The Man Who Knew Infinity

by Robert Kanigel

  • • •

  On February 11, ending a period of silence that had extended over more than a year, Ramanujan wrote his family in India. About this same time, perhaps a little earlier, during a period when he was briefly away from Matlock, he tried to kill himself.

  Today in London, you can buy T-shirts, posters, mugs, and other souvenirs emblazoned with the great labyrinthine grid that represents the London Underground, with its dozen or more distinct lines and hundreds of stations. One day in January or February of 1918, it was at a station somewhere in this network, then smaller and newer, that Ramanujan threw himself onto the tracks in front of an approaching train.

  What happened next would be easy enough to read as a miracle. A guard spotted him do it and pulled a switch, bringing the train screeching to a stop a few feet in front of him. Ramanujan was alive, though bloodied enough to leave his shins deeply scarred.

  He was arrested and hauled off to Scotland Yard. Called to the scene, Hardy, marshaling all his charm and academic stature, made a show of how there, before the police, stood the great Mr. Srinivasa Ramanujan, a Fellow of the Royal Society, and how a Fellow of the Royal Society simply could not be arrested.

  In fact, Ramanujan was not an F.R.S. He would hardly have been immune from arrest in any case, and the police were not fooled for a minute. But they investigated, learned Ramanujan was indeed reputed to be an eminent mathematician, and decided to let him go. “We in Scotland Yard did not want to spoil [his] life,” the officer in charge of the case said later.

  Just what triggered Ramanujan’s desperate bound onto the tracks doesn’t come down to us. Certainly, though, if the mere refusal of his dinner guests to accept a third helping could foment such a storm of shame in him that he had to get up and leave, deeper humiliation might spark action more precipitous still. And in 1917 he had certainly experienced his share of it. Rejected by Trinity. Seemingly abandoned by his wife. Left sick and dependent in the sanatorium, helpless even to command the food he wanted. Unable to produce the work he felt his friends expected of him. Confronted by the knowledge that much of his past work had been rediscovery and, viewed blackly enough, a waste of time.

  And for the feelings all this stirred in him, there was no safety valve, at least not among his English friends. Littlewood was gone. So was Neville; he’d lost his Trinity fellowship in 1917, probably due to his antiwar views, and was off in London. Hardy, meanwhile, was no one with whom he felt relaxed enough to bare his soul.

  More than likely, he did not deliberately set out to kill himself. It was doubtless a rash act, spurred by some new humiliation, unknown to us today, piled on top of all the others. Once again, Ramanujan had acted impetuously when overcome with shame.

  • • •

  Late in February, back at Matlock, Ramanujan learned of his election, on the eighteenth, to the Cambridge Philosophical Society. This was not so much an honor as just one small legitimization of his stature in the scientific world.

  About ten days later, he received a telegram from Hardy, sent from Piccadilly in London.

  He read the telegram once.

  He read it a second time.

  He read it again, the words still congealing in his mind, making no sense: Hardy was advising him of what he already knew, that he had been elected to the Philosophical Society. Which was fine, of course. But he already knew as much. What was Hardy’s point in wiring him?

  Once more he read the telegram, and this time, finally, a new word exploded from the page. It was not the Philosophical Society to which Hardy was advising him he had been named a fellow, but the Royal Society.

  Of 104 candidates for election that year, he was 1 of just 15 elected. “My words are not adequate to express my thanks to you,” he wrote Hardy. “I did not even dream of the possibility of my election.” In May, he would become S. Ramanujan, F.R.S.

  India, which soon heard the news, was thrilled. On March 22, the Madras members of the Indian Mathematical Society wrote Hardy in thanks “for the aid and guidance you have been extending to Mr. S. Ramanujan in his work.” In a postscript, P. V. Seshu Iyer added his personal thanks for the “care you have been bestowing on him during these months when his health has not been good.”

  By May, Ramanujan’s health was still poor. He wrote the Royal Society from Matlock on the seventeenth that he was, just then, too sick to travel to London for his formal admission into the society.

  • • •

  Around this time, he heard from A. S. Ramalingam, the South Indian engineer he’d met, just off the boat from India, at the Cromwell Road reception center. Soon after the declaration of war, Ramalingam had joined the army and in early 1916 had begun work at a shipyard in Jarrow, in the north of England almost in Scotland. Since 1914, the two men had not been in touch. But now, perhaps learning of the Royal Society election, he wrote Ramanujan through Hardy. Hearing nothing in reply, he wrote Hardy directly, learned of Ramanujan’s condition, and wrote Ramanujan at Matlock. Ever the engineer, Ramalingam was nothing if not persevering.

  So, apparently, was his whole family. In one of his letters home he had mentioned food rationing. That was all it took. For two months, they had been showering him with South Indian food. Finally, he cabled home, “Stop sending food.” By now he had parcel upon parcel of it, all piled up. Maybe, he wrote Ramanujan now, he might like to share in the booty?

  Ramanujan wrote back asking for some ghee, the special butter, clarified by boiling to resemble oil, and some spicy Madras-style foods. These Ramalingam promptly sent. One thing led to another, and soon, on Sunday, June 16, Ramalingam was visiting him at Matlock, where he stayed until after lunch on Tuesday. For three days they talked—of the war, of Christian missions, of conditions in India, and of much else. Ramalingam had heard Ramanujan’s mental state was impaired, but saw no evidence for it now.

  His physical state, though, was another story. “I was shocked and horrified,” he wrote Hardy after returning to Jarrow a few days later, “to find him in the thin, weak and emaciated state I found him in.” His illness, the suicide attempt, his food problems at Matlock, had taken their toll.

  Ramalingam’s letter went on for twelve large lined pages documenting Ramanujan’s condition, recording the views of his doctors, detailing his meal schedule, and suggesting improvements to his care. But in all its length, there is nothing like “As you are doubtless aware … ,” or “As Ramanujan may have told you … ,” or “As you may have learned from Ramanujan when you saw him last… .” Nothing he’d learned from Ramanujan during the three days gave Ramalingam reason to abridge his letter in the slightest, or to intimate that anything in it might already be known to Hardy. Rather, it reads like a middle manager’s report intended for a high executive presumed to lack all detailed knowledge of the subject.

  Ramalingam’s letter, long as it was, had a clear focus. “It is with regard to food that I have to write somewhat harshly and tersely and at a good length,” Ramalingam wrote. Ramanujan, he as much as said, was killing himself by slow starvation.

  • • •

  Diet was a big part of any sanatorium “cure.” Tuberculosis patients were called “consumptives” because the disease consumed them. Almost invariably, weight loss went with it, and one prevalent notion held that fattening up the patient could slow or reverse the disease’s course.

  For breakfast, Matlock tried to feed Ramanujan scrambled eggs on toast, with tea. For lunch, rice, chilies, and mustard fried in butter, cucumber and lemon and, sometimes, green peas. Whatever it was, it was awful, the cooks regularly botching things. Ramanujan wrote Ramalingam the day after his friend left, complaining that the new cook had ruined the appalappu, rice flour fried in oil or ghee; she’d burned some, while leaving others raw. “The curried rice,” he complained, spelling out the word in Tamil, “was just like akshata”—raw rice, used only on ritual occasions, and not meant to be eaten. Boiled rice: the poor woman couldn’t even get that right.

  Despite its priority claim on rationed
foods, the sanatorium couldn’t seem to procure some foods Ramanujan liked. Like bananas. Or cheese, for the macaroni and cheese he enjoyed; Ramalingam later sent him some. Butter, meanwhile, was so expensive in the wake of wartime price hikes that the Matlock administration grumbled about frying his potatoes in it.

  Something, Ramalingam could see, had to give. While at the sanatorium, he asked if he could cook something for his friend. “No, you can’t go to the kitchen,” he was told. Could he write out a recipe and have the cook follow it? This suggestion, too, met resistance.

  Sanatoriums, of course, were used to food complaints and typically dismissed them as manifestations of disease. Tuberculosis patients were supposed to be especially finicky. One whose complaint reached the Ministry of Health, for example, was written off as suffering from “the warped temperament occasionally found associated with his malady which makes him impatient and discontented with institution discipline.”

  The real problem, Ramalingam could see, was Ramanujan’s stubbornness. “He is thinking of his vegetarianism even at the expense of his health and life,” he wrote Hardy. “But one cannot but think of him as cranky and headstrong when he refuses cream and, say, plums on it.” Writing to Ramanujan the same day, he minced no words:

  I will have to be a bit harsh with you. Both from my talk with Dr. Ram and after my second thoughts, I am impressed with your being so particular about your palate. Well, you will have to choose between … controlling your palate and killing yourself. You must try and get yourself to like porridge or oatmeal, cream, etc. My friends have strongly advised me not to let you indulge in pickles and chillies… .

  I am not going to the extremes and asking you to take beef tea or Bovril [trade name of a concentrated beef extract] though considering your life, my asking you to take such a thing is quite excusable, nay desirable, and even unavoidable. Be reasonable and don’t be bigoted.

  If there was a time to relax his vegetarianism, this was it. Orthodox Jews, who also proscribe certain foods, may relax the laws of kashrut when otherwise health would be impaired. But Brahminical practice makes no such dispensation, and Ramanujan was not about to make one either.

  Sometime before, probably even before entering Matlock, Ramanujan was enjoying one of his occasional spells out of hospital and staying at a lodging house catering to Indians in London. At breakfast, he drank a commercial beverage, Ovaltine, represented to him as vegetarian. Later that day, idly examining the can, he saw listed among its ingredients some trace of animal product. Mortified, he had to get out of there. Abruptly, he packed his bags and was out the door; it was Vizagapatnam and the Chatterji dinner all over again.

  This time, as he neared Liverpool Street Station to catch the train for Cambridge, tons of bombs from silent, high-flying German zeppelins came raining down on the city. This was likely the raid of October 19, 1917, in which twenty-seven people were killed. One bomb fell behind a row of working-class cottages, destroying three of them, killing four women and eight children. Yet Ramanujan felt he was being personally punished for drinking the Ovaltine. Later, writing the landlady to explain his precipitous departure, he pictured the raid, in the words of a friend who heard the story later, as “punishment meted out to him by God for having partaken of anything non-vegetarian.”

  If anything, Ramanujan had become even more finicky. At one point he’d been on a diet largely of bread and milk; now he would no longer eat them. Nor would he eat Matlock’s porridge. He demanded only South Indian food.

  “Be reasonable,” Ramalingam had written him. But any temptation to be “reasonable” ran hard up against the unsavory reality of English cooking. Even those of Ramanujan’s Indian friends less particular than he, or who had forsaken vegetarianism altogether, could have told Ramanujan what all Europe knew—that English food was heavy, ill prepared, maddeningly bland, and monotonous. When Gandhi, also a vegetarian, came to England a generation earlier, he wrote that “even the dishes that I could eat were tasteless and insipid.” As for Ramanujan, Neville would recall: “I have known him ask with unaffected apologies if he might make his meal of bread and jam because the vegetables offered to him were novel and unpalatable.”

  After his Matlock visit, something Dr. Kincaid had said gnawed at Ramalingam’s composure. Ramanujan, the doctor assured him, could eat anything he liked, even spicy pickles and chilies. Yet it was Ramalingam’s understanding that tuberculosis patients should not get foods like that—unless, that is, they were dying. He wrote Hardy:

  When the patient has gone too far to be remedied, and when it is a question of only a few weeks or months, it matters little [what he eats], as long as the patient feels happy and comfortable in the last days of his life. In permitting me to give anything to Ramanujan to eat, is this the object of Dr. Kincaid?

  It is anguishing and breaking one’s heart to feel that Ramanujan, with his wonderful capabilities and valuable contributions, should be given up for such as hopeless. War with all its horrors might have made us callous to the wholesale slaughter and loss of lives but surely should Ramanujan be given up?

  11. SLIPPED FROM MEMORY

  In the fall of 1918, Ramanujan’s name was once again put in for a Trinity fellowship. Hardy, apparently too closely identified with Ramanujan by now and long embroiled in Trinity politics, was this time discouraged from putting up his name. So Littlewood (who was for a time back in Cambridge, done in by overwork and a concussion) did instead. The racial issue flared. One foe of Ramanujan’s candidacy, Littlewood wrote later, “went about openly saying that he wasn’t going to have a black man as Fellow.”

  Word of the suicide attempt had gotten around, and Ramanujan’s opponents seized on it. Didn’t the college bylaws expressly require good mental health? And wasn’t a suicide attempt evidence that Ramanujan lacked it? “Grave doubts were being felt about his mental state,” Littlewood’s friend and former Tripos coach, R. A. Herman, told him.

  So Littlewood, who was himself too ill to show up in person, wrote a report taking on the rumors and furnishing two medical certificates to the effect that Ramanujan was indeed mentally sound.

  “This evidently shocked the moderate members of the Election Committee,” Littlewood wrote later, “and it was moved and passed that they be not read.” The election could now proceed on the merits of Ramanujan’s case. Of course, Ramanujan had a most emphatic argument in his favor—the three letters that now graced his name. For a Fellow of the Royal Society to be denied a Trinity fellowship would be a scandal. “You can’t reject an F.R.S.,” Littlewood told Herman, who opposed Ramanujan. “Yes,” Herman replied, “we thought that was a dirty trick.” Littlewood, we may imagine, just smiled.

  By now, Ramanujan was out of Matlock. Ramalingam had written Hardy of Ramanujan’s wish to leave it and go to London, where he could get Indian food more easily and, perhaps, receive visitors more conveniently. Ramalingam didn’t think that was a good idea. What about the air raids? He suggested instead that Ramanujan go to southern Italy, or the south of France, where the climate might do him good, or at least some place in England less prone to attack.

  But Ramanujan got his way and now, learning of the Trinity fellowship, was a patient at a small hospital overlooking a perfectly proportioned little square in the heart of London, on which George Bernard Shaw had lived in the 1890s and Virginia Woolf for four years until 1911. Fitzroy House was a grand five-story townhouse with an oval winding staircase punched up through its center and a massive front door reminiscent of a castle gate. While there, Ramanujan saw several specialists, but his diagnosis remained as uncertain as ever. Bouts of high fever still came in irregular bursts. He had pain no one could trace. He was on tap for a tooth extraction around this time, and one doctor even attributed all his pain to that.

  “My heartfelt thanks for your kind telegram,” Ramanujan wrote Hardy from Fitzroy House when he got the good news. “After your success in getting me elected by the Royal Society my election at Trinity probably became very much less diffic
ult this year.”

  He wrote that letter on a Friday, probably October 18. The following Monday, still elated, he wrote Hardy: “Please tell Mr. Littlewood and Major MacMahon that I thanked them very much. Had it not been for your pains and their encouragement, I would be neither the fellow of the one nor that of the other.” Then he asked for some details about his fellowship.

  That was paragraph one. Paragraph two began: “I have considered more or less exhaustively about the congruency of p(n) and in general that of pr(n) … by four different methods”—the first of which bore on a result that, he added, “you are publishing now… .”

  As Hardy had foreseen, the honors accorded him, especially the F.R.S., had lifted Ramanujan’s spirits—leading to what Neville would term “a brief period of brilliant invention” beginning about the spring of 1918. The paper Ramanujan mentioned, delivered to the Cambridge Philosophical Society two weeks before, represented its fullest flowering.

  • • •

  “A recent paper by Mr. Hardy and myself,” it began, referring to their joint work on partitions published earlier that year

  contains a table calculated by Major MacMahon, of the values of p(n), the number of unrestricted partitions of n, for all values of η from 1 to 200. On studying the numbers in this table I observed a number of curious congruence properties, apparently satisfied by p(n). Thus

  (1) p(4), p(9), p(14), p(19), … ≡ 0 (mod 5),

  (2) p(5), p(12), p(19), p(26), … ≡ 0 (mod 7),

  and so on, right down the page.

  The paper was entitled “Some Properties of p(n), the Number of Partitions of n,” and what made it important was that until now most “properties” of the partition function had eluded discovery. The number of partitions, p(n), recall, refers to how many ways you can add up numbers to get n. But of even such basic facts as, for example, whether the partition function was odd or even for a particular n, mathematicians remained ignorant.