G. H. Hardy: The Pure Mathematician

by C. P. SNOW

IT WAS a perfectly ordinary night at Christ’s high table, except that Hardy was dining as a guest. He had just returned to Cambridge as Sadleirian professor, and I had heard something of him from young Cambridge mathematicians. They were delighted to have him back: he was a real mathematician, they said, the purest of the pure. He was also unorthodox, eccentric, radical, ready to talk about anything. This was 1931, and the phrase was not yet in English use, but in later days they would have said that in some indefinable way he had star quality. So from lower down the table I kept studying him. He was then in his early fifties; his hair was gray, above skin so deeply sunburned that it stayed a kind of Red Indian bronze. His face was beautiful — high cheekbones, thin nose, spiritual and austere but capable of dissolving into convulsions of internal gaminlike amusement. He had opaque brown eyes, bright as a bird’s, a kind of eye not uncommon among those with a gift for conceptual thought. Cambridge at that time was full of unusual and distinguished faces, but even then, I thought that night, Hardy’s stood out.

As we sat around the combination-room table, drinking wine after dinner, someone said that Hardy wanted to talk to me about cricket. I had been elected only a year before, but Christ’s was then a small college, and the pastimes of even the junior fellows were soon identified. I was taken to sit by him. I was not introduced. He was, as I later discovered, shy and self-conscious in all formal actions, and had a dread of introductions. He just put his head down, as it were, in a butt of acknowledgment, and without any preamble whatever, began: “You’re supposed to know something about cricket, aren’t you?”

Yes, I said, I knew a bit.

Immediately he began to put me through a moderately stiff viva. Did I play? What sort of performer was I? I half guessed that he had a horror of persons, then prevalent in academic society, who devotedly studied the literature but had never played the game. I trotted out my credentials, such as they were. In the end he smiled with immense charm, with childlike openness, and said that Fenner’s (the university cricket ground) next season might be bearable after all, with the prospect of some reasonable conversation.

Thus I owed my friendship with Hardy to having wasted a disproportionate amount of my youth on cricket. It was a major piece of luck for me; this was intellectually the most valuable friendship of my life. Hardy’s mind was brilliant and concentrated; so much so that by his side anyone else’s seemed a little muddy, a little pedestrian and confused. He wasn’t a great genius, as Einstein and Rutherford were. He said, with his usual clarity, that if the word meant anything, he was not a genius at all. At his best, he said, he was for a short time the fifth best pure mathematician in the world. Since his character was as beautiful and candid as his mind, he always made the point that his friend and collaborator Littlewood was an appreciably more powerful mathematician than he was, and that his protégé Ramanujan really had natural genius in the sense (though not to the extent, and nothing like so effectively) that the greatest mathematicians had it.

There was something else, though, at which he was clearly superior to Einstein or Rutherford or any other great genius; and that was at turning any work of the intellect, major or minor or sheer play, into a work of art. It was that gift above all, I think, which made him, almost without realizing it, purvey such intellectual delight. When A Mathematician’s Apology was first published, Graham Greene in a review wrote that along with Henry James’s notebooks, this was the best account of what it was like to be a creative artist.

Hardy was born in 1877 into a modest professional family. His father was Bursar and Art Master at Cranleigh, then a minor public (English for private) school. His mother had been senior mistress at the Lincoln Training College for teachers. Both were gifted and mathematically inclined. In his case, as in that of most mathematicians, the gene pool doesn’t need searching for. Much of his childhood, unlike Einstein’s, was typical of a future mathematician’s. He was demonstrating a formidably high IQ even before he learned to talk. At the age of two he was writing down numbers up to millions (a common sign of mathematical ability). When he was taken to church he amused himself by factorizing the numbers of the hymns; he played with numbers from that time on.

It was an enlightened, cultivated, highly literate Victorian childhood. His parents were probably a little obsessive, but also very kind. Childhood in such a Victorian family was as gentle a time as anything we could provide, though probably intellectually somewhat more exacting. His was unusual in just two respects. In the first place, he suffered from an acute self-consciousness at an unusually early age, long before he was twelve. His parents knew he was prodigiously clever, and so did he. He came top of his class in all subjects. But as the result of coming top of his class, he had to go in front of the school to receive prizes, and that he could not bear. Dining with me one night, he said that he deliberately used to try to get his answers wrong so as to be spared this intolerable ordeal. His capacity for dissimulation, though, was always minimal: he got the prizes all the same.

Some of this self-consciousness wore off. He became competitive. As he says in his autobiography, A Mathematician’s Abology: ‘I do not remember having felt, as a boy, any passion for mathematics, and such notions as I may have had of the career of a mathematician were far from noble. I thought of mathematics in terms of examinations and scholarships: I wanted to beat other boys, and this seemed to be the way in which I could do so most decisively.” Nevertheless, he had to live with an overdelicate nature.

He was the classical anti-narcissist. He could not endure having his photograph taken: so far as I know, there are three photographs in existence. He would not have any looking glass in his rooms, not even a shaving mirror. When he went to a hotel, his first action was to cover all the looking glasses with towels.

The other unusual feature of his childhood was more mundane. His family had no money, only a schoolmaster’s income, but they were in touch with the best educational advice of late-nineteenthcentury England. That particular kind of information has always been more significant in England than any amount of wealth. The scholarships have been there all right, if one knew how to win them. There was never the slightest chance of the young Hardy being lost, as there was of the young Einstein. From the age of twelve Hardy had only to survive, and his talents would be looked after.

At twelve, in fact, he was given a scholarship at Winchester, then and for long afterward the best mathematical school in England, simply on the strength of some mathematical work he had done at Cranleigh. There he was taught mathematics in a class of one; in classics he was as good as the other top collegers. Later, he admitted that he had been well educated, but he admitted it reluctantly. He disliked the school, except for its classes. Like all Victorian public schools, Winchester was a pretty rough place, and he never went near it after he had left it. But he left it, with the inevitability of one who had got on to the right tramlines, with an open scholarship to Trinity.

HARDY duly obtained a Trinity Fellowship, after getting the highest place in the Mathematical Tripos Part II, at the age of twenty-two. On the way, there were two minor vicissitudes. The first was theological, in the high Victorian manner. He had decided — I think before he left Winchester — that he did not believe in God. With him, this was a black-and-white decision, as sharp and clear as all other concepts in his mind. Chapel at Trinity was compulsory. Hardy told the dean, no doubt with his own kind of shy certainty, that he could not conscientiously attend. The dean, who must have been a jack-in-office, insisted that Hardy should write to his parents and tell them so. They were orthodox religious people, and the dean knew — and Hardy knew much more — that the news would give them pain.

Hardy struggled with his conscience. He wasn’t worldly enough to slip the issue. He wasn’t even worldly enough — he told me one afternoon at Fenner’s, for the wound still rankled — to take the advice of more sophisticated friends, such as George Trevelyan and Desmond MacCarthy, who would have known how to handle the matter. In the end he wrote the letter. Partly because of that incident, his religious disbelief remained active ever after. He refused to go into any college chapel even for formal business, like electing a master. He had clerical friends, but God was his personal enemy.

The second minor upset of his undergraduate years was professional. Almost since the time of Newton and all through the nineteenth century Cambridge had been dominated by the examination for the old Mathematical Tripos. This was an examination in which the questions were usually of considerable mechanical difficulty, but unfortunately it did not give any opportunity for the candidate to show mathematical imagination or insight or any quality that a creative mathematician needs.

In his first term at Trinity, Hardy found himself caught in this system. He was to be trained as a racehorse, over a course of mathematical exercises which at nineteen he knew to be meaningless. He was sent to a famous coach, to whom most potential Senior Wranglers went. This coach knew all the obstacles, all the tricks of the examiners, and was sublimely uninterested in mathematics itself. After considering changing his subject to history, Hardy had the sense to find a real mathematician to teach him who advised him to read Jordan’s famous Cours d’ Analyse.

“I shall never forget the astonishment with which I read that remarkable work, the first inspiration for so many mathematicians of my generation,” Hardy wrote in his Apology, “and learned for the first time as I read it what mathematics really meant. From that time onwards I was in my way a real mathematician, with sound mathematical ambitions and a genuine passion for mathematics.”

He was Fourth Wrangler in 1898. This faintly irritated him, he used to confess. He was enough of a natural competitor to feel that though the race was ridiculous, he ought to have won it. In 1900 he took Part II of the Tripos, a more respectworthy examination, and got his right place and his fellowship.

From that time on Hardy’s life was in essence settled. He knew his purpose, which was to bring rigor into English mathematical analysis. He did not deviate from the researches, which he called “the one great permanent happiness of my life.” There were no anxieties about what he should do. Neither he nor anyone else doubted his great talent.

In many senses, then, he was unusually lucky. He did not have to think about his career. From the time he was twenty-three he had all the leisure that a man could want, and as much money as he needed. A bachelor don in Trinity in the 1900s was comfortably off. Hardy was sensible about money, spent it when he felt impelled (sometimes for singular purposes, such as fifty-mile taxi rides), and otherwise was not at all unworldly about investments. He played his games and indulged his eccentricities. He was living in some of the best intellectual company in the world — G. E. Moore, Whitehead, Bertrand Russell, Trevelyan, the high Trinity society which was shortly to find its artistic complement in Bloomsbury. (Hardy himself had links with Bloomsbury, both of personal friendship and of sympathy.) In a brilliant circle, he was one of the most brilliant young men — and in a quiet way, one of the most irrepressible. He was elected to the Royal Society at thirty-three.

Much of his life Hardy was happier than most of us. He had a great many friends, of surprisingly different kinds. These friends had to pass some of his private tests: they needed to possess a quality which he called “spin” (this is a cricket term, and untranslatable: it implies a certain obliquity or irony of approach; of recent public figures, Macmillan and Kennedy would get high marks for spin, Churchill and Eisenhower not). But he was tolerant, loyal, extremely high-spirited, and in an undemonstrative way, fond of his friends. I once was compelled to go and see him in the morning, which was always his set time for mathematical work. He was sitting at his desk, writing in his beautiful calligraphy. I murmured some commonplace politeness about hoping that I wasn’t disturbing him.

He suddenly dissolved into his mischievous grin. “As you ought to be able to notice, the answer to that is that you are. Still, I’m usually glad to see you.” In the sixteen years we knew each other, he didn’t say anything more demonstrative than that except on his deathbed, when he told me that he looked forward to my visits.

I think my experience was shared by most of his close friends. But he had, scattered through his life, two or three other relationships, different in kind. These were intense affections, absorbing, nonphysical, and exalted. The one I knew about was for a young man whose nature was as spiritually delicate as his own. To many people of my generation, such relationships would seem either unsatisfactory or impossible. They were neither the one nor the other; and unless one takes them for granted, one doesn’t begin to understand the temperament of men like Hardy or the Cambridge society of his time. He didn’t get the satisfactions that most of us can’t help finding; but he knew himself unusually well, and that didn’t make him unhappy. His inner life was his own and very rich. The sadness came at the end. Apart from his devoted sister, he was left with no one close to him.

With sardonic stoicism he says in the Apology — which for all its high spirits is a book of desperate sadness — that when a creative man has lost the power or desire to create, “it is a pity but in that case he does not matter a great deal anyway, and it would be silly to bother about him.” That is how he treated his personal life outside mathematics. Mathematics was his justification. It was easy to forget this in the sparkle of his company; just as it was easy in the presence of Einstein’s moral passion to forget that to himself his justification was his search for the physical laws. Neither of those two ever forgot it.

IN 1911 Hardy began a collaboration with Littlewood which lasted thirty-five years. In 1913 he discovered Ramanujan and began another collaboration. All his major work was done in these two partnerships, most of it in the one with Littlewood, the most famous collaboration in the history of mathematics. The Hardy-Littlewood researches dominated English pure mathematics, and much of world pure mathematics, for a generation. It is too early to say, so mathematicians tell me, to what extent they altered the course of mathematical analysis or how influential their work will appear in a hundred years. Of its enduring value there is no question.

At first glance, neither of these men would have seemed the easiest of partners. It is hard to imagine either of them suggesting the collaboration, yet one of them must have done so. No one has any evidence how they set about it. Much of the time they were not even at the same university. Hardy talked to me over a period of many years on almost every conceivable subject except the collaboration, although he did say that it had been the major fortune of his creative career.

About his discovery of Ramanujan, he showed no secrecy at all. It was, he wrote, the one romantic incident in his life. One morning early in 1913, there was among the letters on his breakfast table a large untidy envelope decorated with Indian stamps. When he opened it, he found sheets of paper by no means fresh, on which, in a non-English holograph, was line after line of symbols. Hardy glanced at them without enthusiasm. The letter, written in halting English, signed by an unknown Indian, asked him to give an opinion of these mathematical discoveries. The script appeared to consist of theorems, most of them wildor fantastic-looking, one or two already well known, laid out as though they were original. There were no proofs of any kind. Hardy was not only bored but irritated. It seemed like a curious kind of fraud. He put the manuscript aside and went on with his day’s work.

But the Indian manuscript nagged away at the back of his mind. Wild theorems. Theorems such as he had never seen before, nor imagined. A fraud of genius? Or an unknown mathematician of genius? Back in his rooms in Trinity, he had another look at the script. He sent word to Littlewood that they must have a discussion after hall. By nine o’clock or so they were in Hardy’s rooms, with the manuscript stretched out in front of them.

That is an occasion at which one would have liked to be present. Hardy, with his combination of remorseless clarity and intellectual panache (he was very English, but in argument he showed the characteristics that Latin minds have often assumed to be their own); Littlewood, imaginative, powerful, humorous. Apparently it did not take them long. Before midnight they knew and knew for certain. The writer of these manuscripts was a man of genius. That was as much as they could judge that night. It was only later that Hardy decided that Ramanujan was, in terms of natural mathematical genius, in the class of Gauss and Euler, but that he could not expect, because of the defects of his education, and because he had come on the scene too late in the line of mathematical history, to make a contribution on the same scale.

It all sounds easy, the kind of judgment great mathematicians should have been able to make. But Hardy was not the first eminent mathematician to be sent the Ramanujan manuscripts. There had been two before him, both English, both of the highest professional standard, and both had returned the manuscripts without comment. They have both been dead for many years, and I don’t think history relates what they said, if anything, when Ramanujan became famous. Anyone who has been sent unsolicited material will have a sneaking sympathy with them.

Anyway, the following day Hardy went into action. Ramanujan must be brought to England, Hardy decided. Money was not a major problem. Trinity has usually been good at supporting unorthodox talent (the college did the same for Kapitsa a few years later). Once Hardy was determined, no human agency could have stopped Ramanujan, but they needed a certain amount of help from a superhuman one.

Ramanujan turned out to be a poor clerk in Madras, living with his wife on twenty pounds a year. But he was also a Brahman, unusually strict about his religious observances, with a mother who was even stricter. It seemed impossible that he could break the prescriptions and cross the water. Fortunately his mother had the highest respect for the goddess of Namakkal. One morning she made a startling announcement. She had had a dream on the previous night in which she saw her son seated in a big hall among a group of Europeans, and the goddess had commanded her not to stand in the way of her son’s fulfilling his life’s purpose.

Tn 1914 Ramanujan arrived in England. So far as Hardy could detect (though in this respect I should not trust his insight far) Ramanujan, despite the difficulties of breaking the caste proscriptions, did not believe much in theological doctrine, except for it vague pantheistic benevolence, any more than Hardy did himself. But he did certainly believe in ritual. When Trinity put him up in college, Hardy used to find him ritually changed into his pajamas, cooking vegetables rather miserably in a frying pan in his own room.

Their association was a strangely touching one. Hardy did not forget that he was in the presence of genius, but genius that was, even in mathematics, almost untrained. Ramanujan had not been able to enter Madras University because he could not matriculate in English. According to Hardy’s report, he was always amiable and good-natured, but no doubt he sometimes found Hardy’s conversation outside mathematics more than a little baffling. He seems to have listened with a patient smile on his good, friendly, homely face. Even inside mathematics they had to come to terms with the difference in their education. Ramanujan was self-taught; he knew nothing of the modern rigor; in a sense, he didn’t know what a proof was. In fact, Hardy was obliged to teach him some formal mathematics as though Ramanujan had been a scholarship candidate at Winchester.

Hardy said that this was the most singular experience of his life. What did modern mathematics look like to someone who had the deepest insight but who had, literally, never heard of most of it? Together they produced five papers of the highest class, in which Hardy showed supreme originality of his own. Generosity and imagination were for once rewarded in full.

This is a story of human virtue. Once people had started behaving well, they went on behaving better. It is good to remember that England gave Ramanujan such honors as were possible. The Royal Society elected him a Fellow at the age of thirty (which, even for a mathematician, is very young). Trinity also elected him a Fellow in the same year. He was the first Indian to be given either of these distinctions. He was amiably grateful. But he soon became ill. It was difficult in wartime to move him to a kinder climate.

Hardy used to visit him, as he lay dying in hospital at Putney. It was on one of those visits that there happened the incident of the taxicab number. Hardy had gone out to Putney by taxi, as usual his chosen method of conveyance. He went into the room where Ramanujan was lying. Hardy, always inept about introducing a conversation, said, probably without a greeting and certainly as his first remark: “The number of my taxicab was 1729. It seemed to me rather a dull number.” Ramanujan immediately replied: “No, Hardy! No, Hardy! It is a very interesting number. It is the smallest number expressible as the sum of two cubes in two different ways.”

That is the exchange as Hardy recorded it. It must be substantially accurate. He was the most honest of men; and further, no one could possibly have invented it. Ramanujan died of tuberculosis, back in Madras, two years after the war. As Hardy wrote in the Apology, in his roll call of mathematicians: “Galois died at twenty-one, Abel at twenty-seven, Ramanujan at thirty-three, Riemann at forty. . . . I do not know an instance of a major mathematical advance initiated by a man past fifty.”

IF IT had not been for the Ramanujan collaboration, the 1914—1918 war would have been darker for Hardy than it was. But it was dark enough. Like many of his Edwardian intellectual friends, he had a strong feeling for Germany. Germany had, after all, been the great educating force of the nineteenth century. To Eastern Europe, to Russia, to the United States, it was the German universities which had taught the meaning of research. Hardy hadn’t much use for German philosophy or German literature: his tastes were too classical for that. But in most respects the German culture, including its social welfare, appeared to him higher than his own.

So Hardy, like Russell and many of the other Cambridge intelligentsia, did not believe that the war should have been fought. Further, with his ingrained distrust of English politicians, he thought the balance of wrong was on the English side. He could not find a satisfactory basis for conscientious objection; his intellectual rigor was too strong for that. In fact, he volunteered for service under the Derby scheme, and was rejected on medical grounds. But he felt increasingly isolated in Trinity, much of which was vociferously bellicose.

Russell was dismissed from his lectureship, in circumstances of overheated complexity (Hardy was to write the only detailed account of the case a quarter of a century later, in order to comfort himself in another war). Hardy’s close friends were away at the war. Littlewood was doing ballistics as a second lieutenant in the Royal Artillery. Their collaboration was interfered with, though not entirely stopped. It was the work of Ramanujan which was Hardy’s solace during the bitter college quarrels.

I thought he was, for once, less than fair to his colleagues. Some were pretty crazed, as men are in wartime. But some were long-suffering and tried to keep social manners going. After all, it was a triumph of academic uprightness that they should have elected his protégé Ramanujan, at a time when Hardy was barely on speaking terms with some of the electors, and not at all with the others.

Still, he was harshly unhappy. As soon as he could, he left Cambridge. He was offered a chair at Oxford in 1919 and immediately walked into the happiest time of his life. He had already done great work with Ramanujan and Littlewood, but now the collaboration with Littlewood rose to its full power. Hardy was, in Newton’s phrase, “in the prime of his life for invention,” and this came in his early forties, unusually late for a mathematician.

Coming so late, this creative surge gave him the feeling, more important to him than to most men, of timeless youth. He was living the young man’s life, which was first nature to him. He played more tennis, and got steadily better at it. He made a good many visits to American universities and loved the country. He was one of the few Englishmen of his time who was fond, to an extent approximately equal, of the United States and the Soviet Union. He was certainly the only Englishman of his or any other time to write a serious suggestion to the Baseball Commissioners, proposing a technical emendation to one of the rules. The twenties, for him and for most liberals of his generation, was a false dawn. He thought the misery of the war was swept away into the past.

He was at home in New College as he had never been in Cambridge. The warm domestic conversational Oxford climate was good for him. It was there, in a college at that time small and intimate, that he perfected his own style of conversation. There was company eager to listen to him after hall. They could take his eccentricities. He was not only a great and good man, they realized, but an entertaining one. If he wanted to play conversational games, or real games on the cricket field, they were ready to act as foils. In a casual and human fashion, they made a fuss over him.

No one seemed to care — it was a gossipy college joke — that he had a large photograph of Lenin in his rooms. Hardy’s radicalism was somewhat unorganized, but it was real. He had been born, as I have explained, into a professional family: almost all his life was spent among the haute bourgeoisie; but in fact, he behaved much more like an aristocrat, or more exactly, like one of the more romantic projections of an aristocrat. Some of this attitude, perhaps, he had picked up from his friend Bertrand Russell. But most of it was innate. Underneath his shyness, he just didn’t give a damn.

He got on easily, without any patronage, with the poor, the unlucky and diffident, those who were handicapped by race. He preferred them to the people whom he called the large-bottomed; the description was more psychological than physiological, though there was a famous nineteenth-century Trinity aphorism by Adam Sedgwick: “No one ever made a success in this world without a large bottom.” To Hardy the large-bottomed were the confident, boom-imperialist bourgeois English. The designation included most bishops, headmasters, judges, and all politicians, with the single exception of Lloyd George.

Just to show his allegiances, he accepted one public office. For two years (1924-1926) he was president of the Association of Scientific Workers. He said sarcastically that he was an odd choice, being “the most unpractical member of the most unpractical profession in the world.” But in important things he was not so unpractical. He was deliberately standing up to be counted. When, much later, I came to work with Frank Cousins, it gave me a certain quiet pleasure to reflect that I had exactly two friends who had held office in the Trade Union movement, Cousins and G. H. Hardy.

THAT late, not quite Indian, summer in Oxford in the twenties was so happy for Hardy that people wondered that he ever returned to Cambridge, which he did in 1931. I think there were two reasons. First and most decisive, he was a great professional. Cambridge was still the center of English mathematics, and the senior mathematical chair there was the correct place for a professional. Second, and rather oddly, he was thinking about his old age. Oxford colleges, in many ways so human and warm, are ruthless with the old; if he remained at New College, he would be turned out of his rooms as soon as he retired, at the age of sixty-five, from his professorship; whereas if he returned to Trinity, he could stay in college until he died. That is in effect what he managed to do.

When he came back to Cambridge — which was the time that I began to know him — he was in the afterglow of his great period. He was still happy. He was still creative, not so much as in the twenties, but enough to make him feel that the power was still there. He was as spirited as he had been at New College. So we had the luck to see him very nearly at his best.

In the winter, after we had become friendly, we gave each other dinner in our respective colleges once a fortnight. In the summer, it was taken for granted that we should meet at the cricket ground. Except on special occasions, he still did mathematics in the morning, and did not arrive at Fenner’s until after lunch. To complete his pleasure in a long afternoon watching cricket, he liked the sun to be shining and a companion to join in the fun. Technique, tactics, formal beauty — those were the deepest attractions of the game for him. I won’t try to explain them; they are incommunicable unless one knows the language, just as some of Hardy’s classical aphorisms are inexplicable unless one knows the language either of cricket or of the theory of numbers, and preferably both. Fortunately for a good many of our friends, he also had a relish for the human comedy.

He would have been the first to disclaim that he had any special psychological insight. But he was the most intelligent of men, he had lived with his eyes open and read a lot, and he had obtained a good generalized sense of human nature — robust, indulgent, satirical, and utterly free from moral vanity. He was spiritually candid as few men are (I doubt if anyone could be more candid), and he had a mocking horror of pretentiousness, selfrighteous indignation, and the whole stately pantechnicon of the hypocritical virtues.

After one of the short Cambridge seasons, there was a University match. Arranging to meet him in London was not always simple, for he had a morbid suspicion of mechanical gadgets (he never used a watch), in particular of the telephone. In his rooms in Trinity or his flat in St. George’s Square, he used to say, in a disapproving and slightly sinister tone, “If you fancy yourself at the telephone, there is one in the next room.” Once in an emergency he had to ring me up; angrily his voice came at me: “I shan’t hear a word you say, so when I’m finished I shall immediately put the receiver down. It’s important you should come round between nine and ten tonight.” Clonk.

Yet, punctually, he arrived at the University match. There he was at his most sparkling, year after year. Surrounded by friends, men and women, he was quite released from shyness. He was the center of all our attention, which he didn’t dislike. Sometimes one could hear the party’s laughter from a quarter of the way around the ground.

In those last of his happy years, everything he did was light with grace, order, a sense of style. Cricket is a game of grace and order, which is why he found beauty in it. His mathematics, so I am told, had these same aesthetic qualities, right up to his last creative work. I have given the impression, I fancy, that in private he was a conversational performer. To an extent, that was true, but he was also, on what he would have called nontrivial occasions (meaning occasions important to either participant), a serious and concentrated listener. Hardy didn’t suck impressions and knowledge out of other’s words as Lloyd George did, but his mind was at one’s disposal. When, years before I wrote it, he heard of the concept of The Masters, he cross-examined me, so that I did most of the talking. He produced some good ideas. I wish he had been able to read the book, which I think he might have liked. Anyway, in that hope I dedicated it to his memory.

THROUGH the thirties he lived his own version of a young man’s life. Then suddenly it broke. In 1939 he had a coronary thrombosis. He recovered, but real tennis, squash, the physical activities he loved were over for good. The war darkened him still further, just as the First War had. To him they were connected pieces of lunacy, we were all at fault; he couldn’t identify himself with the Second World War — once it was clear the country would survive — any more than he had done in 1914. One of his closest friends died tragically. And — I think there is no doubt these griefs were interconnected — his creative powers as a mathematician at last in his sixties left him.

That is why A Mathematician’s Apology is, if read with the textual attention it deserves, a book of such haunting sadness. Yes, it is witty and sharp, with intellectual high spirits: yes, the crystalline clarity and candor are still there; yes, it is the testament of a creative artist. But it is also, in an understated stoical fashion, a passionate lament for creative powers that used to be and that will never come again. I know nothing like it in the language, partly because most people with the literary gift to express such a lament don’t come to feel it: it is very rare for a writer to realize, with the finality of truth, that he is absolutely finished.

Seeing him in those years, I couldn’t help thinking of the price he was paying for his young man’s life. It was like seeing a great athlete, for years in the pride of his youth and skill, so much younger and more joyful than the rest of us. suddenly have to accept that the gift has gone. Hardy recovered enough physically to have ten minutes batting at the nets, or to play his pleasing elaboration (with a complicated set of bisques) of Trinity bowls. But he was often just plain bored.

I wasn’t much help to him in those last years. I was deeply involved in wartime Whitehall; I was preoccupied and often tired; it was an effort to get to Cambridge. But I ought to have made the effort more often than I did. I have to admit, with remorse, that there was not exactly a chill, but a gap in sympathy, between us. He lent me his flat in Pimlico — a dark and seedy flat with the St. George’s Square gardens outside and what he called an “old brandy” attractiveness — for the whole of the war. But he didn’t like my being so totally committed. People he approved of oughtn’t to give themselves wholeheartedly to military functions. He never asked me about my work. He didn’t want to talk about the war. While I, for my part, was impatient and didn’t show anything like enough consideration. After all, I thought, I wasn’t doing this job for fun; as I had to do it, I might as well extract the maximum interest. But that is no excuse.

At the end of the war I did not return to Cambridge. I visited him several times in 1946. His depression had not lifted; he was physically failing, short of breath after a few yards’ walk. He was glad that I had gone back to writing books: the creative life was the only one for a serious man. As for himself, he wished that he could live the creative life again; his own life was over.

In the early summer of 1947 I was sitting at breakfast when the telephone rang. It was Hardy’s sister: he was seriously ill, would I come up to Cambridge at once, would I call at Trinity first? At the time, I didn’t grasp the meaning of the second request. But I obeyed it, and in the porter’s lodge at Trinity that morning found a note from her: I was to go to Donald Robertson’s rooms; he would be waiting for me.

Donald Robertson was Professor of Greek and an intimate friend of Hardy’s; he was another member of the same high, liberal, graceful Edwardian Cambridge. Incidentally, he was one of the few people who called Hardy by his Christian name. He greeted me quietly. Outside the windows of his room it was a calm and sunny morning. He said, “You ought to know that Harold has tried to kill himself.”

Yes, he was out of danger; he was for the time being all right, if that was the phrase to use. But Donald was, in a less pointed fashion, as direct as Hardy himself. It was a pity the attempt had failed. Hardy’s health had got worse: he could not in any case live long; even walking from his rooms to hall had become a strain. He had made a completely deliberate choice. Life on those terms would not endure; there was nothing in it. He had collected enough barbiturates; he had tried to do a thorough job, and had taken too many.

In the Evelyn nursing home, Hardy was lying in bed. As a touch of farce, he had a black eye. Vomiting from the drugs, he had hit his head on the lavatory basin. He was self-mocking. He had made a mess of it. Had anyone ever made a bigger mess? i had to enter into the sarcastic game. I had never felt less like sarcasm, but I had to play. I talked about other distinguished failures at bringing off suicide. What about German generals in the last war? Beck, Stülpnagel, they had been remarkably incompetent at it. It was bizarre to hear myself saying these things. Curiously enough, it seemed to cheer him up.

After that, I went to Cambridge at least once a week. I dreaded each visit, but early on he said that he looked forward to seeing me. He talked a little, nearly every time I saw him, about death. He wanted it; he didn’t fear it; what was there to fear in nothingness? His hard intellectual stoicism had come back. He would not try to kill himself again. He was prepared to wait.

Mostly, though — about fifty-five minutes in each hour I was with him — I had to talk cricket. It was his only solace. I had to pretend a devotion to the game which I no longer felt, which in fact had been lukewarm in the thirties except for the pleasure of his company. Now I had to study the cricket scores as intently as when I was a schoolboy. He couldn’t read for himself, but he would have known if I had been bluffing. Sometimes, for a few minutes, his old vivacity would light up. But if I couldn’t think of another question or piece of news, he would lie there, in the kind of dark loneliness that comes to some people before they die.

It was hard enough for me to have to talk cricket. It was harder for his sister, a charming intelligent woman who had never married and who had spent much of her life looking after him. With a humorous skill not unlike his own old form, she collected every scrap of cricket news she could find, though she had never learned anything about the game.

Once or twice the sarcastic love of the human comedy came bursting out. Two or three weeks before his death, he heard from the Royal Society that he was to be given their highest honor, the Copley Medal. He gave his Mephistophelian grin, the first time I had seen it in full splendor in all those months. “Now I know that I must be pretty near the end. When people hurry up to give you honorific things there is exactly one conclusion to be drawn.”

After I heard that, I think I visited him twice. The last time was four or five days before he died. There was an Indian test team playing in Australia, and we talked about them.

It was in that same week that he told his sister, “If I knew that I was going to die today, I think I would still want to hear the cricket scores.” He managed something very similar. Each evening that week before she left him, she read a chapter from a history of Cambridge University cricket. One such chapter contained the last words he heard, for he died suddenly, in the early morning.