New Lecture Hall, Harvard University
IN THE LECTURE he did not give, Hardy said: As a child I believed in more than I do now. For one thing I believed in ghosts. This was mostly thanks to my mother, who told me when I was very young that a ghost haunted our house in Cranleigh, the ghost of a girl who had died in my bedroom of typhoid, many years before, on the eve of what would have been her wedding day. Neither Gertrude nor I ever encountered this ghost, whose behavior, according to my mother, was generally benign. Occasionally—but only when my mother was alone in the house—the ghost would play a tinkling melody on the piano that my mother did not recognize and that sounded out of tune even when the piano had just been tuned. Or the ghost stamped her foot, like a child having a tantrum. Her encounters with the ghost my mother reported dutifully to us (but never to my father); as we listened, we would affect the benevolent and condescending patience of the governess putting the restless, tale-telling child to bed. For even then, my sister and I were confirmed rationalists; and we took it for granted that our mother was a rationalist, too, that she told these stories only to amuse and bewitch us, although once I came home from school to find her white as a sheet, gazing in astonishment at the piano.
The odd part is, I think I believed in her ghost more than she did—this though I never had a single personal encounter with the creature who had died in my bedroom. Today, if I were compelled to choose between Christianity and that occult program that attributes to the dead the capacity to trouble and console the living, or to pass cryptic messages through the curtain that divides their realm from ours, or to possess the bodies of animals, or trees, or bureaus, I should still plump for ghosts. The idea that a spirit might linger on this earth makes an intuitive sense to me that the vision imposed upon us by Christianity, of a vague, dull heaven and a horrible, fascinating hell, never will.
Not that I've had much personal experience of ghosts. The only "visitations" I ever received took place over the course of the decade or so following the death of my friend Gaye. Whenever Gaye "appeared," in those years, I would at first question my own sanity, and wonder if I should fly to the nearest asylum, or to Vienna. Then I would question my own rationalism, and wonder if I should wire O. B., who was affiliated with the Society for Psychical Research. Then I would question my own questioning: what was this apparition, after all, if not the belated expression of an old impulse, the one that drives the solitary child to invent an imaginary friend? For I missed Gaye terribly in those years; I missed his voice, and his arch tongue, and his refusal to suffer fools gladly. I wasn't an idiot. I didn't conjure him in the hope that he would console or reassure me. On the contrary, I wanted him to tell me the truth, even when it was brutal. His arrivals not only made me less lonely, they contradicted a doctrine that would have placed him, for a host of reasons, in some deep and terrible realm of a Boschian hell, rather than allow him to float about Cambridge in his smoking jacket and Westminster tie, observing our capers with bemused detachment. In the same way I suspect that my mother's ghost, struck down on the eve of her wedding, represented to her an ideal of marriage all the more alluring for its having been preserved forever in the amber of imminence.
Like me, Gaye was an atheist. As he told it, his war with God dated to very early in his childhood. According to our religious education, God was supposed to be an entity neither animal nor man nor any combination of the two. Nor was God a plant. This entity was supposed to exist, as you or I or the sun or the moon exist, but not as King Lear or Little Dorrit or Anna Karenina exist. And it was supposed to have a mind, not unlike our own minds, but grander, because it had created him and me and everything else in the universe.
Gaye accepted none of this. Neither did I. I've never seen how any sane or rational person could. No doubt in a hundred years only the most primitive of peoples will still worship the Christian God, and then our unbelief will be vindicated.
Oddly enough, given its supposed liberalism, atheism was much frowned upon at Cambridge. Even in the Society there were few who admitted to being atheists. Instead the brethren were forever trying to wrap their religious skepticism in vague, "emotional" statements about "God" and "Paradise." That shit McTaggart, for instance, with his snug little Trinity College of a Heaven, and all the archangel undergraduates buggering one another while seraphim and cherubim fetch cups of tea; or Russell, who envisioned a universe also like Trinity—aloof, rife with inefficiency, arrogant. His idea was that what mattered in religion was not the specificity of the dogma but the feelings that underlay belief: feelings, in his words, "so deep and so instinctive as to remain unknown to those whose lives are built upon them."
As you have no doubt already surmised, I hold no truck with any of these efforts to placate the clerics. Christian devotion of any sort, in my opinion, is anathema to thought. I don't believe Ramanujan was especially devout either, despite all the nonsense he talked about the goddess Namagiri and what have you. He just said what he'd been raised to say, and if he believed in any of it, he believed in it as I believed in Gaye's ghost.
What I have never quite been able to make out is how God can become as real to the unbeliever as to the believer.
Let me give an example. In the spring of 1903, on a sunny afternoon at the very beginning of the cricket season, I went off to Fenner's to watch a match. I was in a good humor. That day the world, as it so rarely does, seemed kindly and beneficent to me. No sooner had I taken my seat, however, than the rain started pouring down. Naturally I had not brought my umbrella. Curses, I thought, and went back to my rooms to change.
The afternoon of the next match was equally beautiful. This time, however, I decided to prepare myself. I brought not only an umbrella—an enormous one, borrowed from Gertrude—but put on a raincoat and galoshes. And wouldn't you know it? The sun shone all the day.
The afternoon of the third match, I risked leaving the umbrella behind. It rained again.
The afternoon of the fourth match, I brought not just the umbrella, not just the raincoat and galoshes, but three sweaters, a dissertation, and a paper that the London Mathematical Society had asked me to referee. Before I left, I said to my bedmaker, "I hope it rains today, because then I'll be able to get some work done."
This time it did not rain, and I was able to spend the afternoon watching cricket.
From then on, I referred to the umbrella, the papers, and the sweaters as my "anti-God battery." The umbrella I saw as being of particular importance. In order not to have to return it to Gertrude, I bought her a new one, with her initials engraved on the handle.
Usually, in this little game, I got the best of God. But sometimes God got the best of me.
One summer, for instance, I was sitting in the sun at Fenner's with my usual arsenal of sweaters and work, enjoying the play, when suddenly the batsman put down his bat and complained to the umpires that he could not see. Some sort of reflection was casting a glare that got in his eyes. The umpires searched for the source of the glare. Glass? There were no windows on that side of the grounds. An automobile? No road.
Then I saw: on the sidelines stood a portly vicar with an enormous cross hung round his neck. The sunlight was bouncing off the cross. I called an umpire's attention to the ungainly medallion, and the vicar was asked, very politely, to take it off.
That vicar: I remember that, though ultimately he complicit with the umpire's request, first he had to protest and argue and deny for a while. He wasn't about to give up his cross without a fight. Of course he had an enormous arse. He belonged to that category of men whom I call the "large-bottomed," by which I mean something as spiritual as it is physical: a certain complacency that comes from always having your place in the world affirmed. From never having to struggle or feel yourself to be an outsider.
I can't claim credit for the phrase. It has been drifting around Trinity since the eighteenth century, traceable, I am told, to a geologist called Sedgwick. "No one," he is reputed to have uttered, "ever made a success in this world without a large bottom."
Of course, the world is filled, and always has been, with large-bottomed mathematicians, most of whom claim to believe in God. And how, I have often wondered, do they reconcile their faith with their work? Most don't even try. They just file religion away in one drawer and mathematics in another. Filing things away in different drawers and not thinking about the contradictions is a classic trait of the large-bottomed.
Some, though, aren't content with this solution. These mathematicians are in many ways more vexing because they try to explain mathematics in terms of religion, as an aspect of what they call God's "grand design." According to them, any scientific theory can be made compatible with Christianity on the grounds that it is part of a divine plan. Even Darwin's ideas about evolution, which seem to negate the existence of God, can be swaddled in a doctrine that has God stirring the primordial soup, sparking the process of mutation and survival of the fittest with each turn of his magical spoon. Then there are the papers that for some reason large-bottomed men seem always to feel the need to send to me, offering ontological proofs for God's existence. I throw them in the rubbish bin. Because all this effort to make mathematics part of God is part of the effort to make mathematics useful, if not to the state, then to the church. And this I cannot abide.
Only once in my life, I am proud to say, have I made a contribution to practical science. Years ago, before we started playing tennis together, Punnett and I used to play cricket. One afternoon after the match, he asked me for help with a question concerning Mendel and his theory of genetics. A geneticist with the unfortunate name of Udny Yule (the war would later make us enemies) had published a paper arguing that if, as Mendel suggested, dominant genes always won out over recessive ones, then over time a condition known as brachydactyly—leading to shortened fingers and toes, and caused by a dominant gene—would increase in the human population until the ratio of those with the condition to those without would be three to one. Although this obviously wasn't the case, Punnett was at a loss as to how he might counter the argument. Yet I saw the answer at once, and wrote it up in a letter that I posted to Science.
"I am reluctant to intrude in a discussion concerning matters of which I have no expert knowledge," I wrote, "and I should have expected the very simple point which I wish to make to have been familiar to biologists." It was not, of course, even though, as I phrased it, "a little mathematics of the multiplication-table type" was enough to show that Yule was wrong and the ratio would in fact remain fixed.
Much to my surprise, this little letter made me famous in genetics circles. Soon the geneticists started referring to my little proof as "Hardy's Law," which embarrassed me, both because I never in my life wished to have anything so monolithic as a law named in my honor, and because this particular law lent ballast to a theory that has as often been used to argue for God's existence as against it.
Yet I had one reason to be glad. Over the years I had read many newspaper articles decrying what the doctors had just then started calling "homosexuality," complaining of its prevalence and making predictions that if the "disposition," already "on the rise," should continue to "spread," the human race itself would risk extinction. Of course, in my considered opinion, the extinction of the human race is immensely desirable, and would benefit not only the planet but the many other species that inhabit it. Even so, the mathematician in me could not help but balk at the fallacy behind the warning. It was the same fallacy that Hardy's Law had demolished. Just as, if Udny Yule was correct, there should eventually be more brachydactylics than normal-fingered and -toed men and women, so, if the articles were correct, inverts should soon outnumber normal men and women, when the truth, of course, is that ratio will remain fixed.
Yet all that, ultimately, is beside the point—which, I suppose, is the point, the one that Ramanujan understood better than any of us.
When a mathematician works—when, as I think of it, he "goes into" work—he enters a world that, for all its abstraction, seems far more real to him than the world in which he eats and talks and sleeps. He needs no body there. The body, with its blandishments, is an impediment. I was foolish, I see now, even to bother trying to explain the tripos to O. B. Analogy can only take you a certain distance, and in mathematics, it's not long before you reach the point where analogy fails.
This was the world in which Ramanujan and I were happiest—a world as remote from religion, war, literature, sex, even philosophy, as it was from that cold room in which, for so many mornings, I drilled for the tripos under Webb. Since then, I have heard of mathematicians imprisoned because they were dissenters or pacifists, and then relishing the rare solitude that a gaol gave them. For them, gaol was a respite from the vagaries of having to feed themselves and dress themselves and earn money and spend it; a respite, even, from life, which, for any true mathematician, is not the thing, but the thing that interferes.
A slate and some chalk. That's all you need. Not pianos or thimbles or nails or saucepans. Not sledgehammers. Certainly not Bibles. A slate and some chalk, and that world—the real world—is yours.