The Man Who Knew Infinity

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The Man Who Knew Infinity Page 57

by Robert Kanigel


  Indian Student Hostel, 258

  Edison, Thomas Alva, 347

  Education Times, 77, 168, 171

  Edward VII, King of England, 101, 136, 157, 211

  Edwardian Turn of Mind, The (Hynes), 140, 148

  Einleitung in die Funkionentheorie (Stoltz and Gmeiner), 153

  Einstein, Albert, 111, 340, 359, 366, 373

  Elliptic functions, 61, 169, 205

  modular, 247

  Elliptic integrals, 80, 201

  Ellis, Havelock, 126, 140, 142, 143, 146–47

  Emden (ship), 314

  England

  after armistice, 310–11, 363

  conditions for Indian students in, 256–58

  cooking in, 299

  in Great War, 212–14, 235, 262

  tuberculosis in, 265–68, 270

  Enlightenment, the, 287

  Erdos, Paul, 338, 350, 358

  Eton, 112, 113, 120

  Euclid, 86, 131, 216–17

  Euler, Leonhard, 50, 147, 205, 208, 221, 247–48, 250, 287, 340

  Euler-Maclaurin summation formula, 90

  Eves, Howard, 340

  Exponential growth, 217

  Fearnside, C. F., 320

  Fearon, W. A., 121, 122, 124, 133

  Fellow of Trinity, A (St. Aubyn), 124–25

  Fermat, Pierre de, 81, 147, 221

  Fichte, Johann Gottlieb, 287

  First Eastern General Hospital, 213, 227, 260

  First Indian War of Independence, 99

  Fitzgerald, Edward, 2

  Fitzroy House, 300, 311

  Formalism, 205–6

  Forster, E. M., 138, 141

  Forsythe, Andrew Russell, 132, 150–51, 233, 291

  Foster, Michael, 54

  Fourier series, 157

  Four Years in an English University (Satthianadhan), 256–57

  Fractions, continued, 57, 215

  France

  after armistice, 364

  in Great War, 211–14, 227, 235, 260, 277, 307, 311

  Nazi occupation of, 369

  Franco-Prussian War, 363

  Franz Ferdinand, Archduke, 211

  Frechet (mathematician), 340

  Frullani’s integral theorem, 183

  Fuller, Sir Bampfylde, 102

  Functional analysis, 366

  Functional notation, 61–62

  Gallipoli, Battle of, 235

  Gamma functions, 167

  negative values of, 159

  Ganapathy, M. M., 318

  Gandhi, Indira, 353–54

  Gandhi, Mohandas K., 99, 185, 241, 299, 314, 330, 351

  Gandhi, Rajiv, 351

  Gauss, Karl Friedrich, 147, 150, 160, 167, 169–70, 218, 287

  Gaye, R. K., 136, 139

  Generating functions, 247

  Genetics, 146

  Geometry, 86, 119, 149, 152, 208–9

  algebraic, 344

  George V, King of England, 96, 99, 157, 200

  Germany

  after armistice, 363

  in Great War, 211–14, 227, 229, 262, 298, 306–7, 314

  Nazi, 365, 368, 369

  tuberculosis in, 267, 270

  in World War II, 340

  Girton College, Cambridge, 142, 307

  Gmeiner (mathematician), 153

  Gonville & Caius College, Cambridge, 126

  Gopalachary, K., 282

  Gosh, Umes Chandra, 171

  Government College (Kumbakonam), 27, 28, 45–47, 49, 51, 53, 54, 77, 90, 101, 198, 293

  Govindaraja Iyengar, N., 56

  Graham, W., 103–4, 261

  Grama devata (village gods), 33, 35

  Granlund, Paul, 352

  Grant, Duncan, 139

  Grant-Duff, Mountstuart George, 84

  Great War, 18, 211–14, 227–29, 234–35, 244, 246, 259–64, 267, 276–77, 298, 306–7, 310–11, 314–15, 347, 361, 363, 365

  Greeks, ancient, 86, 88, 165, 287

  Gregory, James, 209

  Griffith, C. L. T., 103–5

  Grouping like terms, 42

  Guns of August, The (Tuchman), 212

  Hadamard, Jacques, 218, 285–87

  Haldane, J. B. S., 353, 366

  Hanumantha Rao, B., 178

  Hardy, G. H., 4, 5, 7, 109–57, 197, 198, 213, 216–17, 221, 222, 232, 238, 242, 302, 303, 305, 326, 329, 333, 334, 337–41, 343–47, 349–51, 356–73

  in Apostles, 137–41

  arranges for Ramanujan to come to Cambridge, 191–92

  atheism of, 109, 117, 286

  birth of, 113

  childhood of, 114–20

  collaborative papers with Littlewood, 157, 165, 228, 264

  collaborative papers with Ramanujan, 248–52, 276, 301, 338, 340, 368

  correspondence with Ramanujan, 107, 159–79, 181, 183–84, 187, 190, 198, 209, 216, 218–19, 229, 248, 255, 323–24, 328, 337, 341

  and cult of uselessness, 146–48

  death of, 369

  elected to Royal Society, 145–46

  and Great War, 228, 229, 234, 260, 276–77, 361, 363, 365

  homosexuality of, 139–44

  honors received by, 366–67, 369, 373–74

  importance of Ramanujan’s memory to, 369–73

  in London Mathematical Society, 208, 231, 245, 276, 291

  and meals at Trinity, 239, 240

  nature of relationship with Ramanujan, 271–72, 275–80, 289

  Neville and, 186, 191

  and Ramanujan’s notebooks, 204, 280, 313

  at Oxford, 361–65, 370

  physical appearance of, 109

  political views of, 366

  and Ramanujan at Cambridge, 201–7, 210, 219–20, 230, 231, 233–35, 245, 246, 252–57, 289–91, 315

  and Ramanujan’s death, 331, 332, 336, 337, 361–63

  and Ramanujan’s illness, 263, 264, 271, 290, 295–300, 312, 321, 322, 328

  on Ramanujan’s intuition, 215–16, 220, 223–27

  and Ramanujan’s return to India, 307, 309–10

  and Ramanujan’s spirituality, 280, 283, 284, 286, 288–89

  rigor of, 151–54

  and Royal Society, 291–96, 300, 301

  suicide attempt by, 368–69

  and Tripos, 128, 129, 132–36, 155–56

  on unconscious activity, 285–86

  in United States, 364

  at Winchester, 120–26

  wins Trinity College scholarship, 125–26

  writing style of, 151–52, 371–72

  Hardy, Gertrude Edith (sister), 113–18, 136, 139, 368, 369

  Hardy, Isaac (father), 113–18, 120, 126, 136

  Hardy, Sophia Hall (mother), 113–18, 136, 139

  Hardy-Weinberg Law, 146, 148

  Hari Rao, N., 46, 76

  Harold, Earl of Wessex, 133

  Harrod, Roy, 141

  Harrow, 112, 113, 120

  Hartley, L. P., 5

  Harvard University, 165, 366, 372–73

  Hastings, Battle of, 133

  Haverford College, 289

  Heisenberg, Werner, 373

  Henry VIII, King of England, 128

  Herman, R. A., 300

  Hermite (mathematician), 169, 210, 287

  Highly composite numbers, 231–32, 234, 337

  Hilbert, David, 220, 226

  Hill, A. V., 365

  Hill, M.J. M., 103–6, 176

  Himmelfarb, Gertrude, 140, 141, 147

  Hindu (newspaper), 67–68, 95, 195, 237, 273, 317, 347

  Hinduism, 7, 11, 17, 19–21, 23, 24, 29–31, 33–35, 54, 71–72, 96, 282, 283, 288

  ban on foreign travel in, 185

  mathematics in, 86

  History of the English-Speaking Peoples (Churchill), 133

  Hitler, Adolf, 365, 373

  Hobbes, Thomas, 109

  Hobbs, Jack, 109, 364, 366

  Hobson, E. W., 106–7, 145, 170–72, 291, 358, 364

  Hodges, Andrew, 139, 278

  Holman, Donald, 260

  Home Rule League,
314

  House of Commons, 157

  House of Lords, 157, 242–43

  Howard, John Brerton, 260

  Huxley, Julian, 124

  Hynes, Samuel, 140, 148

  Hyperbolic cosines, 176

  Hypergeometric series, 57, 80, 167, 204

  Identities, 303, 305–6, 313, 340

  Illinois, University of, 346

  Illustrated Weekly of India, 356, 358

  Imaginary numbers, 59, 208

  In a World I Never Made (Wootton), 261

  India Office, 172, 174, 184, 190–92, 332

  Indian Civil Service (ICS), 99–100, 102, 162, 322

  Indian Mathematical Society, 77–79, 85, 86, 96, 98, 171, 180, 189, 295, 315, 347, 356, 357

  Journal of, 85–87, 90–93, 182, 188, 219, 230, 315, 334–35, 337

  Indian Meteorological Department, 174

  Indian National Congress, 314

  Indian National Science Academy, 355

  Indian Statistical Institute, 215

  Indian Universities Act (1904), 178

  Infinite series, 47, 87–89, 145, 161, 167, 171, 177, 216

  applications of, 349

  Bernoulli numbers and, 90

  pi and, 209

  theta functions as, 323

  Infinity, 66, 160

  Ingalls, Daniel, 23

  Institute for Advanced Study, 346

  Institutes of Manu, 21

  Integers, 59, 61

  Integrals, 145

  definite, 90, 182–83

  elliptic, 80, 201

  theorems on, 161, 165–67

  Intermediate Sex, The (Carpenter), 140

  Introductio in analysin infinitorum (Euler), 205

  Introduction to the History of Mathematics (Eves), 340

  Introduction to the Theory of Numbers, An (Hardy and Wright), 302

  Irrational numbers, 59, 154

  Jacobi, Karl Gustav Jacob, 65, 168, 169, 205, 256, 283, 323

  Jackson, Henry, 213, 227, 261, 263

  James, William, 287

  Janaki (Ramanujan’s wife), 69–71, 96–98, 178, 180–81, 189, 194, 229, 256, 258, 316–20, 322, 327–31, 333, 336, 342, 351–53

  Komalatammal and, 96, 97, 271–75, 316, 318–20, 327

  Jeans, James Hopwood, 136, 287–88

  Jesus College, Cambridge, 126

  Jews, 365–66

  Joan of Arc, 190

  Johnson, W. Woolsey, 153

  Jordan, Camille, 134–35, 145, 148, 149, 172

  Jung, Carl, 372

  Kac, Mark, 281, 338

  Kapalaswara Temple, 82

  Kasturirangar Iyengar, S., 195, 237

  Keers, R. Y., 267

  Kelvin, Lord, 131, 150

  Keynes, John Maynard, 138, 139, 141, 170

  Kincaid, Dr., 299

  King’s College, Cambridge, 1, 126, 138, 214, 230, 307

  Kipling, Rudyard, 101, 262, 278–79

  Klein, Felix, 226

  Kloosterman (mathematician), 344

  Koch, Robert, 265, 269

  Komalatammal (Ramanujan’s mother), 11–14, 18–20, 34, 36–37, 47, 54, 65, 68–73, 180, 256, 259, 312, 322, 354, 357

  Janaki and, 96, 97, 271–75, 316, 318–20, 327

  orthodoxy of, 186

  and Ramanujan’s death, 326–27, 329–33

  and Ramanujan’s return to India, 316

  and trip to England, 188–91, 194, 195, 271

  Krishna Rao, R., 78, 199, 224

  Krishnaswami Iyer, C.R., 84

  Krishnaswami Iyer, S., 26, 27

  Kronecker (mathematician), 210

  Kshatriyas, 20, 21

  Kula devata (family deity), 35–36

  Kuppuswami, Dr., 72

  Kupuswamy (Ramanujan’s grandfather), 17

  Lakshmi Narasimhan (Ramanujan’s brother), 12, 316, 318, 331, 334

  Landau, Edmund, 363, 365

  Laplace, Marquis Pierre Simon de, 168

  La Poussin, Charles J. de, 285

  Larmor, Sir Joseph, 260–61

  La Vallée-Poussin (mathematician), 218

  Leçons sur les fonctions de variables réeles (Borel), 153

  Lee, Alice, 118

  Legendre, Adrien Marie, 160, 169, 210

  Lehigh University, 364

  Lehmer, Emma, 346, 350

  Leibniz, Gottfried von, 89, 148, 165, 209, 210, 287

  Lenin, V. I., 366

  Letters from an Indian Clerk (television special), 4–5, 352

  Levy, Paul, 276

  Lincoln Diocesan Training College, 113, 114

  Littlehailes, Richard, 178, 182, 192–94

  Littlewood, J. E., 135, 139, 141, 145, 151, 152, 163–65, 186, 192, 198, 213, 220, 221, 224, 226, 233, 238–40, 242, 251, 254, 280–81, 288, 295, 340, 341, 358, 366, 370

  collaborative papers with Hardy, 157, 165, 228, 264

  in Great War, 228, 229, 234, 277

  and London Mathematical Society, 208

  and Ramanujan at Cambridge, 201, 205–7, 210, 315

  on Ramanujan-Hardy collaboration, 253

  and Ramanujan’s letters, 163, 165, 168–69, 173, 181, 216

  on rigor, 150

  and Royal Society, 291, 292

  and Trinity Fellowship for Ramanujan, 299–301

  and Tripos system, 132, 133, 155–56

  Liverpool University, 204

  Lloyd George, David, 193

  Loder, John de Vere, 259

  Lodge, Oliver, 255

  Logarithms, 217–18

  Lomas, John, 139

  London, University of, 115

  London Mathematical Society, 104–6, 111, 164, 170, 208, 229, 245, 261, 276, 291, 324, 336, 350, 369

  Proceedings of, 145, 162, 225, 231, 248, 252, 291, 305, 306, 313, 336, 337, 371

  London Observer, 263

  Loney, S. L., 27, 44, 163

  Louvain (Belgium), 213–14

  Love, A. E. H., 134, 145, 172

  Lusitania (ship), 229

  Lytton Committee on Indian Students, 242, 257

  Macaulay, Lord, 2, 101, 163

  Mach, Ernst, 90

  MacMahon, Major Percy Alexander, 250, 251, 301–3, 305, 306, 336

  McMurry, Nan Marie, 328

  Madhava, K. B., 180

  Madras, University of, 24, 52, 233, 263, 290, 311, 331, 336, 352

  Centre for Advanced Studies in Mathematics, 355

  See also Presidency College Madras Christian College, 74, 75, 92, 101, 182

  Madras Engineering College, 103

  Madras High Court, 178

  Madras Medical College, 321

  Madras Port Trust, 94–98, 102, 159, 175, 178–80, 293, 312, 317

  Madras Presidency, 15–17, 95, 99

  Magdalene College, Cambridge, 126, 264

  Magpie & Stump debating society, 137

  Mahabharata, 20, 29

  Mahalanobis, Prasantha Chandra, 1–4, 66, 214–15, 224, 230, 241

  Mahammakham festival, 15

  Maisky, J., 366

  Majlis, 245

  Mallet, C., 191–92

  Mallikeswarar Temple, 342

  Manchester, University of, 164, 366

  Manchester Guardian, 371

  Manners and Morals Among the Victorians (Himmelfarb), 140

  Marlborough, 112

  Marne, Battle of the, 212

  Marshall, Francis, 124

  Mask of Shame, The (Wurmser), 50

  Mathematical Association, 155

  Mathematical Gazette, 47, 152–53

  Mathematician’s Apology (Hardy), 147, 152, 285, 369

  Mathematician’s Miscellany, A (Littlewood), 163

  Mathematische Zeitschrifi (journal), 370

  Matlock House Sanatorium, 269–71, 290, 294, 296–300, 306, 311

  Maxwell, James Clerk, 130, 137, 150

  Maynard, Catherine, 118

  Mechanics, statistical, 348–49

  Mendel, Gregor, 146

  Mendelssohn, Felix, 344

  Mendip Hills Sanatorium, 265, 269
, 270

  Men of Mathematics (Bell), 65

  Michelangelo, 350

  Michelson, Albert, 291

  Middlemast, E. W., 94, 101, 102, 195, 315

  Milton, John, 345

  Mittag-Leffler, Gösta, 363, 370

  Modular equations, 204, 210, 348

  Modular functions, elliptic, 247

  Moghul empire, 32

  Mordell, Louis J., 169, 170, 226, 253, 254, 337, 338, 365

  Moore, G. E., 137, 147, 276–77

  Much Ado About Nothing (Shakespeare), 142

  Muslims, 32, 33, 86

  Muthalpiet High School, 342

  Muthu, Dr., 196, 265

  Myers (philosopher), 287

  Nagoya (ship), 314, 321

  Namberumal Chetty, 326

  Nandy, Ashis, 68, 335, 371

  Nanjunda Rao, M. C., 317

  Narasimha, 101, 106

  Narasimha Iyengar, K., 188, 195, 318, 328–29

  Narayana Iyengar, K., 19, 74

  Narayana Iyengar, M. T., 91, 188

  Narayana Iyer, S., 95–98, 102–3, 106, 174, 178, 180, 182, 184–85, 189–90, 195–96, 210, 219, 229, 258, 317, 332, 357

  Narayanan, W., 333, 352

  Narayanaswami, Dr., 74

  Narayanaswamy Iyer, G. V., 327

  Narosa Publishing House, 351

  National Cadet Corps of India, 351

  National India Association, 200

  National Union of Scientific Workers, 366

  Nature (magazine), 336, 363, 365

  Nayak kings, 29

  Negative numbers, 59

  Nehru, Jawaharlal, 99, 330, 351, 354, 356

  Nelson, Lord, 278

  Nesting of square roots, 86–87

  Nevasa (ship), 195–99, 202, 256, 265, 311, 314, 315

  Neville, Alice, 200, 202, 259

  Neville, E. H., 46, 47, 57, 65, 75, 78, 150, 169, 171, 177–79, 184, 186–87, 190–92, 198–202, 211, 212, 238–40, 242, 245, 264, 277, 295, 299, 316, 335–36, 357–58

  New College, Oxford, 125, 361–63

  New India (newspaper), 314

  Newman, Morris, 340

  Newnham College, Cambridge, 142, 238

  Newsome, David, 143

  Newton, Isaac, 2, 89, 131, 148–51, 165, 209, 239, 256, 287, 345

  New York Times, The, 373

  Nicholas, Tressilian, 276

  Notation systems, 60–63

  Bernoulli’s, 90

  Newton’s, 149

  Non-Conscription Fellowship, 277

  Number theory, 6, 63, 152, 161, 169, 246, 249, 339, 340, 343

  additive, 303

  analytical, 249, 340

  probabilistic, 338

  Numerical computation, 63

  Ohio State University, 364

  Orders of Infinity (Hardy), 160, 164, 216

  Osler, William, 268

  Oslo, University of, 366

  Oxford University, 100, 126, 131, 139, 144, 257, 305, 368

  Hardy at, 361–65, 370

  Pachaiyappa’s College, 52–55, 57, 65, 70, 74, 93, 106, 194, 281, 282, 315, 321

  Parliament Bill, 157

  Parthasarathy Temple, 179, 186

 

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