# Ramanujan: Friendship and exquisite forms

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When I stopped there one evening this week, the front door was padlocked. A blue sign said the place opened at 9am. I relaxed for a while, below another blue sign that said: “Tinnai Pial—Visitors wait here. Place for relaxing in the evening.”

The next morning, Kathleen and I arrived at 9.15am, expecting to find it open. It was still padlocked. A genial old man sat where I had sat the previous evening. When will it open, I asked. “11,” said the old man, smiling and helpfully holding up two index fingers, in case I hadn’t understood his Tamil “11”. Then he shouted: “Paati! (Grandmother!), “come here! There are guests to see Ramanujan’s home!”

A wiry old woman appeared, shaking her head. “You can only go in at 11,” she said, also holding up two index fingers. As we resigned ourselves to waiting, she tottered away and returned with a number on a sheet of paper. “Call it,” she said, pointing. When I did, Suresh at the other end listened, asked a few questions and said, suddenly: “OK, OK. Wait 10 minutes. I will send someone to let you in.”

Just so did we finally enter a great Indian’s home. Srinivasa Ramanujan grew up in this house on Sarangapani street in Kumbakonam, just a few steps from the spectacular Sarangapani temple. It was from here that he walked daily to the nearby Town High School. It was here that he began playing with numbers. It was here that he started stumbling on the wonders that he eventually wrote about to the mathematician G.H. Hardy, in far-off Cambridge, England.

Hardy was, as history records, flabbergasted. How could a clerk in Tamil Nadu have come up with these remarkable results? He arranged for Ramanujan to come to Cambridge to work with him and the rest is, of course, more history.

Here in Kumbakonam, the nearby SASTRA University has been maintaining Ramanujan’s home as a simple museum. Each room carries the little blue plaque explaining what it is. The one in the front room even tells us that Ramanujan used to sit there looking out of the window all day. Reading those bald words, I think I got a sense of the substance of the man who once lived here, of his truly uncommon mind. I could almost see him—a short, perhaps slightly stocky boy there in front of me, his mind whirring as he watches the world go by on Sarangapani street.

The room in the centre, bathed by light from a skylight overhead, displays some of the fruits of that whirring. In three large glass-fronted frames are a few dozen letters and certificates and descriptions of mathematical results. At least twice—1903 and 1906—he won prizes from his nearby high school “as a reward of merit and an incentive to further improvement”. The incentives must have worked, because the school also awarded Ramanujan a “special prize for proficiency in mathematics”.

Plenty of tributes to that proficiency are on display—like the examples of his love of magic squares. A famous one—that he actually did not create—features his birthday (22-12-1887), and is tweaked to commemorate his birth centenary in 1987. But there are his “five-rowed squares for 65 and 66”, and an explanation of how to generate such squares.

One page derives this pleasing pattern involving square roots:

3 = sqrt 9

= sqrt (1+8)

= sqrt (1+(2 x 4))

= sqrt (1+(2 x sqrt 16))

= sqrt (1+(2 x sqrt (1+15)))

= sqrt (1+(2 x sqrt (1+(3 x 5))))

= sqrt (1+(2 x sqrt (1+(3 x sqrt 25))))

= sqrt (1+(2 x sqrt (1+(3 x sqrt (1+24)))))

= sqrt (1+(2 x sqrt (1+(3 x sqrt (1+(4 x 6))))))

And of course you can go on ad infinitum.

There’s a page explaining the “Rogers-Ramanujan Identities”, and another one about the “Hardy-Ramanujan Rademacher series for p(n)”. There’s one of the formulae he found to calculate pi. There are two references to the “taxicab number” from the famous story about him and Hardy (see my column “Srinivasa Ramanujan: The 1729 Man”, *goo.gl/JK0HCG*), titled “Little-known Background Of The Taxicab Story” and “Another Way To Fix The Taxicab Number”—which together tell the tale of how and why Ramanujan found 1729 interesting. I found out how he “counted primes of different forms”, and learnt that he “was a manipulative genius”—although I don’t think that is meant in any sense other than his ability to manipulate numbers.

All that and so much more, in a life touched by genius. But such a short life! Sadly, also on display is a hint of what finally defeated him: a letter in his own handwriting, dated 17 May 1918, from the Matlock Sanatorium in Derbyshire. “Owing to my ill health,” he writes to an anonymous “Sir”, “I am unable to travel to London at present.” Next to it, from 1920, is his Corporation of Madras death certificate.

Ramanujan “found exquisite forms among powers of numbers”, and “he revelled in his friendship with numbers”. Those sentences speak of his simplest, yet most profound legacy.

Walking here, I asked several people where to find his home. All knew how to find Sarangapani and the other Kumbakonam temples. Not one had so much as heard of Ramanujan. But as we waited, the old man who held up his index fingers told us: “I stop here for a few minutes every morning on my way to work. Such a great man.”

*Once a computer scientist, Dilip D’Souza now lives in Mumbai and writes for his dinners. A Matter Of Numbers explores the joy of mathematics, with occasional forays into other sciences. *

*Comments are welcome at **dilip@livemint.com. Read Dilip’s *Mint *columns at *www.livemint.com/dilipdsouza