was a man at war with God, in Whom he claimed not to believe, entirely wedded to his mathematicianship (often apparently pursued competitively: Hardy looked upon much of life as a cricket match, so to speak, complete with score-cards), fundamentally deeply lonely, evidently anti narcissistic (as evidenced by his deep aversion to mirrors), and even suicidal at one point toward the end of his life as he feared the waning of his powers. So it is that many of Hardy’s writings must be appraised with these things in mind — they are very idiosyncratic, and their author was a troubled and tragic figure, despite his brilliance and the beauty of his mathematics.

That said, I want to highlight one particularly touching account in the book under review, this Hardy “reader,” by none other than Freeman J. Dyson, an equally idiosyncratic Englishman, but one whose works burst with a rather different sentiment: even today, at 92 he is full of joie de vivre, as any of his interviews testify — there are a number available online; I recommend this one. Dyson’s take on Hardy is both realistic and quite touching, with his comments going back to the days when Dyson was a student at Cambridge during the war years, taking courses with Hardy. In the present book, on p. 111, we come across the following passage from a 1967 letter from Dyson to C. P. Snow, the author of the fabulous introduction to A Mathematician’s Apology: “I was always amazed that so great a mathematician (we considered him the best in the world) should spend so much of his time and energy in lecturing to so small a class [Cambridge was essentially deserted in World War II]. And each lecture was carefully prepared, like a work of art, with the intellectual dénouement appearing as if spontaneously in the last five minutes of the hour. For me these lectures were an intoxicating joy, and I used to feel sometimes an impulse to hug that little old man in the white cricket-sweater two feet away from me, to show him somehow how desperately grateful we were for his willingness to go on talking.” There is a quality of real poignancy about this account by Dyson, given the realities of Hardy’s life at that time, with his death in 1947 not far away, as the book certainly makes clear.

The G. H. Hardy Reader is liberally equipped with biographical material, both of a formal sort and in the shape of anecdotes; one gains a very clear picture of Hardy, the man. Littlewood, Ramanujan, Bertrand Russell, E. C. Titchmarsh, Edmund Landau (one of my all-time favorites), Harald Bohr, George Pólya, and even John Maynard Keynes make their appearances. Hardy’s devoted sister, Gertrude, who nursed him during his final illness right after the war and who taught at St. Catherine’s School in Surrey, is featured on pp. 115–120. Beyond this there is a great deal of material in the book by Hardy himself, his vaunted style amply on display both in his writing mathematics and his writing about mathematics and mathematicians — and also such things as cricket and golf.

Indeed, the book is a cornucopia of all things Hardy and is very well put together indeed. It succeeds both as a book to be read linearly and a book to browse again and again. Finally, as regards the mathematics per se covered in this Reader, suffice it to say that it’s beautiful — it is an example of the artistry Hardy that held so dear and that he set himself as a goal.

Michael Berg is Professor of Mathematics at Loyola Marymount University in Los Angeles, CA.