One day in 1939, while dusting his bookcase, Hardy had his first heart attack. He was sixty-two at the time. In its wake, he could no longer play tennis, or squash, or cricket. His creativity waned. One listing of his most important papers (it included every one of those on which he had worked with Ramanujan) included none beyond 1935. Now, his output declined by even a crude quantitative yardstick—from half a dozen or so per year in the late 1930s to one or two per year.
His waning mathematical powers depressed him. So did the new war with Germany. But around 1941, when young Freeman Dyson came up to Cambridge from Hardy’s old school, Winchester, and for two years attended his lectures, Dyson couldn’t see it. To him Hardy was still a god. He and three other advanced students all sat around a table in a small room in the old Arts School, listened, and watched Hardy from a few feet away:
He lectured like Wanda Landowska playing Bach, precise and totally lucid, but displaying his passionate pleasure to all who could see beneath the surface… . Each lecture was carefully prepared, like a work of art, with the intellectual denouement 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.
Hardy retired from the Sadleirian Chair in 1942.
The year before, a photographer for the British magazine Picture Post snapped his picture at a rugby match. There he was on a chilly winter day, cigarette in hand, all rolled up in flannels, watching Cambridge defeat Oxford, 9 to 6. The photograph later appeared in one of the volumes of his collected papers. His sister didn’t like it. “It makes him look so old,” she said.
But he was old.
By 1946, he was virtually an invalid. Snow pictured him as “physically failing, short of breath after a few yards’ walk.” His sister came to nurse him (though the Trinity rules were so strict that she had to leave his rooms at night).
In early 1947, he tried to kill himself by swallowing barbiturates. But he took so many that he vomited them up, hit his head on the lavatory basin, and wound up with an ugly black eye for his trouble.
Later that year, the Royal Society notified him that he was to receive its highest honor, the Copley Medal. “Now I know that I must be pretty near the end,” he told Snow. “When people hurry up to give you honorific things there is exactly one conclusion to be drawn.”
On November 24, Snow wrote his brother Philip: “Hardy is now dying (how long it will take no one knows, but he hopes it will be soon) and I have to spend most of my spare time at his bedside.”
It was soon. Hardy died on December 1, 1947, the day he was to be presented the Copley Medal. He left his substantial savings and the royalties of his books, once having provided for his sister, to the London Mathematical Society. “His loss,” wrote Norbert Wiener, “brought us the sense of the passing of a great age.”
• • •
The 1939 heart attack began the long physical and emotional slide that led to his suicide attempt. And it was in its wake, about a month after France fell to the Nazis, that he put the finishing touches to A Mathematician’s Apology, his paean to mathematics. Snow saw the Apology “as a book of haunting sadness,” the work of a man long past his creative prime—and knowing it. “It is a melancholy experience for a professional mathematician to find himself writing about mathematics,” wrote Hardy. Painters despised art critics? Well, the same went for any creative worker, a mathematician included. But writing about mathematics, rather than doing it, was all that was left him.
And yet, the sadness is at the prospect of a rich, full life nearing its end, not bitterness at a life ill-spent. Pride runs through the Apology, too, and pleasure, and deep satisfaction.
I still say to myself when I am depressed, and find myself forced to listen to pompous and tiresome people, “Well, I have done one thing you could never have done, and that is to have collaborated with both Littlewood and Ramanujan on something like equal terms.”
Ramanujan. All these twenty years later, Ramanujan remained part of him, a bright beacon, luminous in his memory.
“Hardy,” said Mary Cartwright, his student during the 1920s and whom Hardy would describe as the best woman mathematician in England, “practically never spoke of things about which he felt strongly.” Yet at one remove from his listener, on the printed page, he became a little freer. And there he revealed Ramanujan’s hold on him: “I owe more to him,” he wrote, “than to any one else in the world with one exception [Littlewood?] and my association with him is the one romantic incident in my life.”
In the years after his death, Hardy began rummaging through Ramanujan’s papers and notebooks. That, as many other mathematicians were to learn, could be tough going. After arriving in Oxford, Hardy wrote Mittag-Leffler that he had prepared a short paper from Ramanujan’s manuscripts, “but it was hardly substantial enough for the Acta [the journal Mittag-Leffler edited]. I am now trying to make a more important one. But it is not possible to do it very rapidly, as all of Ramanujan’s work requires most careful editing.”
By 1921, he had culled from Ramanujan’s papers enough to prepare a sequel to Ramanujan’s work on congruence properties of partitions. The manuscript from which he was working, Hardy wrote in a note appended to the paper, which appeared in Mathematische Zeitschrift, “is very incomplete, and will require very careful editing before it can be published in full. I have taken from it the three simplest and most striking results, as a short but characteristic example of the work of a man who was beyond question one of the most remarkable mathematicians of his time.”
Hardy’s own papers over the years were fairly littered with Ramanujan’s name: “Note on Ramanujan’s Trigonometrical Function cq(n) and Certain Series of Arithmetical Functions” appeared in 1921; “A Chapter From Ramanujan’s Notebook” in 1923; “Some Formulae of Ramanujan” in 1924. Then more in the mid-1930s: “A Formula of Ramanujan in the Theory of Primes”; “A Further Note on Ramanujan’s Arithmetical function τ(n).” Hardy appreciated the debt he owed Ramanujan and Littlewood: “All my best work,” he wrote, “has been bound up with theirs, and it is obvious that my association with them was the decisive event of my life.”
Hardy was thirty-seven when he met Ramanujan, living out his boyhood dream as a Fellow of Trinity, already an F.R.S. But his collaboration with Littlewood had only just begun, and he would come to view his early contribution to mathematics, though formidable by standards other than his own, as unspectacular.
Then, abruptly, Ramanujan entered his life.
Ramanujan was, if nothing else, a living, breathing reproach to the Tripos system Hardy despised. Sheer intuitive brilliance coupled to long, hard hours on his slate made up for most of his educational lacks. And he was so devoted to mathematics that he couldn’t bother to study the other subjects he needed to earn a college degree. This “poor and solitary Hindu pitting his brains against the accumulated wisdom of Europe,” as Hardy called him, had rediscovered a century of mathematics and made new discoveries that would captivate mathematicians for the next century. (And all without a Tripos coach.)
Is it any wonder Hardy was beguiled?
From then on, over the next thirty-five years, Hardy did all he could to champion Ramanujan and advance his mathematical legacy. He encouraged Ramanujan. He acknowledged his genius. He brought him to England. He trained him in modern analysis. And, during Ramanujan’s life and afterward, he placed his formidable literary skills at his service.
“Hardy wrote exquisite English,” the Manchester Guardian would say of him, citing especially his obituary notice of Ramanujan as “among the most remarkable in the literature about mathematics.” To mathematician W. N. Bailey, it was “one of the most fascinating obituary notices that I have ever read.” And it was Hardy’s book on Ramanujan, more than anything he knew about him otherwise, that convinced Ashis
Nandy to make Ramanujan a prime subject of his own book. Hardy’s pen fired the imagination, shaping Ramanujan’s reception by the mathematical world.
It began in 1916, when Hardy reported to the university authorities in Madras on Ramanujan’s work in England; one look at it and they asked that it be prepared for publication. In it, Hardy wrote of the “curious and interesting formulae” Ramanujan had in his possession, of how Ramanujan possessed “powers as remarkable in their way as those of any living mathematician,” that his gifts were “so unlike those of a European mathematician trained in the orthodox school,” that his work displayed “astonishing individuality and power,” that in Ramanujan “India now possesses a pure mathematician of the first order.” This was scarcely the sort of language apt to pass unnoticed among mathematicians, Indian or British, accustomed to the sort of flat, gray prose normally appearing in their journals. Someone once said of Hardy that “conceivably he could have been an advertising genius or a public relations officer.” Here was the evidence for it.
Hardy’s long obituary of Ramanujan appeared first in the Proceedings of the London Mathematical Society in 1921, a little later in the Proceedings of the Royal Society, then again in Ramanujan’s Collected Papers in 1927. In it, he told Ramanujan’s story. He invested it with feeling. His language lingered in memory. “One gift [Ramanujan’s work] has which no one can deny,” he concluded—“profound and invincible originality.”
He would probably have been a greater mathematician if he had been caught and tamed a little in his youth; he would have discovered more that was new, and that, no doubt, of greater importance. On the other hand he would have been less of a Ramanujan, and more of a European professor, and the loss might have been greater than the gain.
Snow, who first met Hardy in 1931, revealed that for all Hardy’s shyness, “about his discovery of Ramanujan, he showed no secrecy at all.” Mary Cartwright recalled that “Hardy was terribly proud, and rightly, of having discovered Ramanujan.” Ramanujan had enriched his life. He didn’t want to forget Ramanujan, and he didn’t.
On February 19, 1936, Hardy wrote S. Chandrasekhar from Cambridge: “I am going to give some lectures (here and at Harvard) on Ramanujan during the summer.” They would become the basis for Ramanujan: Twelve Lectures on Subjects Suggested By His Life and Work. “A labor of love,” one reviewer called it.
The Harvard lecture was part of the great university’s celebration of the three-hundredth anniversary of its founding. The bash culminated in three grand Tercentenary Days, from September 16 to 18. Harvard Yard, now a great outdoor theater with seventeen thousand seats, was awash with silk hats, crimson bunting, and colorful academic costumes. On the second evening, at 9:00 P.M., upward of half a million people lined both banks of the Charles River for two hours of fireworks.
The following morning, under a steady drizzle and dark, brooding clouds (the leading edge of a hurricane moving up the Atlantic Coast), sixty-two of the world’s most distinguished biologists, chemists, anthropologists, and other scholars received honorary degrees. They marched in a procession from Widener Library and took their places on stands erected in front of the pillars of Memorial Church at the yard’s north end. Psychoanalyst Carl Jung was among them. So was Jean Piaget, the pioneer student of child development. So was English astrophysicist Sir Arthur Eddington. So was Hardy. The citation honoring him, slipped within the red leather presentation book stamped with Harvard’s Veritas seal, called him “a British mathematician who has led the advance to heights deemed inaccessible by previous generations.”
During his stay at Harvard, Hardy was put up at the house of a prominent lawyer, who later became a United States senator. Both he and his host, according to one account, were worried: whatever would they talk about? “The lawyer was no better prepared to discuss Zeta functions than the mathematician to comment upon the rule in Shelley’s case.” So they seized on their common enthusiasm—baseball. The Red Sox were in town, and Hardy was at Fenway often to watch them.
In the weeks prior to the grand finale, a Tercentenary Conference of Arts and Sciences brought to Harvard more than twenty-five hundred scholars for lectures under broad rubrics of knowledge like “The Place and Functions of Authority,” and “The Application of Physical Chemistry to Biology.” Einstein’s wife was ill, so he sent word that he couldn’t come. Nor could Werner Heisenberg, author of the uncertainty principle, who was advised at the last minute that he was needed for eight weeks’ service in Hitler’s army. Their absence notwithstanding, it was an august group, including no fewer than eleven Nobel Prize winners. “Highbrows at Harvard,” Time headed its account. The New York Times covered some of the public lectures, including Hardy’s.
At about nine in the evening of the conference’s first day, Hardy—wizened, gray, and almost sixty now—rose before his audience in New Lecture Hall. “I have set myself a task in these lectures which is genuinely difficult,” he told them, in the measured cadences that were the mark of his speech and of his prose.
and which, if I were determined to begin by making every excuse for failure I might represent as almost impossible. I have to form myself, as I have never really formed before, and to try to help you to form, some sort of reasoned estimate of the most romantic figure in the recent history of mathematics; a man whose career seems full of paradoxes and contradictions, who defies almost all the canons by which we are accustomed to judge one another, and about whom all of us will probably agree in one judgment only, that he was in some sense a very great mathematician.
And then Hardy, the memory still fresh of the day a quarter century before when an envelope stuffed with formulas arrived in the mail from India, began to tell about his friend, Ramanujan.
The passport photo. Ramanujan in 1919, on his way back to India. “He looks rather ill,” G. H. Hardy wrote when he first saw the photo in 1937, “but he looks all over the genius he was.” Master and Fellows of Trinity College, Cambridge
Komalatammal, Ramanujan’s mother, and the decisive influence on him in his youth. No photo of K. Srinivasa Iyengar, Ramanujan’s father, is known to exist. Ragami’s Collections, Madras, South India
Ramanujan’s house, on Sarangapani Sannidhi Street, Kumbakonam, South India. Once, while in high school, he found that a formula he had thought original with him actually went back 150 years. Mortified, he hid the paper on which he had written it in the roof of the house. Ragami’s Collections, Madras, South India
A recent photo of the pial, or front porch, of Ramanujan’s house in Kumbakonam. Here he would sit for hours and work on mathematics while his friends played in the street.
Ramanujan scored high on this examination, which he took when he was nine. But later, once he discovered mathematics and lost interest in all else, he regularly failed his exams. (Here, the English spelling of his Tamil name was rendered as Ramanujam.) Ragami’s Collections, Madras, South India
A recent photo of the Sarangapani Temple, just up the street from Ramanujan’s house, which is visible on the right.
At Town High School, in his hometown of Kumbakonam, Ramanujan was still a conventionally good student, earning prizes and winning praise from his elders. Here, the school’s campus in a recent photograph.
They call it Ramanujan Hall today, in honor of Town High School’s most distinguished alumnus. The “m” at the end reflects how Ramanujan’s Tamil name often gets transliterated into English. It was under this spelling that it first appeared in Indian mathematical journals.
S. Tirunarayanan, born in 1905 when Ramanujan was 17. His older brother would tease him, carry him on his shoulders, tell him stories. Ragami’s Collections, Madras, South India
Janaki, Ramanujan’s wife, in a picture taken after Ramanujan’s death. As a widow, and mostly cut off from Ramanujan’s family, she supported herself as a seamstress. Ragami’s Collections, Madras, South India
Narayana Iyer, Ramanujan’s immediate boss at the Madras Port Trust, one of his most ardent champions, and himself a fine math
ematician. When the two worked on mathematics, often until late into the night, Ramanujan’s penchant for collapsing many steps into one left him dazed. “You must descend to my level of understanding,” he would complain. Ragami’s Collections, Madras, South India
P. V. Seshu Iyer. One of Ramanujan’s mathematics teachers at Government College in Kumbakonam and later one of his supporters. But one friend recalled Ramanujan complaining that Seshu Iyer, like everyone else, had at first been “indifferent” to him and his work. Ragami’s Collections, Madras, South India
After Ramanujan married, he scoured South India for a job or a patron, his friends often putting him up for a while. One night, while staying with a friend at Victoria Hostel in Madras, shown here in a recent photo, he compared his impoverished lot to that of Galileo, persecuted by the Inquisition and misunderstood in his own time.
Soon after Ramanujan received his first encouraging letter from Hardy in Cambridge, he was named research scholar at the University of Madras. Freed from money worries for the first time in his life, he would come here, to the Connemara Library, seen here in a recent photo, and lose himself in mathematics.
Shrine to the goddess Namagiri, Ramanujan’s family deity, in a recent photo. It was here in the South Indian town of Namakkal that Ramanujan came in late 1913 with Narayana Iyer. He stayed on the temple grounds for three nights and by the end had resolved to go to England, in defiance of Hindu tradition.
E. W. Hobson (previous) and H. F. Baker. Both were eminent Cambridge mathematicians. Both received Ramanujan’s appeals for help. Both dismissed them. Master and Fellows of Trinity College, Cambridge
The Man Who Knew Infinity Page 47
