The death centenary of Srinivasa Ramanujan, which fell on 26 April 2020. Sadly, went largely unnoticed in India. Even Google did not know, or did not find any need to doodle.
To mark the occasion, I had written a rather long essay for the OPEN magazine which published it online on the same day (see here). I had given it to them only the previous night. Those interested in a slightly different version, with more pictures, please see here.
While researching for the piece, I had come across reminiscences of Ramanujan by many of his contemporaries from school, college in Kumbakonam and Madras, Cambridge University, and elsewhere. These are available in “Ramanujan: The Man and the Mathematician” written/collated by S.R. Ranganathan, mathematician and father of library science in India, and published in 1967 by Asia Publishing House. Later editions are available. The excerpts given in this article are based on Ranganathan’s short book. Some of these anecdotes have also been recounted in Robert Kanigel’s classic biography of Ramanujan, The Man Who Knew Infinity, which was made into a movie with the same title.
Ramanujan reached England on 14 April 1914. About three months later, on 28 July 1914, the Great War (later called the First World War) started. Many young men, including lecturers and students, were drafted for the war effort. Those who refused to join, like Bertrand Russell, had to serve time in prison. The universities bore a deserted look as compared to normal times. As a result, the remaining students, especially the Indians, got to know each other better.
Two of Ramanujan’s Indian contemporaries at Cambridge were P.C. Mahalanobis and C.D. Deshmukh, both of whom went on to play a significant role in policy making in the early years after Indian independence. Kanigel notes how, of the two group photographs surviving from this period, Ramanujan was at the centre.
Interestingly, Ramanujan’s birthday, 22 December, is celebrated as Mathematics Day and that of Mahalanobis, 29 June, as Statistics Day. Deshmukh went on to join the Indian Civil Service and become the first Indian Governor of the Reserve Bank of India. Mahalanobis joined the Indian Educational Service and as Member of the Planning Commission, was instrumental in formulating the Second Five Year Plan. He had also established the Indian Statistical Institute. There are memorial lectures in the name of all the three, and prizes in names of both Ramanujan and Mahalanobis.
Reminiscences of C.D. Deshmukh
C.D. Deshmukh was former Finance Minister, Government of India; Chairman, University Grants Commission; Vice Chancellor, Delhi University; and Governor, Reserve Bank of India.
As Deshmukh recalled, “To my generation, who matriculated in the early years of the second decade of this century, the romance of the find of Ramanujan and his being enabled to proceed to Cambridge for advanced studies in Mathematics were well known from the newspapers. Nevertheless, it was a thrill to me to discover on reaching Cambridge in July 1915 that I was going to be a contemporary of Ramanujan at this famous seat of learning.” But he was at Jesus College, while Ramanujan was at Trinity College.
Deshmukh says that he got to know Ramanujan soon, and that their acquaintance developed into a close friendship. Ramanujan was a strict vegetarian. As “he suspected that even vegetarian food ordered from the college kitchen would be polluted with undetectable animal fats, he used to cook food for himself and his guests in person.” Deshmukh also got occasionally invited to these meals on a Sunday, where Ramanujan “apologised in a solicitous way about the spicy rasam...” Deshmukh adds that “The meals so served were quite delicious, especially as Ramanujan used to regale us with mathematical conundrums and puzzles which he took care to ensure were not above the heads of his non-mathematical friends.”
When Ramanujan stayed in London, he stayed at a lodging house where Deshmukh also later stayed. Two of the earlier residents there were Vithalbhai Patel and Vallabhbhai Patel. They had come to know about the place through common friends. In early 1918, as recounted by the landlady, Ramanujan had made a casual visit to the place. The deadly Zeppelin aircrafts were raiding London. Ramanujan had breakfast assuming it was pure vegetarian. On being told that the beverage was Ovaltine, he had a casual look at the tin, and was horrified to find that it contained powdered egg. Upset, he soon packed up and left for the Liverpool station to catch a train to Cambridge. He later wrote to the landlady informing that as he was near the station, there was heavy bombing in the vicinity. and that it was with great difficulty that he could catch a train. He was convinced that the raid was divine retribution for having “non-vegetarian”.
As Deshmukh summed up, “This incident illustrates very vividly the child-like simplicity which was such an engaging trait of Ramanujan. His was a most lovable personality with a God-fearing temperament and a humility which is seldom found in such geniuses.”
After Deshmukh left Cambridge, in early 1918, he did not meet Ramanujan much. But, on hearing of his illness, he called on him at the hospital. As Deshmukh continues, “Ramanujan was nursed in bed for TB but I doubt if he had been informed that his was a hopeless case. He did not appear unduly down-cast and told me, I think, that he was looking forward to returning to India as soon as he was in a fit condition to travel. But his condition steadily worsened and the fell disease was very soon to carry him away and deprive the country of its most outstanding mathematical genius.”
Some of these anecdotes on Ramanujan are also reproduced in in Deshmukh’s autobiography, The Course of My Life.
Reminiscences of Dr. P.C. Mahalanobis
Mahalanobis joined King’s College, Cambridge, in October 1913. As narrated by Mahalanobis, “I was attending some mathematical courses at that time including one by Professor Hardy. A little later, we heard that S Ramanujan, the mathematical prodigy, would come to Cambridge. I used to do my tutorial work with Mr Arthur Berry, Tutor in Mathematics of King’s College. One day I was waiting in his room for my tutorial, when he came in after having taken a class in elliptic integrals.
Berry: Have you met your wonderful countryman, Ramanujan?
Mahalanobis: I have heard that he has arrived; but I have not met him so far.
Berry: He came to my elliptic integrals class this morning.
(This was sometime after full term had begun, and I knew Mr. Berry had already given a few lectures on that subject.)
Mahalanobis: What happened? Did he follow your lectures?
Berry: I was working out some formulae on the blackboard. I was looking at Ramanujan from time to time to see whether he was following what I was doing. At one stage, Ramanujan’s face was beaming and he appeared to be greatly excited. I asked him whether he would like to say anything. He then got up from his seat, went to the blackboard, and wrote some of the results which I had not yet proved. Ramanujan must have reached those results by pure intuition. His facility in the theory of numbers was in a large measure intuitive. He made numerous conjectures, like other pure mathematicians. Many of the results apparently came to his mind without any effort. He was, however, aware that a good deal of intellectual effort would be required to establish his philosophical theories.”
Mahalanobis struck a good friendship with Ramanujan very soon. It came about in a somewhat strange way. On a visit to Ramanujan’s room one day, soon after his arrival, he found Ramanujan sitting very near the fire. It had turned very cold. Mahalanobis asked whether he was keeping warm at night. He replied that he was feeling cold despite wearing his overcoat and having a shawl wrapped around. Mahalanobis went to the bedroom and found that his bed had a number of blankets but all tucked in tightly, with a bed cover spread over them. Ramanujan had not known that he should turn back the blankets before getting into the bed. “The bed cover was loose; he was sleeping under that linen cover with his overcoat and shawl. I showed him how to get under the blankets. He was extremely touched. I believe this was the reason why he was so kind to me.”
Another anecdote: “On Sunday mornings, Ramanujan and I went out for long walks. One Sunday it had been arranged that we would both have our breakfast in my room and then go out for a walk. It was a cold morning with some snowfall. I was a bit late in getting up and was shaving in my bedroom when he arrived. I asked him to wait in the sitting room. When I came out, I found that he was reading Loney’s Dynamics of a particle with great interest. Seeing me, he put back the book on the table and said that it was very interesting. Evidently, he had never studied dynamics but had got interested in what he was reading.”
Yet another: “…During these walks our discussions ranged over a wide variety of subjects. He had some progressive ideas about life and society but no reformist views. Left to himself, he would often speak of certain philosophical questions. He was eager to work out a theory of reality which would be based on the fundamental concepts of “zero”, “infinity” and the set of finite numbers. I used to follow in a general way, but I never clearly understood what he had in mind. He sometimes spoke of “zero” as the symbol of the Absolute (Nirguna-Brahmam) of the extreme monistic school of Hindu philosophy, that is, the reality to which no qualities can be attributed, which cannot be defined or described by words, and which is completely beyond the reach of the human mind. According to Ramanujan, the appropriate symbol was the number “zero”, which is the absolute negation of all attributes. He looked on the number “infinity” as the totality of all possibilities, which was capable of becoming manifest in reality and which was inexhaustible. According to Ramanujan, the product of infinity and zero would supply the whole set of finite numbers. Each act of creation, as far as I could understand, could be symbolised as a particular product of infinity and zero, and from each such product would emerge a particular individual of which the appropriate symbol was a particular finite number. I have put down what I remember of his views. I do not know the exact implication. He seemed to have been perhaps emotionally more interested in his philosophical ideas than in his mathematical work. He spoke with such enthusiasm about the philosophical questions that sometimes I felt he would have been better pleased to have succeeded in establishing his philosophical theories than in supplying rigorous proofs of his mathematical conjectures.”
On Ramanujan’s personality: “Ramanujan had a somewhat shy and quiet disposition, a dignified bearing, and pleasant manners. He would listen carefully to what other people were saying but would usually remain silent. If he was asked any question, or on rare occasions, if he joined in any general conversation, he would speak frankly, but briefly. Whilst speaking to a friend or in very small groups, he would, however, expound his own ideas with great enthusiasm, not only on philosophical questions but occasionally also on other subjects in which he was seriously interested. Although I could not follow his mathematics, he left a lasting impression on my mind. His bright eyes and gentle face with a friendly smile are still vivid in my mind.”
The last anecdote relates to Ramanujan’s speed at solving complex puzzles. This was how Kanigel described it in his book:
“The popular English magazine Strand had long carried a page, entitled “Perplexities,” devoted to intriguing puzzles, numbered and charmingly titled, like “The Fly and the Honey,” or “The Tessellated Tiles,” the answers being furnished the following month. Each Christmas, though, “Perplexities” expanded, the author fitting his puzzles into a short story.
Now, in December 1914, “Puzzles at a Village Inn” took readers to the imaginary town of Little Wurzelfold, where the main topic of interest was what had just happened in Louvain.
In late August, pursuing an explicit policy of brutalization against civilian populations, German troops began burning the medieval Belgian city of Louvain, on the road between Liege and Brussels. House by house and street by street they set Louvain to the torch, destroying its great library, with its quarter million books and medieval manuscripts, and killing many civilians. The burning of Louvain horrified the world, galvanized public opinion against Germany, and united France, Russia, and England more irrevocably yet. “The March of the Hun,” English newspapers declared. “Treason to Civilization.” It was an early turning point of the war, doing much to set its tone. Louvain came to symbolize the breakdown of civilization. And now it reached even the “Perplexities” page of Strand.
One Sunday morning soon after the December issue appeared, P. C. Mahalanobis sat with it at a table in Ramanujan’s rooms in Whewell’s Court. Mahalanobis was the King’s College student, just then preparing for the natural sciences Tripos, who had found Ramanujan shivering by the fireplace and schooled him in the nuances of the English blanket.
Now, with Ramanujan in the little back room stirring vegetables over the gas fire, Mahalanobis grew intrigued by the problem and figured he’d try it out on his friend.
“Now here’s a problem for you,” he yelled into the next room
“What problem? Tell me,” said Ramanujan, still stirring. And Mahalanobis read it to him.
“I was talking the other day,” said William Rogers to the other villagers gathered around the inn fire, “to a gentleman about the place called Louvain, what the Germans have burnt down. He said he knowed it wellused to visit a Belgian friend there. He said the house of his friend was in a long street, numbered on this side one, two, three, and so on, and that all the numbers on one side of him added up exactly the same as all the numbers on the other side of him. Funny thing that! He said he knew there was more than fifty houses on that side of the street, but not so many as five hundred. I made mention of the matter to our parson, and he took a pencil and worked out the number of the house where the Belgian lived. I don’t know how he done it.”
Perhaps the reader may like to discover the number of that house.
Through trial and error, Mahalanobis (who would go on to found the Indian Statistical Institute and become a Fellow of the Royal Society) had figured it out in a few minutes. Ramanujan figured it out, too, but with a twist. “Please take down the solution,” he said [still stirring the pot] – and proceeded to dictate a continued fraction, a fraction whose denominator consists of a number plus a fraction, that fraction’s denominator consisting of a number plus a fraction, ad infinitum. This wasn’t just the solution to the problem, it was the solution to the whole class of problems implicit in the puzzle. As stated, the problem had but One solution-house no. 204 in a street of 288 houses; 1+2 + … 203 = 205 + 206 + … 288. But without the 50-to-500 house constraint, there were other solutions. For example, on an eight-house street, no. 6 would be the answer: I + 2 + 3 + 4 + 5 on its left equaled 7 + 8 on its right. Ramanujan’s continued fraction comprised within a single expression all the correct answers.”
“Mahalonobis was astounded. How, he asked Ramanujan, had he done it?”
“Immediately I heard the problem it was clear that the solution should obviously be a continued fraction; I then thought, Which continued fraction? And the answer came to my mind.”
© G. Sreekumar 2021.
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