The Man Who Knew Infinity
Page 57
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