The Man Who Knew Infinity

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by Robert Kanigel


  Whitehead, Henry. The Village Gods of South India. Calcutta: The Association Press (in association with Humphrey Milford, Oxford University Press), 1916.

  Wiener, Norbert. Ex-Prodigy. New York: Simon and Schuster, 1953.

  ———. “Godfrey Harold Hardy, 1877–1947.” Bulletin of the American Mathematical Society 55 (1949): 72–77.

  ———. I Am a Mathematician. Garden City, N.Y.: Doubleday, 1956.

  Williams, Mary Elizabeth. A Bibliography of John Edensor Littlewood. Elizabeth, N.J.: Pageant-Poseidon Press, 1974.

  Woolf, Leonard. Beginning Again. New York: Harcourt, Brace & World, 1963.

  ———. Sowing. New York: Harcourt, Brace & Co., 1960.

  Worswick, Clark, and Ainslie Embree. The Last Empire. Millerton, N.Y., 1976.

  Wurmser, Leon. The Mask of Shame. Baltimore: Johns Hopkins University Press, 1981.

  Young, Laurence. Mathematicians and Their Times. Amsterdam: North-Holland Publishing Co., 1981.

  Author’s Note and Acknowledgements

  In writing the life of Ramanujan, I faced the barriers of two foreign cultures, a challenging discipline, and a distant time. As I am expert in none of these, I owe a debt of gratitude to the many persons who have helped me surmount those barriers—who have consented to interviews, spent hours explaining recondite areas of mathematics or Indian cultural life, guided me to out of the way documents in libraries and archives, read and criticized early drafts, befriended me in England and India—and, back in Baltimore, offered a supportive hand or word of advice. I am abashed at how much space I require to simply say thank you, but it is an apt measure of my debt.

  First, thanks are due Judy, who has borne more husbandly changes of mood than any person should have to bear, and to whom I owe much in the way of nurturing, encouragement, and support. Those intangibles are easy to take for granted when you have them, but almost impossible to get along with when you don’t.

  To Judy and my sister Rachele, and their refusal to tell me what I wished to hear at a crucial point, I owe an approach to writing about the mathematics to which otherwise I might not have turned.

  Thanks go to Davy, whose Daddy was gone in England and India for three months and then, for the year and a half it took to write this book, was too much in the office and not enough with him. “So how’s the Ramanujan book?” he asked me one day when he was five. I hope that one day he’ll read it and be able to answer for himself.

  To my parents, Bea and Charles Kanigel, for leaving me fascinated equally by words, numbers, people, and ideas.

  To Michael, Kevin, and Jonathan, to Harry and Rachele, and to Elise and Liz—all of them, each in their own way, irreplaceable parts of my life.

  To Bill Stump for encouraging a young writer twenty years ago.

  To V. Viswanathan, of Madras, who made room for a confused American in an already overstuffed auto-rickshaw. To him, his brother V. Meenakshisundaram of the Madras Port Trust, to S. Sankara Narayanan and V. Subramanyam, and to the many other members of his family who befriended me in Madras, I owe a debt of kindness I cannot possibly repay.

  To Sambandam, Vijaya, Mahalingam, and all their family in Kumbakonam, for their boundless hospitality.

  To the “Gang of Three”—three American mathematicians, admirers and students of Ramanujan, who have helped me to understand his work, and who have read the manuscript along the way, invariably peppering their excellent advice with dollops of needed encouragement: George Andrews, Pennsylvania State University; Richard Askey, University of Wisconsin; and Bruce Berndt, University of Illinois. Without the help of these three men this book could not have been written.

  To Robert Rankin of Glasgow, Scotland, whose research into the lives of Ramanujan and Hardy has materially contributed to this book, and who has been unfailingly patient in responding to my trans-Atlantic queries.

  To Freeman Dyson, for taking such interest in the book, rounding up old letters, reading the manuscript, and making important suggestions.

  To Barbara Grossman, whose idea this book was, and who has placed the full force of her personality behind it. To Joy Smith for her diligence and unfailing good nature. To Erich Hobbing, David Frost, and others at Scribner’s for their help and talents. To Zoë English Kharpertian for her fine job of copyediting.

  To Vicky Bijur, my agent, for the important role she played in bringing this book into being, and for the almost frightening efficiency with which she has acted in my behalf along the way.

  To Jane Alexander, who sent me to India the first time and has been a friend since.

  So many have helped, in small ways and large, to make this book possible that it seems scarcely possible to remember them all. I apologize to any I may have inadvertently omitted.

  In America: Sudarshan Bhatia and Asha Rijhsinghani. V. Anantharaman and Malini. Ashvin Rajan. Ranjan Roy, Beloit College. Henry S. Tropp, Humboldt State University. S. Chandrasekhar, University of Chicago. Arthur Magida. Gary Leventhal. Ann Finkbeiner and Cal Walker. Ken Gershman. Lee and Phyllis Jaslow. Mildred Foster. Carolyne, Kathy, and everyone at the Red Balloon. William Dyal and Thomas Slakey, St. John’s College, Annapolis. Warren Kornberg, Mosaic magazine. Jacek Mostwin, Johns Hopkins Hospital. Steve Fisher. Alan Sea. Adrianne Pierce, Johns Hopkins University. John Halperin, Vanderbilt University. Maurice St. Pierre, Morgan State University. Suzanne Holland, Harvard magazine. George W. Comstock, Johns Hopkins University School of Hygiene and Public Health. S. Bhargava, University of Illinois, Urbana. Wayne Markert, University of Baltimore.

  In Britain: Emma and Jonathan Leigh, Cranleigh School. Kevin Gray, Trinity College. Béla Bollobás, Trinity College. Charles Burkill, Cambridge. Mary Cartwright, Cambridge. Rajiv Krishnan, Christ’s College. Roger David Hugh Custance, Winchester College. Guy Newcombe, Trinity College. Vince Darley, Trinity College. John Vickers, St. John’s College. R. Robson, Trinity College. Constance Willis, Cambridge. Deborah and Bryan J. B. Gauld, Putney. Theodor Schuchat and Louise Harper, London. Paul and Clare Friedman, London. S.J. Mann, Cranleigh School. Susan M. Oakes, London Mathematical Society. J. D. Webb, Cambridge City Council. Tom Doig, Cambridge Folk Museum. Pat Kattenhorn, India Office Library.

  In India: Janaki Ammal, the widow of Ramanujan, and her son, W. Narayanan, and his family, Triplicane, Madras. T. V. Rangaswami (“Ragami”), Triplicane, Madras. A. P. Victor, Kuala Lumpur, Malaysia. P. K. Srinivasan, Association of Mathematics Teachers of India, Madras. T. M. Srinivasan and T. M. Kasturirangan, Madras. John Herbet Anand, Mylapore, Madras. R. Janarthanan, Kumbakonam. R. Viswanathan, headmaster, and V. Vaidynathan, assistant headmaster, Town Higher Secondary School, Kumbakonam. S. Subbarathinan, Erode. A. Nazimuddin and H. Sharmila, Madras. K. Elangovan, Kodumudi. R. Chandrasekhar, Kodumudi. A. Sanguttuvan, Erode. L. Rajagopolan, S. Elango and D. G. Ramamurthy, Kumbakonam. A. Saranathan and his family, Kumbakonam. S. Govindaraja Battachariar and P. Vasunathan, Uppiliapan Koil, Thirunageswaram. T. U. Bhanumurthy and Kalyanalakshmi, Madras. M. Vinnanasan, Kumbakonam. K. S. Padmanabhan, Ramanujan Institute, Madras. K. Narayanan and A. V. Chandrasekhar, The Hindu. A. Ranganathan, Madras. K. Rajamani, Kumbakonam. T. C. Krishna and his family, Madras. Bhama Srinivasan, University of Illinois, Chicago. P. P. Kulkarni, Nagpur. And, of course, the unforgettable Hari, of Madras.

  • • •

  I wish also to express my gratitude to the staffs of the many libraries in the United States, England, and India who have helped me in the quiet, faceless, but unfailingly competent way we all expect of them. That, of course, is the problem: it’s so easy to take the library for granted when it has the book or document you need, and to grumble when it doesn’t. But the very concept of the library, as a place to store, preserve, and give access to books, was thrown into sharp focus during my five weeks in India. There, libraries cannot always treat their treasures with the expensive care Western libraries can lavish on theirs. In one, I found books and journals set out on the floor, piled this way and that, the pages of even recent books crumbling, dusty and mildew
ed. And yet never have I seen libraries so intensively used, books so hungrily devoured. In one small library in Erode, I saw every seat at every table taken, and many people standing in the aisles to read.

  My appreciation, then, goes to librarians, archivists, and other staff at the following institutions:

  Baltimore: The Milton S. Eisenhower Library of Johns Hopkins University. William H. Welch Medical Library. Enoch Pratt Free Library—central library, St. Paul Street branch, and telephone reference service.

  Washington, D.C.: Library of Congress.

  Cambridge, Mass.: Harvard University Archives.

  Princeton, N.J.: Seely G. Mudd Manuscript Library.

  Cambridge, England: University Library of Cambridge University, and the libraries of these Cambridge colleges: Trinity, St. John’s, Gonville & Caius. Scientific Periodicals Library. Cambridgeshire Collection. Cambridge Folk Museum.

  London: Royal Society Library. India Office Library. University of London. National Maritime Museum, Greenwich.

  Elsewhere in England: Guildford Public Library (Local Studies Collection). Cranleigh School, library and archives. Cranleigh Library. St. Catherine’s School Library, Bramley. New College Library, Oxford. University of Reading.

  Erode: Public Library.

  Madras: Connemara Library, University of Madras. Archives of The Hindu. British Embassy Library. Fort St. George Museum. Madras Museum.

  Index

  Abel, Niels Henrik, 147, 150, 169–70, 366

  Acta Mathematica (journal), 363, 370

  Additive theory of numbers, 303

  Advisory Committee for Indian Students, 174, 184

  Agincourt, Battle of, 163

  Algebra, 41–44, 46, 53, 60, 86, 119, 149, 161, 205, 366

  computer, 349

  genetics and, 146

  Algebraic geometry, 344

  Allen, G. C., 126

  Allied Powers, 212

  Alternative Sciences (Nandy), 335

  American Mathematical Monthly, 336

  American Physical Society, 348

  Analytical Club, 85

  Analytical number theory, 249, 340

  Ananda Rao, 230

  Anantharaman, 55, 72, 190, 282, 290, 318, 332–33

  Andrews, George, 6, 252, 325, 326, 344–46, 349, 350–52

  Anna University, 351–52

  Apostles. See Cambridge Apostles

  Applied mathematics, 347–49

  Archimedes, 209

  Are Conjectandi (Bernoulli), 90

  Aristotle, 287

  Arithmetical functions, 343

  Arnold, Thomas, 112, 121

  Arybhata, 86

  Askey, Richard, 280, 350–52

  Athens, University of, 366

  Atomic research, 348

  Atshara Abishekam (ritual practice), 13

  Australian National University, 349

  Bach, Johann Sebastian, 344, 350, 351

  Bacon, Francis, 239

  Bailey, W. N., 202, 231, 371

  Baker, H. F., 106, 170–72, 291, 358

  Balakrishna Iyer, S., 78, 321

  Ballistics, 228

  Barnes, E. W., 151, 233, 243, 261, 277, 290

  Bauer (mathematician), 167

  Baxter, R. J., 349

  Bayeux tapestries, 133

  Beethoven, Ludwig van, 346, 350

  Belgium

  in Great War, 211–14, 227, 260, 277

  tuberculosis in, 267

  Bell, E. T., 65, 81, 256, 280, 287

  Below the Magic Mountain (Bryder), 270

  Benedictine order, 126

  Bergson, Henri, 157

  Berlin, University of, 365

  Berndt, Bruce, 183, 204–5, 280, 344, 346, 350, 351

  Bernoulli, Jacob, 89

  Bernoulli numbers, 89–92, 105, 161, 203

  Berry, Arthur, 201–2

  Bertrand Russell and Trinity (Hardy), 277

  Besant, Annie, 314

  Bhagavad-Gita, 30, 179

  Bhaskara, 86

  Bhavaniswami Rao, 106

  Bieberbach, Professor, 366

  Birmingham, University of, 204, 366

  Birth of Britain, The (Churchill), 133

  Bloomsbury literary movement, 111, 137, 141

  Bohr, Niels, 365

  Bollobás, Béla, 253

  Bolshevik Revolution, 306

  Borel (mathematician), 153

  Borwein, Jonathan M., 208

  Borwein, Peter B., 208

  Bose, J. C., 335, 336

  Bounded errors, 251–52

  Bourne, A. G., 103

  Boyles, Robert, 291

  Brahmagupta, 86, 209

  Brahmins, 20–26, 29–33, 36, 46, 51, 54, 77, 81–82, 112, 174, 210, 354

  dietary regulations of, 240–41, 298

  foreign travel forbidden for, 174, 185–86, 198, 240, 316, 329

  morning ritual of, 244

  Brighton Railway, 113

  British East India Company, 82, 99

  British India Lines, 195, 311

  Bromwich, T.J. I’A., 104, 105, 145, 176, 245, 284, 291

  Brouwer, Luitzen, 340

  Bryder, Linda, 270, 290

  Budapest, University of, 338

  Buddhism, 32

  Bulstrode, H. Timbrell, 266–67, 270

  Burkill, J. C., 254

  Burma Oil Company, 314

  Butler, Henry, 213

  Byron, George Gordon, Lord, 2, 345

  Calculus, 46, 89, 148–50, 153, 161, 249

  differential, 56

  integral, 166, 183

  pi in, 209

  California Institute of Technology, 364

  Cambridge Apostles, 137–41, 147, 157, 172, 228, 276

  Cambridge Magazine, 260, 277

  Cambridge Philosophical Society, 130, 245, 276, 295, 301, 303, 306

  Cambridge Review, 152, 307

  Cambridge Shakespeare Society, 136, 137, 142

  Cambridge Tracts in Mathematics and Mathematical Physics, 160

  Cambridge University, 1–4, 6, 40, 66, 100, 105–7, 109–11, 124, 126–33, 145, 154, 157, 163, 170, 226, 253, 285, 332, 344, 345, 361–65, 367, 368, 372

  arrangements to bring Ramanujan to, 172, 174, 190–94

  debating societies at, 137

  and Great War, 212–13, 227–29, 244, 246, 259–61, 311

  homosexuals at, 140–44

  Newton’s influence at, 148–50

  Ramanujan at, 198, 200–207, 210–15, 219–20, 228–31, 233–35, 237–46, 252–59, 289–91, 315, 330, 351, 357

  Tripos system at, see Tripos system

  See also specific colleges

  Cambridge University Press, 337, 341

  Camford Observed (Rose and Ziman), 361

  Campbell, Islay Makimmon, 259

  Cancer research, 348

  Cardus, Neville, 123

  Carmichael, Robert, 337

  Carnot’s Cycle, 131

  Carpenter, Edward, 140

  Carr, George Shoobridge, 39–46, 57, 58, 72, 90, 92, 105, 164, 173, 203, 253, 356

  Carstairs, G. Morris, 23

  Cartwright, Mary, 156, 171, 364, 369, 372

  Case of the Philosopher’s Ring, The (Collins), 109

  Caste system, 20–23, 112, 314

  Cauchy, Augustine Louis, 150, 287

  Cauchy’s theorem, 249

  Central College (Bangalore), 91

  Central Powers, 212

  Chandler, Laura, 118

  Chandrasekhar, Subrahmanyan, 329–30, 333, 335, 352, 354, 372

  Chandrasekar, P. S., 321, 322, 330

  Charley’s Aunt (play), 231

  Chatterji, G. C., 230–31, 237–39, 275

  Chattopadhyaha, Mrilani, 237–38

  Chaudhuri, Nirad C., 75, 243

  Chengalvarayan, K., 315

  Chettiar, Alagappa, 355

  Chicago, University of, 364

  Chola Empire, 15

  Churchill, Winston, 133

  Circle method, 249, 252, 324

  Clarke,
Eustace Thomas, 116

  Class system, British, 112, 113

  Colinette House, 311–12, 319

  Collins, Randall, 109

  Collins, Robert, 261

  Colorado, University of, at Boulder, 340

  Combinatorics, 250

  Combinatory Analysis (MacMahon), 305

  Commercial Printing Press, 341

  Composite numbers, 231–32, 234, 337

  Comptes Rendus, 252

  Compton, Herbert, 55, 101, 102, 272

  Computers, 349

  Congruences, 302–3, 306, 313, 339, 370

  Connemara Library (Madras), 180

  Continued fractions, 57, 215

  Continuous functions, 134

  Continuous quantities, 249

  Convergent series, 88

  Conversazione Society, 137

  Coombs, “Iron Man,” 364

  Corpus Christi College, Cambridge, 212, 256

  Cotterell, C. B., 193

  Course in Pure Mathematics, A (Hardy), 153

  Cours d’analyse de I’Ecole Polytechnique (Jordan), 134, 149, 172

  Cranleigh School, 113–20, 123, 126, 136, 142, 171, 172

  Crystallography, 348

  Cubic equations, 27

  Cubism, 157

  Curzon, Lord, 99

  Darling (mathematician), 168

  Davenport (mathematician), 344

  Davies, Arthur, 174, 184, 190

  Davies, P. D. O., 267–68

  Decemviri debating society, 137

  Dedekind (mathematician), 150

  Definite integrals, 90, 182–83

  Delhi, University of, 348

  Deligne, Pierre, 343, 344

  Denmark, tuberculosis in, 267

  Denton, Eliza, 118

  Derby, Lord, 228

  Descartes, René, 287

  Deshmukh, C. D., 230

  Dewsbury, Francis, 192–93, 233, 234, 307, 309–12, 317–18, 322, 337, 345, 362

  Diaghilev, Serge, 157

  Dickinson, Goldsworthy Lowes, 138, 228

  Discovery of India (Nehru), 354

  Discrete quantities, 249

  Divergent series, 80, 174, 203

  Dougall-Ramanujan Identity, 167

  Doyle, Arthur Conan, 109, 325

  Dravidian peoples, 32, 33

  Dryden, John, 239

  Dubos, Jean, 270

  Dubos, René, 270

  Dudley Smith, Charles Jervoise, 260

  Dyson, Freeman, 339–41, 346, 349, 368

  Ecole Polytechnique, 285

  Eddington, Sir Arthur, 372

  Edinburgh, University of, 366

 

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