“devices to stimulate the imagination.” Hardy, Collected Papers, 598.
“which is to my mind unequalled.” Quoted in H. T. H. Piaggio, “Three Sadleirian Professors,” The Mathematical Gazette 15 (1931): 464.
Thought impossible without words. Hardy, Collected Papers, 837.
Act of writing gave him pleasure. Bollobás, Littlewood’s Miscellany, 118.
Hardy on Johnson’s book. Hardy, Collected Papers, 819.
“of far greater intrinsic difficulty.” Hardy, Pure Mathematics, vi.
“look and behave very much like a line.” Ibid., 4.
“little better than nonsense.” Arthur Berry, The Mathematical Gazette 5 (July 1910): 304.
“to reform the Tripos.” Hardy, Collected Papers, 537.
“so long as its standard is low.” Ibid., 528.
“into a marginal first.” Ibid., 537.
“Our English way.” H. B. Heywood, “The Reform of University Mathematics,” The Mathematical Gazette 12 (1925): 323.
“high-souled frustration.” Littlewood, Miscellany, 71.
“an acrobat.” C. J. Hamson, [untitled], Trinity Review (1986): 23.
“he was so kind to the weak ones.” A variant of the story appears in M. L. Cartwright, “Some Hardy-Littlewood Manuscripts,” Bulletin of the London Mathematical Society 13 (1981), 294.
“in the same generous terms.” Titchmarsh, 454.
Hardy would discuss Bergson. R. Clark, 169.
an undergraduate. Wiener, Ex-Prodigy, 183.
“truths and values.” Woolf, Beginning Again, 20.
Hardy’s routine. Snow, Apology foreword, 31.
CHAPTER FIVE
covered with Indian stamps. Snow, Apology foreword, 30. Unless otherwise noted, most of the account describing the receipt of Ramanujan’s letter is drawn from Snow, 30–38.
“I beg to introduce myself.” Ramanujan, Collected Papers, xxiii.
“enclosed papers.” Ramanujan’s letters are in the Cambridge University Library. Most of them appear in Ramanujan, Collected Papers, xxiii–xxx and 349–355.
late January 1913. Snow, Apology foreword, 31, gives the time as simply “January.” Ramanujan wrote him on January 16. Time for mail to reach England was usually less than two weeks. A day between January 26 and January 31 seems most likely.
a practical joke. Snow, 30–31, speaks of Hardy getting manuscripts from “cranks,” viewing Ramanujan’s as possibly a “fraud.” Neville, in the Reading Manuscript, expands on this theme considerably.
“some curious specialization of a constant.” Hardy, “Obituary,” 494.
“prodigy.” Littlewood, Miscellany, 66.
The books Littlewood studied. Ibid.
“a rough-hewn earthy person.” Bateman and Diamond, 33.
“unfortunately very saintly.” Littlewood, “Reminiscences.”
long-term relationship with a married woman. The relationship was one of many decades’ standing. The woman was the wife of Dr. Streatfeild, Bertrand Russell’s physician. Littlewood’s daughter is Ann Johannsen. Bollobás, Littlewood’s Miscellany, 18. Interviews with Béla Bollobás, Charles Burkill.
“storm and smash a really deep and formidable problem.” Hardy, quoted in Burkill, 61.
it went to Hardy as referee. Littlewood, Miscellany, 78.
turned out to be flawed. Bateman and Diamond, 29.
“only three really great English mathematicians.” This has become a commonplace in mathematical circles.
recently moved into rooms on D Staircase. Trinity College records.
probably in Littlewood’s rooms. Snow, 33, says it was Hardy’s rooms. But Bollobás, in “Ramanujan—A Glimpse,” 76, says it was Littlewood’s. Mary Cartwright, who was Littlewood’s student and collaborator, pictures Littlewood as invariably expecting people to come to see him. She deems it unlikely that they met in Hardy’s rooms.
“seemed scarcely possible to believe.” Hardy, “Obituary,” 494.
“I should like you to begin.” Hardy’s response to Ramanujan’s letter over the next few pages is largely drawn from Hardy, Ramanujan, 7–10.
“curious and entertaining.” Hardy, in Ramanujan, Collected Papers, xxv.
“theorems sent without demonstration.” Neville, “Ramanujan” (Nature 149), 293.
“a man of altogether exceptional originality and power.” Hardy, Nature (1920): 494–495.
before midnight. This is the canonical version, according to Snow. But in an interview, Béla Bollobás emphasizes that Ramanujan’s formulas were complicated, his results astounding; that even Hardy and Littlewood may have needed more than an evening to evaluate them; that, while true to the spirit of the events, Snow may conceivably have collapsed several evenings’ work into one.
“really an easy matter.” Mordell, “Ramanujan,” 643.
“another of those monstrosities.” Bell, 314.
“a distinguished and conspicuous figure.” Hardy, Collected Papers, 751.
suggesting great imagination or flair. H. T. H. Piaggio, “Three Sadleirian Professors,” The Mathematical Gazette 15 (1931): 463.
“An old stick-in-the-mud.” Interview, Mary Cartwright.
new and original—but not better. I owe to inventor Jacob Rabinow this insight into the natural and normal human resistance to the new.
“Indian Bazaar.” Cranleigh School Magazine, May 1887, 112.
“I was a depressed class.” Interview, Mary Cartwright.
“the large bottomed.” Snow, Apology foreword, 42.
“for the downfall of their opposites.” Snow, “The Mathematician,” 70.
“forget the sensation.” Neville, “Ramanujan” (Nature 149), 293.
Hardy had sprung into action. Snow, Apology foreword, 34, says it was the next day. In any case, Hardy got in touch with the India Office before he even wrote Ramanujan.
“I was exceedingly interested by your letter.” Letter, Hardy to Ramanujan, 8 February 1913.
Later in the month, Davies met with Ramanujan. Letter, Ramanujan to Hardy, 22 January 1914.
On February 25. Memo, Sir Francis Spring. S. R. Ranganathan, 29.
“anxiety as to his livelihood.” P. K. Srinivasan, 55.
Hardy’s imprimatur. That Walker’s assessment was formed largely by Hardy’s letter is not the way the story usually comes down to us. Hardy (Collected Papers, 703) says Walker “was far too good a mathematician not to recognize [the quality of Ramanujan’s work], little as it had in common with his own. He brought Ramanujan’s case to the notice of the Government.” But the contrary conclusion, that Walker’s recommendation came only in the wake of Hardy’s letter, seems unavoidable. For one thing, in Spring’s memo (Suresh Ram, 27–28), he notes that Walker “disclaimed ability to judge Mr. Ramanujan’s work and said that Mr. Hardy of Trinity College, Cambridge, was in his opinion the most competent person to arrive at a judgement of the true value of the work. Mr. Ramanujan had already been in correspondence with Mr. Hardy, a letter of whose dated 8 February 1913—just 17 days before Dr. Walker’s visit here—is in this file.” Lining up Walker behind Ramanujan smacks of an orchestration of Madras opinion by Spring and Narayana Iyer.
“who views my labours sympathetically.” Letter, Ramanujan to Hardy, 27 February 1913. Cambridge University Library.
fortified by Hardy’s letter. Hardy’s letter to the Secretary for Indian Students had also reached Madras. See S. R. Ranganathan, 34.
“invincible originality.” Hardy, Collected Papers, 720.
Ramanujan’s second letter. 27 February 1913.
“perfect in manners, simple in manner.” Neville, “The Late” (Nature 106), 662.
“his name would live for one hundred years.” Transcript, Nova 1508, 18.
“not done by ‘humble’ men.” Hardy, Apology, 66.
“what we can do for S. Ramanujan.” Suresh Ram, 29.
syndicate’s action. See Suresh Ram, 28–31; S. R. Ranganathan, 30–31; letter, K. Venkatachaliengar to Bruce Berndt, s
upplied by Berndt.
“with all their vehement speeches.” Letter, K. Venkatachaliengar to Bruce Berndt.
By April 12, Ramanujan had learned the good news. Letter, Ramanujan to Registrar, University of Madras, 12 April 1913. Madras Port Trust.
“a vice in Kumbakonam.” Neville, “Ramanujan” (Nature 149), 293.
a corruption of Tiru Alli Keni. Krishnaswami Nayadu, 30. The description of the Triplicane tank and adjacent temple is drawn from personal observation and Das, 245.
Pallava king’s gift of land. Krishnaswami Nayadu, 30.
moved back to Triplicane. Family Record.
threshold for paying full dues. Journal of the Indian Mathematical Society (February 1917), 19.
work with Narayana Iyer. S. R. Ranganathan, 31.
math books from K. B. Madhava. P. K. Srinivasan, 132.
Ramanujan at the Connemara. S. R. Ranganathan, 31.
Serve food in his hand. Ibid., 90.
his mother made it for him. Interview, Janaki.
a little science experiment. Interview, Janaki. Ashis Nandy, 131, speaks of Ramanujan “teaching her the elements of science,” but places this after Ramanujan’s return from England, not before.
“the one you were working on before eating.” Interview, Janaki. Nandy pictures Ramanujan as “using her as a secretary,” again referring to the post-England period.
She didn’t ask him to, and he didn’t volunteer. Interview, Janaki.
“How maddening his letter is …” Letter, Littlewood to Hardy, in Ramanujan, The Lost Notebook, 383.
“your obvious mathematical gifts.” P. K. Srinivasan, 56.
“what little I have.” Letter, Ramanujan to Hardy, 17 April 1913. Cambridge University Library.
August get-together. S. R. Ranganathan, 12.
submitted some theorems. Journal of the Indian Mathematical Society 5, no. 5: 185.
perhaps out to win over … Littlehailes. Letter, K. Venkatachaliengar to Bruce Berndt.
he looked forward to studying Ramanujan’s results. Memo, Narayana Iyer, 31 October 1913. Madras Port Trust.
“Does Ramanujan know Polish?!?” S. R. Ranganathan, 12.
Quarterly Reports. See Berndt, Ramanujan’s Notebooks, part I, 295; and Berndt, “Quarterly Reports.”
“to discover new pathways through the forest.” Berndt, “Quarterly Reports,” 516.
“ ‘new and interesting.’ ” Berndt, Ramanujan’s Notebooks, part I, 297.
“the result is wrong.” P. K. Srinivasan, 57.
“no human agency.” Snow, Apology foreword, 34.
Ramanujan’s version. Letter, Ramanujan to Hardy, 22 January 1914. Cambridge University Library.
“a dead man in their estimation.” T. Ramakrishna.
“disregard the orders of the caste?” Gandhi, 37.
with men from the villages bringing their wives and children. J. Chartres Molony, A Book of South India (London: Methuen & Co., 1926). Cited in Lewandowski, 53.
the area around Triplicane’s Parthasarathy Temple. A detailed map in Lanchester, unpaged, shows residential patterns in Madras.
“not a man like Littlewood.” Letter, Hardy to Mittag-Leffler, about 1920. Robert Rankin, Glasgow.
Senate House. Muthiah, 106; personal observation.
“a man at once diffident and eager.” Neville, Reading Manuscript.
“opposition … withdrawn.” Neville, “Ramanujan” (Nature 149), 293.
Influences on Ramanujan to go to England. S. R. Ranganathan, 36.
“weight of my influence.” Ramachandra Rao, 88.
“the fulfillment of his life’s purpose.” Neville, “Ramanujan” (Nature 149), 293.
in late December of 1913. Family Record.
Ramanujan wrote back home. Family Record . .
three nights. P. K. Srinivasan, 114; Bharathi, 48.
“I locked myself up in the attic.” Quoted by C. T. Rajagopal, Mathematics Teacher (India) 11A (1975), 119.
“within a very few months.” Letter, Ramanujan to Hardy, 22 January 1914.
he had come to say good-bye. P. K. Srinivasan, 100.
Ramanujan’s other doubts. Letter, Ramanujan to Hardy, 22 January 1914; and Neville, “Ramanujan” (Nature 149), 293.
Father-in-law’s concerns. K. R. Rajagopalan, 33.
Mother’s concerns. Ibid., 32–33.
actually shook his hand. K. R. Rajagopalan, 34.
“the glory that belonged to Madras.” Neville, Reading Manuscript.
“where they longed to see him.” Neville, Reading Manuscript.
Neville wrote Hardy. Neville, “Ramanujan” (Nature 149), 294.
a worried reply. Letter, Mallet to Hardy, 11 February 1914. The Library, University of Reading.
“I’m writing in a hurry.” Letter, Hardy to Neville. The Library, University of Reading.
“unknown geniuses.” Neville, “Ramanujan” (Nature 149), 294.
“the most interesting event.” P. K. Srinivasan, 59.
“hidden under a bushel in Madras.” Ibid., 61. If Venkatachaliengar’s account of the syndicate meeting is accurate, Littlehailes had by now changed his tune.
“if not transcendental, order of genius.” Ibid., 64.
“by no means the worst brain.” Quoted in Slater, Southern India, 262.
“for the full development of personality.” Ibid., 263.
“His Excellency cordially sympathizes.” S. R. Ranganathan, 35.
On March 11. S. R. Ranganathan, 37.
On March 14. Interview, Janaki. “Three days before he left …”
Now, he wept. Interview, Janaki.
while her mother-in-law was at the temple. Kalyanalakshmi Bhanumurthy, “The Man Behind the Mathematics,” The Hindu, 20 December 1987.
she was so young and pretty. K. R. Rajagopalan, 35.
“as if … obeying a call.” Ramachandra Rao, 88.
driving him around town on his motorcycle. S. R. Ranganathan, 36.
“nothing but vegetable food.” Ramachandra Rao, 88.
How, he pleaded, was he to wear them? P. K. Srinivasan, 134; S. R. Ranganathan, 62.
she wouldn’t recognize him. K. R. Rajagopalan, 35.
his friends stayed up with him. S. R. Ranganathan, 71.
a special wharf. The Port of Madras: Past, Present and Future, 8. Ramanujan’s friend K. Narasimha Iyengar reports, in S. R. Ranganathan, 70, that Spring prevailed on Ramanujan and Neville to leave from Madras, not the more usual Bombay.
The Nevasa. Details drawn from (British) National Maritime Museum Information File; BI Centenary, 1856–1956, by George Blake (London: Collins, 1956); “The Notable ‘Nevasa,’ ” by J. H. Isherwood, in Sea Breezes, new series 21 (1956): 28–31; “End of the ‘Nevasa,’ ” Sea Breezes, new series 5 (1948): 148–149. Ramanujan’s send-off. P. K. Srinivasan, 91–92.
“he may get an inspiration.” Bharathi, 49.
CHAPTER SIX
seasick and unable to eat. P. K. Srinivasan, 3.
On March 19. The picture of Ramanujan’s voyage to England is drawn from Family Record; details about the Nevasa (see chapter 5); Ramanujan’s letters in P. K. Srinivasan; S. R. Ranganathan, 38; K. R. Rajagopalan, 36; P & O Pocket Book (London: Adam and Charles Black, 1908); Lloyds Weekly Shipping Index for the period of the voyage.
withdrew to his … cabin. K. R. Rajagopalan, 36.
“his own history or psychology.” Hardy, Ramanujan, 11.
four-hundred-rupee fare. The second-class fare between London and Bombay was 32 pounds in 1914, or about 480 rupees. British Passenger Liners of the Five Oceans, by C. R. Vernon Gibbs (London: Putnam, 1963), 63.
orthodox Brahmins among them. S. R. Ranganathan, 36.
POSH. A Hundred Year History of the P & O, 1837–1937, by Ernest Andrew Ewart (London: I. Nicholson and Watson, 1937), 112—113.
he posted at least four letters back to India. Family Record.
stamps showing the pyramids. P. K. Srinivasan, 92.
“warmest thanks to your unc
le.” Ibid., 3.
Reception by Neville. Letter, Raymond Neville to Robert A. Rankin, 15 May 1982.
London. See, for example, Geoffrey Marcus, 47.
“a tempo clearly faster.” Woolf, Beginning Again, 16.
Cromwell Road. Report of the [Lytton] Committee on Indian Students.
met A. S. Ramalingam. Rankin, “Ramanujan as a Patient,” 84.
Chestertown Road. Information on the street, and specifically the house at 113, is drawn from an interview with Constance Willis, the current owner, and tour of her house; photos from the Cambridgeshire Collection; and records furnished through J. D. Webb, Building Control Officer, Cambridge City Council.
for two months. In his dedication to Ramanujan of The Farey Series of Order 1025 (Cambridge: Cambridge University Press, 1950), xxvii, Neville remembers it as three months. But this conflicts with Ramanujan’s letter to Krishna Rao of 11 June 1914, in P. K. Srinivasan, 7. There, he says he’s already moved into the college (after less than two months in Cambridge).
Hardy and Neville took care of most of it. P. K. Srinivasan, 7.
dipped his pen in black ink. Terms Book, 1899–1915. Trinity College.
graced by a wondrous spring. Marcus, 112.
King George visited Cambridge. Cambridge Independent Press, 1 May 1914.
Littlewood … saw him about once a week. P. K. Srinivasan, 154.
“very unassuming, kind and obliging.” Ibid., 7.
Berry stood at the blackboard. P. K. Srinivasan, 145.
“even this was pronounced wrongly.” Quoted in K. G. Ramanathan, “Ramanujan: A Life Sketch,” Science Age, December 1987, 22.
he “waddled” across Trinity’s Great Court. Lecture notes, B. M. Wilson. Trinity College. Wilson later crossed out “waddled,” perhaps because he thought the word undignified, but it is clearly visible in the original manuscript.
“inconvenient for the professors.” P. K. Srinivasan, 7.
sad to leave. Interview, Mary Cartwright.
consummate hosts. T. A. A. Broadbent, “Eric Harold Neville,” Journal of the London Mathematical Society 37 (1962): 482.
nearly every day. Hardy, Ramanujan, 11.
perhaps a third. Ibid., 10.
“a mass of unpublished material.” Hardy, Collected Papers, 718.
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