The Man Who Knew Infinity

by Robert Kanigel

  “It is very difficult.” Interview, George E. Andrews, in “Spectacular Genius,” The Hindu, 21 January 1987.

  final flurry of creativity. See McMurry for a perceptive study of the myths surrounding tuberculosis.

  “proportionately keener and brighter.” Seshu Iyer, 85.

  “wild eccentric genius of his youth.” Interview, George E. Andrews, in “Spectacular Genius,” The Hindu, 21 January 1987.

  Crynant inauspicious. Interview, T. V. Rangaswami.

  Namberumal Chetty. Who’s Who in Madras, 1934.

  “Gometra?” Tour of the house conducted by Mr. and Mrs. T. C. Krishna. may briefly have stayed there. Janaki, in an interview, recalls a large “hall” in which Ramanujan stayed, which could have been the large living room.

  scant furniture. P. K. Srinivasan, 163.

  Visitors moved silently. “ ‘His Papers Disappeared Mysteriously,’ ” The Hindu, 21 June 1981.

  Access jealously guarded. P. K. Srinivasan, 162.

  Janaki’s brother with her. Ibid., 163.

  Narayanaswamy Iyer. S. R. Ranganathan, 14.

  “Buoyed up by spes phthisca.” McMurry, 140.

  subscribing to new math journals. Letter, Dewsbury to Hardy, 15 January 1920. Trinity College.

  Chetput pun. S. R. Ranganathan, 93.

  “uniformly kind to me.” S. R. Ranganathan, 91. Janaki confirms that Ramanujan was sure he was going to die.

  piece of hot pepper … K. R. Rajagopalan, 50.

  Bell and stick. Interview, Janaki.

  craved the rasam. P. K. Srinivasan, 136.

  pounded it all together. Interview, Janaki.

  “mentally dead to the world.” P. K. Srinivasan, 111.

  “skin and bones.” S. R. Ranganathan, 91. The account of Ramanujan’s final days is drawn largely from interviews with Janaki and from various accounts she has given over the years.

  relatives stayed away. K. R. Rajagopalan, 51.

  Ramachandra Rao arranged the cremation. P. K. Srinivasan, 88.

  officially recorded his death. The Hindu, 3 January 1988.

  Subrahmanyan Chandrasekhar. See Kameshwar C. Wali, Chandra (Chicago: University of Chicago Press, 1990).

  “I can still recall the gladness.” Andrews et al., 3.

  “We were proud of Mahatma Gandhi.” Muthiah, 6.

  “inspired by his example.” Andrews et al., 5.

  neglected his studies. S. R. Ranganathan, 20.

  “too deep for tears.” Letter, A. Ranganathan, 12 January 1981. Royal Society.

  “entirely under the control.” Letter, Lakshmi Narasimhan to Hardy, 29 April 1920. Trinity College.

  Death of Ramanujan’s father. Interview, V. Viswanathan. I have not learned when Ramanujan’s mother died, but a sister of V. Viswanathan (and granddaughter of Narayana Iyer) reports that when Madras was evacuated during World War II, probably in 1942, she saw Komalatammal in Kumbakonam. She would have been seventy-four.

  “became very often sullen.” Bharathi, 51.

  Komalatammal’s letter. Letter, Komalatammal to Hardy, 25 August 1927. Trinity College.

  “console herself by seeing us.” P. K. Srinivasan, 101.

  worried about how she’d be treated. Interview, Janaki.

  two days before Ramanujan’s death. Ibid.

  next half century. In 1931, according to T. V. Rangaswami, she once met A. S. Ramalingam in Madras.

  work a sewing machine. Interview, Janaki. See also K. R. Rajagopalan, 53.

  “relatives having swindled her.” Letter, S. Chandrasekhar to Hardy, 4 August 1937. Trinity College.

  Janaki and Narayanan. Interview, Janaki. See also K. R. Rajagopalan, 53.

  “And he is no more.” Ramachandra Rao, 87.

  “inefficient and inelastic educational system.” Hardy, Ramanujan, 7.

  “Indianality.” Ramachandra Rao, 89.

  “raised India in the estimation of the … world.” Journal of the Indian Mathematical Society 11 (April 1919), 1.

  “a fluctuation from the norm.” S. Chandrasekhar, “On Ramanujan,” in G. E. Andrews et al., 4.

  “more deeply bound up with the West.” Nandy, 139.

  “boosted our morale.” Interview with P. K. Srinivasan.

  “by the hand of Srinivasa Ramanujan.” Neville, Reading Manuscript.

  “some permanent memorial.” P. K. Srinivasan, 79.

  Wilson and Watson. “My respect for R[amanujan] has increased considerably in the last three months,” Watson wrote Wilson on 28 June 1929. “I have retired from the J.M.B. to gain time for R.” Trinity College.

  “no more romantic personality.” R. D. Carmichael, “Some Recent Researches in the Theory of Numbers,” American Mathematical Monthly 39, no. 3 (1932): 140.

  “so full of human interest.” Mordell, “Ramanujan,” 642.

  “which I immediately read with great interest.” Paul Erdos, “Ramanujan and I,” in Number Theory, Madras 1987, ed. K. Alladi, no. 1395 in the series, Lecture Notes in Mathematics, ed. A. Dold and B. Eckmann (Berlin: Springer-Verlag, 1989), 1. The Hardy-Ramanujan paper is no. 35 in Ramanujan, Collected Papers.

  “unusual and somewhat strange.” Atle Selberg, “Ramanujan and I,” Science Age, February 1988, 37.

  “The chapter … I loved the most.” Freeman Dyson, “A Walk Through Ramanujan’s Garden,” in G. E. Andrews et al., 9.

  “destruction of 1917.” Ibid., 15.

  “originated with Ramanujan.” Morris Newman, “Congruence Properties of the Partition Function,” Report of the Institute in the Theory of Numbers (University of Colorado, 1959).

  “tamed a little.” Hardy, Collected Papers, 720.

  “into touch with Euler.” Littlewood, Miscellany, 86.

  another ten years. Letter, R. J. L. Kingsford to Hardy, 23 August 1929. Trinity College.

  “all by myself as a devotee.” Interview, Freeman Dyson.

  “a stack of browned old paper.” S. Ramaseshan, “Srinivasa Ramanujan,” Proceedings of the Ramanujan Centennial International Conference, ed. R. Balakrishnan et al. (Madras, 1988), 6.

  “even more definite picture.” Littlewood, Miscellany, 86.

  Srinivasan’s project. Interview, P. K. Srinivasan. See also P. K. Srinivasan, vi–x.

  “On Certain Arithmetical Functions.” Ramanujan, Collected Papers, 136–162.

  “very imperfectly understood.” Hardy, Ramanujan, 161.

  “kept at bay.” S. Raghavan, “Impact of Ramanujan’s Work on Modern Mathematics,” Srinivasan Ramanujan Centenary 1987 [special issue of the Journal of the Indian Institute of Science], 46.

  An account by Hardy. Hardy, Ramanujan, 170.

  Bach comparison. Berndt, “Ramanujan—100 Years Old,” 24–29.

  Discovery of the Lost Notebook. Interview, George Andrews. Transcript, Nova 1508, 17. Andrews, Q-Series.

  “And that bothered me.” Interview, Bruce Berndt.

  “substance and depth.” Interview, Freeman Dyson.

  “asked to explain.” Hardy, Some Famous Problems, 4.

  “missing pecuniary reward.” Journal of the Indian Mathematical Society 13, no. 3 (June 1921): 100.

  “better blast furnaces.” Bharathi, 93.

  Plastics. S. Ramaseshan, “Srinivasa Ramanujan,” 11.

  Cancer. Meeting held November 10–12, 1988. The Hindu article was dated 23 December 1988.

  “hard hexagon model.” R. J. Baxter, “Ramanujan’s Identities in Statistical Mechanics,” in Andrews et al., 69–84. See also Gurney Williams III, “The Master of Math,” Omni, December 1987, 58–64.

  “a computer algebra package in his head.” Saraswathi Menon, “Beautiful Important Work,” The Hindu, 22 December 1987.

  “he really didn’t need them.” Andrews, Q-Series.

  “Hype.” Interview, Freeman Dyson. Bruce Berndt has written me with “another ‘application’ of Ramanujan’s mathematics that Dyson calls ‘hype.’ ” William Beyer, a physicist at Los Alamos National Laboratory, has shown how one of Ramanujan’s
formulas can be “very useful in predicting nuclear war.” The formula does not, of course, truly “predict” nuclear war, but rather supplies the basis for a theoretical model for estimating its likelihood.

  “appreciate Ramanujan early.” Askey, 72.

  “I was stunned.” Transcript, Nova 1508, 12.

  “a thrill … indistinguishable.” G. N. Watson, “The Final Problem,” Journal of the London Mathematical Society 11 (1936): 80.

  “a certain character of permanence.” Hardy, Some Famous Problems, 4–5.

  framed and garlanded … portrait. Noted in a videotape made of the celebration.

  the university had noticed. S. R. Ranganathan, 55. S. Chandrasekhar also played a role in seeing to it that Janaki was better cared for.

  Janaki financed Interview, Janaki.

  “Where is the statue?” Hindu, 21 June 1981.

  Granlund sculpture. Interview, Richard Askey.

  Each afternoon. Interview, T. V. Rangaswami. In the mornings, he reports, Janaki was occupied with devotions or cooking.

  broke down and cried. Interview, T. V. Rangaswami.

  left to foreigners. Ramanujan, said P. K. Srinivasan in an interview, “was born in India, reborn in the U.K., and now born again in the U.S.”

  “could not get even a lectureship.” J. B. S. Haldane quoted in sidebar to “True Genius,” by “RGK,” 30.

  “languishing in obscurity.” Bharathi, 36.

  “a new India and a new world?” Nehru, Discovery of India (London: Meridean Books), 1960.

  many Ramanujans. Interview, R. Viswanathan, Kumbakonam.

  “of defaming Ramanujan’s name.” S. Chandrasekhar, “An Incident in the Life of S. Ramanujan … ,” notes deposited in Royal Society.

  Ramanujan Institute. Interview, K. S. Padmanabhan.

  “How many registrars.” S. Ramaseshan, 3.

  “luminescence.” “True Genius,” by “RGK,” 31.

  “our bankruptcy was made manifest.” Report of Joint Secretary D. D. Kapadia, Second Conference of the Indian Mathematical Society, 11–13 January 1919, reported in the Society’s Journal.

  “to win the confidence.” Neville, The Farey Series of Order 1025 (Cambridge: University Press, 1950), xxvii.

  Hardy’s greatest contribution. Quoted in The Hindu, 19 December 1987.

  svayambhu. “True Genius,” by “RGK,” 26.

  “I did not invent him.” Hardy, Ramanujan, 1.

  EPILOGUE

  “principal permanent happiness.” Letter, Hardy to Thomson, 13 December 1919. Cambridge University.

  hard feelings left over from the war. “Life in College was through all these years [of the war] … definitely unpleasant, and the recollection of them was an important factor in my own decision to try to move to Oxford.” Hardy, Russell and Trinity, 10.

  “darker for Hardy.” Snow, Apology foreword, 38.

  “felt he must get away.” Young, 287.

  “Cambridge beguiles.” Rose and Ziman, 44–45.

  “By direction of the Syndicate.” Letter to Hardy, 29 April 1920. Trinity College.

  “a great shock and surprise.” P. K. Srinivasan, 78.

  “all Germans will be relegated.” Quoted in Joseph W. Dauben, “Mathematicians of World War I: The International Diplomacy of G. H. Hardy and Gösta Mittag-Leffler as Reflected in Their Personal Correspondence,” Historia Mathematica 7 (1980): 261–288.

  “trivial changes of sign.” The story has been told in many places. Young, 280, is one of them.

  “modified my former views.” Letter, Hardy to Mittag-Leffler, quoted in Dauben, “Mathematicians of World War I.”

  “happiest time of his life.” Snow, Apology foreword, 40. “After Hardy’s social discomforts at the High Table of Trinity, Hardy expanded and mellowed in a wonderful way, in what was to him the more benign atmosphere of New College. His popularity there was immediate and assured, and he gave back in the intellectual exhilaration of his conversation what he received in sympathetic friendship.” E. A. Milne, obituary of Hardy in Monthly Notices of the Royal Astronomical Society 108 (1948): 46.

  “customary deference of those days.” Mary Cartwright, “Moments in a Girl’s Life,” unpublished manuscript, 5.

  “a delightful time.” Letter, Hardy to president of Princeton University, 24 April 1929. (The letterhead is that of the Mayflower Hotel, Washington, D.C.)

  Ruth as familiar as Hobbs. “He had a similar passion for baseball [as for cricket], which he watched whenever he could when he was in the States.” From a journal referee’s report commenting on an article about Ramanujan and Hardy. Robert Rankin, Glasgow.

  “a wonderful book.” Postcard, Hardy to R. P. Boas, 10 January 1940. Oxford tennis photo. Trinity College.

  retirement. Snow, Apology foreword, 43.

  “one could often hear the party’s laughter.” Snow, “The Mathematician,” 72.

  “a real mathematician.” Snow, Apology foreword, 9.

  “suddenly at least the equal.” Young, 293.

  “deep solicitude.” A. V. Hill, obituary notice in The Mathematical Gazette 22 (May 1948), 51.

  “then I cannot remain in it.” Letter, Hardy to Mordell. St. John’s College.

  “more uncharitable conclusion.” Hardy, Collected Papers, 611.

  “he was with the miners.” J. B. S. Haldane, “A ‘Pure’ Scientist—and a Great One,” Daily Worker (London), 29 December 1947.

  “some mysterious terror to exact thought.” Hardy, Collected Papers, 260.

  some would grumble later. J. C. Burkill, review of Collected Papers of G. H. Hardy, vol. 7, Bulletin of the London Mathematical Society 12 (1980): 226.

  Congratulations from Soviets. Letter, Soviet Ambassador to Hardy, 20 February 1934. Trinity College.

  Honorary degrees. After the ceremony in which he received his degree from Edinburgh, Hardy was strolling with a group of mathematicians when he spotted a mouse. His colleagues, reported The Scotsman (3 December 1947), “were granted the privilege of watching one of the world’s greatest mathematicians stalking it, on hands and knees, around a tree.”

  Hardy’s New Year’s resolutions. J. C. Burkill, entry on Hardy in Dictionary of Scientific Biography.

  his madcap bent. Young, 276.

  “old brandy.” Snow, Apology foreword, 48.

  “aged and shriveled replica.” Wiener, I Am a Mathematician, 152.

  “youthful quickness and power.” Hardy, Collected Papers, 745.

  while dusting his bookcase. Interview, Mary Cartwright.

  his most important papers. Titchmarsh, 458–461.

  “like Wanda Landowska playing Bach.” Letter, Freeman Dyson to C. P. Snow, 22 May 1967. Freeman Dyson.

  “makes him look so old.” Interview, Mary Cartwright. Written in blue ink, almost certainly by his sister, on the photo in the Trinity archives: “He never looked as old as this!”

  Hardy’s suicide attempt. Snow, Apology foreword, 54.

  “one conclusion to be drawn.” Ibid., 57.

  “Hardy is now dying.” Philip Snow, 95.

  “the passing of a great age.” Norbert Wiener, Bulletin of the American Mathematical Society 55 (1949): 77.

  “book of haunting sadness.” Snow, Apology foreword, 50.

  “It is a melancholy experience.” Hardy, Apology, 61.

  “on something like equal terms.” Ibid., 148.

  “about which he felt strongly.” Mary Cartwright, “Moments in a Girl’s Life,” unpublished manuscript, 7.

  “the one romantic incident.” Hardy, Ramanujan, 2.

  “most careful editing.” Letter, Hardy to Mittag-Leffler, about 1920.

  “a short but characteristic example.” Hardy, in Ramanujan, Collected Papers, 232.

  “the decisive event of my life.” Hardy, Apology, 148.

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

  “among the most remarkable.” Manchester Guardian, 2 December 1947.

  “one of the most fascinating obituary notices.
” Quoted in Andrews, Q-Series. a prime subject of his own book. Nandy, 3.

  Hardy’s report on Ramanujan. Hardy, Collected Papers, 491–503.

  “greater than the gain.” Hardy, Collected Papers, 720.

  “no secrecy at all.” Snow, Apology foreword, 30.

  “Hardy was terribly proud.” Interview, Mary Cartwright.

  “I am going to give some lectures.” Letter, Hardy to Chandrasekhar, 19 February 1936. Trinity College.

  “labor of love.” Mordell, “Ramanujan,” 642.

  Harvard Tercentenary celebration. See, for example, Harvard Alumni Bulletin, 30 September 1936. The Tercentenary of Harvard College (Cambridge, Mass.: Harvard University Press, 1937), compiled by Jerome D. Greene; Harvard Magazine, May-June 1986.

  “who has led the advance.” Trinity College.

  “the rule in Shelley’s case.” Newman, The World of Mathematics, vol. 4 (New York: Simon and Schuster, 1956), 2036. According to Newman, the story is told by Supreme Court Justice Felix Frankfurter.

  in Hitler’s army. “Highbrows at Harvard,” Time, 14 September 1936.

  about nine in the evening. Conference schedule, in The Tercentenary of Harvard College, Appendix N, 465.

  “a very great mathematician.” Hardy, Ramanujan, 1.

  Selected Bibliography

  Alexanderson, G. L. The polya Picture Album: Encounters of a Mathematician. Boston: Birkhäuser, 1987.

  Andrews, George E. “An Introduction to Ramanujan’s ‘Lost’ Notebook.” American Mathematical Monthly 86 (1979): 89–108.

  ———. Number Theory. Philadelphia: W. B. Saunders Company, 1971.

  ———. Q-Series: Their Development and Application in Analysis, Number Theory, Combinatorics, Physics, and Computer Algebra. Providence, R.I.: American Mathematical Society, Regional Conference Series in Mathematics, No. 66, 1986.

  ———, Richard A. Askey, Bruce C. Berndt, K. G. Ramanathan, and Robert A. Rankin. Ramanujan Revisited. San Diego: Academic Press, 1988.

  Askey, Richard A. “Ramanujan and Hypergeometric and Basic Hypergeometric Series.” In Ramanujan International Symposium on Analysis, edited by N. K. Thakare. Macmillan India, 1989.

  Association of Mathematics Teachers of India. Ramanujan Centenary Year Souvenir. Proceedings of 22d annual conference, 3–6 December 1987.

  Atkinson, Thomas Dinham. Cambridge Described and Illustrated. London: Macmillan, 1897.