The Man Who Knew Infinity

by Robert Kanigel

  exploratory surgery [for gastric ulcer] considered. Rankin, “Ramanujan as a Patient,” 87, 92.

  Not hydrocele, but cancer. Ibid., 91.

  Blood poisoning. P. K. Srinivasan, 76.

  Tuberculosis—disease, treatment, and history. See, for example, Bryder, Smith, Dubos, Keers.

  one in eight deaths in Britain. Bryder, 1.

  Nervous system-immune system ties. See, for example, Robert Kanigel, “Where Mind and Body Meet,” Mosaic, Summer 1986, 52–60.

  “emotional stress associated with separation.” George W. Comstock et al., “Tuberculosis Morbidity in the U.S. Navy: Its Distribution and Decline,” American Review of Respiratory Disease 110 (1974): 572–580; interview, George W. Comstock.

  wild spasmodic leap. Bryder, 109–110.

  The Danish phenomenon. See Bryder, 109–112.

  “supported by the figures from Denmark.” Keers, 148.

  “admirable epidemiological detective work.” Graham A. W. Rook, “The Role of Vitamin D in Tuberculosis,” Annual Review of Respiratory Disease 138 (1988): 768.

  Davies paper. Tubercle 66 (1985): 301–306.

  “It probably can.” Rook, 769.

  working at night and sleeping by day. Suresh Ram, 40.

  Osler. Quoted in Bulstrode, 3.

  “this dreadfully cold open room.” Bollobás, “Ramanujan—A Glimpse,” 79.

  treatment’s rise to popularity. Smith, 141. Harold Batty Shaw is mentioned in Rankin, “Ramanujan as a Patient,” 91.

  “was little influenced by it.” Bryder, 23.

  “towards carrying out the ‘open air’ treatment.” Bulstrode, 131.

  at least fifty-two British sanatoriums. Keers, 93. But Bryder reports ninety-six “open-air” sanatoriums in England and Wales by 1907.

  Mendip Hills was one of them. Bryder, 25.

  Matlock, as hydropathic establishment. Rankin, “Ramanujan Manuscripts and Notebooks,” 95.

  “bleak and cold.” Dubos, 181.

  Architects competed. Bryder, 50.

  “the rain blowed through.” Bryder, 53.

  “some quarrel.” P. K. Srinivasan, 71.

  “I haven’t got a surname.” Bollobás, “A Glimpse,” 79.

  slipped into it a brief note. Interview, Janaki.

  Mother-in-law troubles. Interview, S. Sankara Narayanan.

  “It is pitiable for the child-wife.” Compton, 119.

  “The tyrannical mother-in-law.” The Hindu, 12 May 1899.

  who in turn would pass it to him. Carstairs, 45, 66.

  more confident and assertive. Interview, S. Chandrasekhar.

  Those close to Janaki. Janaki’s litany of abuse based on interviews with T. V. Rangaswami, “Hari” of Madras, Mr. and Mrs. T. S. Bhanumurthy.

  out of the question. K. R. Rajagopalan, 41.

  Ramanujan’s father stuck up for Janaki. Interview, Janaki.

  Janaki found an excuse to get away. Interview, Janaki.

  money for a new sari. K. R. Rajagopalan, 44. Interview, Janaki.

  Ramanujan’s letters home. Family Record.

  he told his friend Chatterji. Suresh Ram, 44.

  leaflet advising authors. Minutes, London Mathematical Society, 14 March 1918.

  “a look of extreme disapproval.” Tresilian Nicholas Remembers,” Trinity Review, Easter 1969, 13.

  “whose opinions on the war.” Levy, 279.

  Russell and Trinity. See, for example, Hardy’s own Russell and Trinity.

  “little book.” Daily Telegraph, 30 April 1970.

  Hardy kept one mathematician out of the war. Letter, Hardy to Larmor, 28

  March 1916. Royal Society. The mathematician was Chapman.

  “perfectly tangible and definite.” Letter, Hardy to Jenkinson, 12 June 1918. Cambridge University.

  “very standoffish or possibly shy.” Hodges, 117.

  “multiple layers of reserve.” Ibid., 118.

  “parental solicitude.” Seshu Iyer, 85.

  Hardy would choose the former. Hardy, Apology, 153.

  “always a little difficult.” Hardy, Ramanujan, 1.

  “the first to disclaim.” Snow, “The Mathematician,” 69.

  Ramanujan’s tastes in literature and politics. Hardy, Collected Papers, 715.

  “I rely for the facts.” Hardy, Ramanujan, 2.

  “I am to blame.” Hardy, Ramanujan, 11.

  “all but supernatural insight.” Bell, 140.

  “We have no idea.” Ivars Peterson, “The Formula Man,” Science News, 25 April 1987, 266.

  “that has barely been drawn.” Bruce Berndt, “Ramanujan—100 Years Old,” 29.

  “a touch of real mystery.” Littlewood, Miscellany, 90.

  “An ordinary genius.” Mark Kac, Enigmas of Change (New York: Harper & Row, 1985), xxv.

  “unfold before his eyes.” S. R. Ranganathan, 87.

  “appeared to him in a dream.” Ibid., 73.

  penchant for interpreting dreams. P. K. Srinivasan, 97.

  a street peddler hawking pills. S. R. Ranganathan, 84.

  time to prepare astrological projections. Ibid., 91.

  Predicted death. P. K. Srinivasan, 123.

  a temple near Trichinopoly. Ibid., 101.

  “space-time-junction point.” S. R. Ranganathan, 85.

  “the way maya works in this world.” Ibid., 89.

  “I do not believe.” Hardy, Ramanujan, 5.

  “equally true.” Hardy, Collected Papers, 715.

  “Ramanujan was no mystic.” Hardy, Ramanujan, 5.

  “I should not trust his insight far.” Snow, Apology foreword, 35.

  “thinking vaguely.” Hardy, Collected Papers, 733.

  “who gazes at a distant range of mountains.” Ibid., 598.

  “the evidence for all this seems overwhelming.” For this and what follows, see Ibid., 834–838.

  “with some kinds of spiritual beings.” Hadamard, 40–41.

  “never discarded a particle.” Bell, 144.

  strong mystical bent. Bell, 457.

  “the queerest mixture.” Bell, 43.

  “by the grace of God.” “True Genius,” by RGK, Illustrated Weekly of India, 20 December 1987, 31.

  “the Great Architect of the Universe.” James Jeans, The Mysterious Universe (New York: Macmillan), 1930.

  “If we may reject divine bounty.” Bollobás, Littlewood’s Miscellany, 146.

  “no exception.” Hardy, Collected Papers, 719.

  “Hardy’s deep reverence for mathematics.” E. A. Milne, obituary of Hardy in Monthly Notices of the Royal Astronomical Society 108 (1948): 45.

  “if a strict Brahmin.” Hardy, Ramanujan, 4.

  “a quite harmless … economy of truth.” Ibid., 5.

  “atheist evangelical.” Hodges, 118.

  “I never got the feeling they were happy.” New York Times, January 20, 1988.

  racism was a factor. See page 299.

  “cowed down by Dr. Ram.” Rankin, “Ramanujan as a Patient,” 86.

  “make visits difficult.” Bryder, 200. War-borne slashes in rail services around January 1917 must have left Ramanujan all the more isolated (Marwick, 195).

  “cold weary journey.” Rankin, “Ramanujan as a Patient,” 85.

  “comparative solitude.” P. K. Srinivasan, 76.

  he craved the hot dosai. Ibid., 96.

  “singularities.” Transcript, Nova 1508, 15.

  On December 6, 1917. Minutes, London Mathematical Society.

  Royal Society. Year-book of the Royal Society of London, 1919 (London: Harrison and Sons, 1919).

  “one honor he longed for.” Snow, Variety of Men, 84–85.

  On January 24, 1918. Year-book of the Royal Society 1919, 212.

  “no time must be lost.” Rankin, “Ramanujan as a Patient,” 91.

  “useless to speculate.” Hardy, “Obituary,” 495.

  “a poor and solitary Hindu.” Hardy, Ramanujan, 10.

  “the critical years.” Ibid., 6.

  On F
ebruary 11. Family Record.

  One day in January or February of 1918. The account of Ramanujan’s suicide attempt is derived almost solely from S. Chandrasekhar in notes deposited in the Royal Society and appearing in Notes and Records of the Royal Society 30 (1976). Chandrasekhar gives the time of the incident as February 1918. Nandy, 127, says it was “some time in the second half of 1917.” But this seems contradicted by the dates surrounding Ramanujan’s election to the Royal Society, which are intimately bound up with Chandrasekhar’s story. On the other hand, late January, rather than February 1918, cannot be ruled out. By then, Ramanujan had already been put up for membership. On January 25, Hardy wrote Dewsbury and in his reply of March 5 Dewsbury thanked Hardy for “the very clear and explicit statement on the position of Mr. Ramanujan.” Further, he promised to treat Hardy’s letter “as personal and confidential.” Could Hardy have been advising Dewsbury of the suicide attempt? (Dewsbury’s letter is at Trinity College.)

  “We in Scotland Yard.” Chandrasekhar account.

  He read the telegram once. Bollobás, Littlewood’s Miscellany, 137.

  “the aid and guidance.” Letter to Hardy at Trinity College.

  too sick to travel. Letter, Ramanujan to Royal Society, 15 May 1918. Duplicated in Indian Express, 19 December 1987.

  A. S. Ramalingam. Information about him, and most of the account that follows, is drawn from the correspondence appearing in Rankin, “Ramanujan as a Patient,” 79–100.

  fattening up the patient. Bryder, 53.

  “warped temperament.” Bryder, 208.

  Bovril. Oxford English Dictionary.

  no such dispensation. Or so my South Indian informants advise me.

  Abruptly, he packed his bags. S. R. Ranganathan, 79.

  likely the raid of October 19, 1917. There are inconsistencies in the Desmukh account, which records a bombing raid “in early 1918, when the Zeppelin raids were at their worst.” But the Times of London accounts record no zeppelin raids on the capital then, nor indeed raids of any kind. The most recent substantial raid apt to impress Ramanujan as Desmukh records is that on the date given.

  “tasteless and insipid.” Gandhi, 40.

  “novel and unpalatable.” Neville, “The Late” (Nature 106), 662.

  “should Ramanujan be given up?” Rankin, “Ramanujan as a Patient,” 88.

  Ramanujan’s Trinity fellowship. Bollobás, Littlewood’s Miscellany, 136–138; Bollobás, “Ramanujan—A Glimpse,” 79.

  pain no one could trace. Bollobás, Littlewood’s Miscellany, 137.

  “My heartfelt thanks.” Ibid.

  “your pains and their encouragement.” Letter, Ramanujan to Hardy, undated. Trinity College.

  “a brief period of brilliant invention.” Neville, “Ramanujan” (Nature 149), 294.

  “A recent paper.” Ramanujan, Collected Papers, 210–213.

  “great practical importance.” Hardy and Wright, 49.

  “practically no reason to doubt its truth.” Percy Alexander MacMahon, Combinatory Analysis, vol. 2 (Cambridge: Cambridge University Press, 1916), 33.

  Ramanujan was rummaging. Hardy, Ramanujan, 91, puts the year at 1917. But Richard Askey thinks the correspondence surrounding the discovery points more forcibly to 1916.

  someone already had. “It is unlikely,” George Andrews has written of Rogers’s work, “that any important series of papers ever dropped further from sight than these did for the next 20 years.”

  “remember very well his surprise.” Hardy, Ramanujan, 91.

  “no position in diplomacy.” Nature 132 (1933), 701.

  “very little ambition.” Obituary Notices of Fellows of the Royal Society. 1 (1932–1935), 299.

  The correction. Proceedings of the London Mathematical Society 14, Series 2, (1915), endpaper of bound volume.

  “they seem to have escaped notice.” Hardy, in Ramanujan, Collected Papers, 344.

  yet unproved. MacMahon, Combinatory Analysis, vol. 2, 33.

  “regretting that he had overlooked my work.” Letter, Rogers to F. H. Jackson, 13 February [1918], quoted in George E. Andrews, “L. J. Rogers and the Rogers-Ramanujan Identities,” Mathematical Chronicle 11 (1982), 1–15. Letter furnished Andrews by Lucy Slater, Cambridge University.

  “a very creditable pre-war bonfire.” Cambridge Review, quoted in Howarth, 17–18.

  “as if Time and Eternity were one.” Howarth, 18.

  “I think it is now time.” P. K. Srinivasan, 76.

  CHAPTER EIGHT

  “on the road to a real recovery.” P. K. Srinivasan, 76.

  “and caused such grave anxiety.” Seshu Iyer, 85.

  restored the right to make cakes and pastries. Marwick, 271.

  Cambridge casualties. Howarth, 16.

  “rocky headlands rejoiced.” Trevelyan, An Autobiography & Other Essays (London: Longmans, Green and Co., 1949), 37.

  Colinette House. Interview with its current owners, Deborah and Bryan J. B. Gauld; tour of the house and grounds.

  Samuel Mandeville Phillips. Rankin, “Ramanujan as a Patient,” 82.

  a few weeks after the armistice. “She was laid to rest on December 6th in the grave where her husband lies in the churchyard.” The Cranleighan 13 (1919), 76.

  1729. Hardy, Collected Works, 719–720; Snow, Apology foreword, 37.

  would be named University Professor. Memo, Narayana Iyer to Sir Francis Spring, 12 March 1918. Madras Port Trust.

  “the help that has been given me.” P. K. Srinivasan, 46.

  Passport photo. Photo, P. K. Srinivasan, opposite 136.

  Ramanujan brought back to India. The Hindu, 19 December 1987; P. K. Srinivasan, 162; Berndt, “Ramanujan—100 Years Old,” 26.

  the night sky was still aglow. Hoyt, 101. Shell fragments from the attack can be seen today in the Fort St. George Museum, Madras.

  included Ramanujan’s parents and wife. Jagjit Singh, “Srinivasa Ramanujan: A Short Biography—Part I,” Mathematical Education, July-September 1987, 15.

  “When you wear the King-Emperor’s uniform.” Slater, Southern India, 291.

  “keen interest and high anticipation.” Journal of the Indian Mathematical Society 9, no. 1 (February 1917): 13.

  “some surprising discoveries.” S. R. Ranganathan, 37.

  “the emergence of Ramanujan into fame.” Ibid., 64.

  claimed five lives already. Journal of the Indian Mathematical Society 10, no. 6 (December 1918): 1.

  Ramanujan in Bombay and movements after that. Interview, Janaki. Family Record. K. R. Rajagopalan, 46–48.

  Why fret over Janaki? Interview, Janaki.

  two identical letters. Ibid.

  Brother advised her. Ibid.

  “asked to a funeral.” Neville, “Ramanujan” (Nature 149), 294.

  boarded the Bombay Mail. P. K. Srinivasan, 92.

  “I foresaw the end.” Ramachandra Rao, 88.

  Komalatammal’s excuse. Interview, Janaki.

  bundled on to a jutka. P. K. Srinivasan, 92.

  “does not … go far enough.” Spring memo, March 27, 1919. Madras Port Trust.

  when his health improved. Berndt, “Ramanujan—100 Years Old,” 26.

  Madrasi notables. K. R. Rajagopalan, 47–48.

  Luz Church. Muthiah, 137.

  on April 6. Family Record.

  in monthly installments. P. K. Srinivasan, 182.

  a real relationship. Interview, Janaki.

  drank coffee now. Ibid.

  “not a cheerful … Ramanujan.” S. R. Ranganathan, 71.

  “not the original Ramanujan.” P. K. Srinivasan, 101.

  “only devils.” Ibid.

  he seemed troubled. Letter, S. Chandrasekhar to Hardy, 4 August 1937. Trinity College. Other accounts. See Nandy, 131.

  another irritant. Letter, A. Ranganathan, 12 January 1981. Royal Society.

  “diamond eardrops.” Transcript, Nova 1508, 16.

  Coimbatore vs. Kodumudi. Interview with Janaki. Family Record. But in an interview, T. V. Rangaswam
i claims Ramanujan was, at least briefly, in Coimbatore, perhaps later in the year. And K. R. Rajagopalan, 48, also mentions a stay in Coimbatore. But if so, it was brief.

  Ramanujan’s stay in Kodumudi. Interviews with townspeople, including R. Chandrasekhar and K. Elangovan.

  registrar’s office. Interview, Janaki.

  Ramanujan openly rebelled. The story, its timing, and the trouble leading up to it, are based on interviews with Janaki supplemented by the Family Record.

  “If only you had come.” Janaki has repeated this many times over the years, as in the Hindu, 19 December 1987, and plainly clings to the memory of it.

  oil and wash her hair. Interview, “Hari” of Madras, who reports being told the story by Janaki.

  send Janaki packing. Nandy, 130.

  Every Sunday. Family Record

  Fearnside. P. K. Srinivasan, 182.

  Thanjavur pun. This appears in many forms. See, for example, S. R. Ranganathan, 93.

  Komalatammal decreed. Interview, Janaki.

  went on ahead to look for a house. Family Record.

  “insisted on seeing my aunt.” Seshu Iyer, 82.

  dried brinjal slices. P. K. Srinivasan, 103.

  “powerful and penetrating eyes.” S. R. Ranganathan, 75.

  Dr. Chandrasekar. K. R. Rajagopalan, 49; P. K. Srinivasan, 108; letters, A. Ranganathan, 12 January and 26 March 1981. Royal Society.

  “this tuberculosis fever.” K. R. Rajagopalan, 48.

  dead within five years. Keers, 144.

  “still in very bad health.” Letter, Dewsbury to Hardy, 22 December 1919. Trinity College.

  refused to be farther treated. Seshu Iyer and Ramachandra Rao, xviii.

  given up the will to live. Letter, A. Ranganathan, 12 January 1981. Royal Society.

  Resisted going to Madras. Seshu Iyer and Ramachandra Rao, xviii.

  probably a little after the first of the year. Letter, Dewsbury to Hardy, 15 January 1920. Trinity College.

  got only as far as the railway station. Interview, Janaki.

  known as “Gometra.” Interview, Mr. and Mrs. T. C. Krishna, current owners of Gometra.

  “which I call ‘Mock’ theta functions.” Ramanujan, Collected Papers, xxxi.

  “in some ways the very best.” S. Chandrasekhar, Transcript, Nova 1508, 16.

  “we know how beautifully.” G. N. Watson, “The Final Problem,” Journal of the London Mathematical Society 11 (1936): 57.

  “cold, immortal hands.” Ibid., 80.