Ramanujan


On February 22, 1918, a surprisingly cheery man is matched only by the unusually mild weather. He is Srinivasa Aiyangar Ramanujan, India’s up and coming  prodigy mathematician. Although only thirty years old, he had just received word yesterday of his election as a fellow of the Royal Society of London.

K: Congratulations Mr. Ramanujan on your election! Did the news come as a surprise to you?

R: Yes, actually. Just four days ago I was elected a fellow of the Cambridge Philosophical Society! I didn’t think it could get any better, but this is perhaps the greatest honor I’ve ever received. What luck I have!

K: I admire your modesty. Obviously it’s your mathematical genius, rather than luck, that led to these fellowships. But perhaps I am getting ahead of myself. Let’s start at the beginning, no?

R: (chuckles) That seems like a most fitting place.

K: Where were you born in India? People tend to hear ‘India’ and think they know, but in reality the country is so large it could be considered a subcontinent of Asia.

R: I was born in Erode in my grandmother’s, on my mother’s side, house. It’s part of the Tamil Nadu state, but the village itself is about four hundred kilometers southwest of Madras. It’s easier for people to conceive if I relate places by distance from there, given its international stature.

K: When is your birthday?

R: December 22, 1887.

K: What are your earliest childhood memories?

R: I am sure if I recall, or I was told by my mother, but we moved to Kumbakonam when I was one year old. My father was employed there as a clerk in a cloth merchant’s store there. This town is much closer to Madras, roughly two hundred and forty kilometers away.

K: Seeing as your father was a clerk, was he a major influence in your pursuits in mathematics?

R: Surprisingly not. My fascination, and education on, mathematics began in primary school like all the other children. But  I think I questioned the mathematical concepts being taught more than my peers.

K: I’m not sure I follow what you’re eluding to with your deeper intrigue at a young age.

R: For example, I can distinctly remember an instance in fourth grade, while being taught the rules of division. My teacher told the class that a number divided by itself was one. The analogy was that if there were four children and four mangos, each child would get one mango. While the other students accepted this, I could not. What if there were zero mangos and zero people? Certainly they could not each get one then.

K: To skip ahead slightly, did you still have this interest when you entered high school?

R: (nodding) I started high school in 1898 and maintained my curiosity in the subject, but I was an all around scholar back then, a modern Renaissance man if you will.

K: So then what person or event was the deciding factor leading to you devoting your life to mathematical studies?

R: When I was still attending Town High School in Kumbakonam, I found a book that drastically changed my outlook on math. It was called Synopsis of Elementary Results in Pure Mathematics by GS Carr. Using it, I was able to teach myself higher mathematics than I was learning in school.

K: But if I am not mistaken, that book was published in 1856. When did you come across it?

R: 1902 I’d guess. It was incredibly out of date but it remained my only model of how to write mathematical arguments.

K: Honestly, that’s the one criticism I hear about you. Many others think Carr’s concise volume gave you an unfortunate basis for documenting proofs.

R: So I’ve been told. But I am simply grateful I found it at all.

K: What was its most immediate effect on you?

R: I started to research concepts independently.

K: Given your academic performance, is it correct to assume you continued your education in college?

R: Absolutely. I was enrolled in Government College in Kumbakonam on a scholarship in 1904.

K: So when you graduated-

R: -No, I didn’t finish more than a year there. As my focus shifted towards math, it shifted away from my other subjects. So the school did not renew my scholarship.

K: Where did you go from there?

R: Well, this turn meant I had no funding altogether. I ended up running away to Vuzagapatnam without telling my parents. I was more than six hundred kilometers north of Madras now.

K: Why Vizagapatnam?

R: There was no specific reason. I simply continued my research there.

K: How long did you stay?

R: Almost a year. In 1906, I went to Madras. I wanted to go to the University of Madras, but I had to pass the First Arts examination. So I entered Pachaiyappa’s College in hopes of doing just that.

K: So you passed the First Arts exam?

R: Well. . .I fell ill after a few months and stopped attending lectures. I made a futile attempt to take it, but I failed every subject other than mathematics. This of course meant I couldn’t attend the University of Madras.

K: At this point did you look for a job?

R: No, my only job was my research. There was no pay in that however.

K: Had you recovered from sickness?

R: Yes, but then I became ill again in 1908. I had to undergo an operation the following year.

K: Pardon my sidetracking for a moment, but had you contacted your parents since you ran away?

R: Of course, and they weren’t very pleased with that. My mother arranged a marriage for me in my absence. The girl’s name was S Janaki Ammal. She was merely nine years old. Since I was much older, already in my twenties, I did not live with her until a few years down the line.

K: When were you married?

R: July 14, 1909.

K: So you didn’t think it would be time to find stable employment and settle down after you married?

R: (laughs) That probably did not come to mind. I was currently posing and solving problems posted in the Journal of the Indian Mathematical Society. This led to recognition of my abilities in the Madras area.

K: I am quite shocked you didn’t starve during this time.

R: Oh no, I shortly after found my first job.

K: What was it?

R: Just a temporary post with the Accountant General’s Office in Madras. But it was a stepping stone.

K: What did this stepping stone lead you to?

R: I met with Ramachandra Rao. He was a tax collector in Nellore. He was also a founding member of the Indian Mathematical Society.

K: Was he impressed by your work?

R: I believe so. He tried to arrange a scholarship for me, but unsuccessfully. So I applied for a job as a clerk in the Madras Port Trust.

K: That’s an excellent post, especially for one lacking university education.

R: Yes, and I owe part of that to EW Middlemast.

K: What was your relation to him?

R: He was the Professor of Mathematics at The Presidency College in Madras. I never studied under him, but apparently he liked my work. He wrote me a recommendation.

K: When did this position start?

R: The beginning of March, I think, in 1912.

K: Was it conducive to furthering your research?

R: I was lucky enough to be surrounded by men trained in mathematics. The Chief Accountant was SN Aiyar, and he even published a paper on my work in 1913.

K: What was it called?

R: On the Distribution of Primes.

K: Any others who helped your career while you worked at the port?

R: CLT Griffith. He was a professor of civil engineering in Madras, but he knew the professor of mathematics at the University College London. He wrote to him, MJM Hill, sending some of my theorems and a paper I wrote.

K: Was his response positive?

R: No, he simply recommended that  I read Theory of Infinite Series by Bromwich. That disappointed me.

K: Did you write to any established mathematicians yourself?

R: I sent letters with my work to EW Hobson and HF Baker, but neither replied. Then in 1913, I wrote to GH Hardy. Actually, I sent him almost one hundred theorems in the letter.

K: How did you know of Hardy?

R: I read Orders of Infinity, which he published in 1910.

K: I take it that his response  to your letter was much better than the others?

R: The fact that he wrote me at all, and in such a positive light, helped me gain admittance to the University of Madras in a two year program.

K: Once that ended, what did you do?

R: I went to Hardy in Cambridge, Trinity College specifically.

K: Did the fact that you are Hindu complicate any of this?

R: Only slightly. I am an orthodox Brahmin, the highest class in the caste system. Traditionally I would not be allowed to travel to Cambridge. To avoid this, the journey was made into smaller trips.

K: I know that Hindu culture also includes being a strict vegetarian. Were your needs met as far as nutrition went while you collaborated with Hardy?

R: Truthfully, there were problems with this. War had just begun shortly after I left India, and procuring certain foods was nearly impossible. I believe I suffered from malnutrition at this time.

K: How sick were you?

R: Sick enough so that I could not publish between November 1914 and March 1915. It delayed my research to say the least. However, I did receive a degree from Cambridge in 1916, a Bachelor of Science by Research.

K: So you finally obtained formal education and had the credentials to match the intellect.

R: But unfortunately, I became sick yet again in 1917. I had to spend most of the year in nursing homes, unable to concentrate on my work.

K: So you haven’t done much since then?

R: No, I have been trying to regain my health completely.

K: During your time with Hardy though, how much did you publish?

R: Twenty one papers overall, but five were jointly written with Hardy.

K: What are the topics that you enjoy researching the most?

R: I like iterative equations a lot. They are equations where you can plug the results back in to continue a pattern of sorts.

K: I hear you work with pi as well.

R: Pi is just such a mystery; I was drawn to it as I think many mathematicians inevitably are. I kept trying to find accurate ways of defining it.

K: Seeing as I am not a mathematicians, can you express pi in laymen’s terms?

R: The simplest way I found to express pi is
????+(19/22)?
That is 3.14159265262 approximately.

K: Fascinating.

R: That reminds me, I have always loved to study partitions, or how a number can be expressed in different ways. I remember when Hardy came to visit me in the hospital h remarked that his taxi number was 1729, and how ‘dull’ that was. I, on the other hand, saw it differently. It was the smallest number expressible as a sum of cubes in two different ways: ??+? and ??+?.
Hardy and I created a theory on the problem of partitions, which involves the number of ways a number can be expressed. A partition of n, such that n is a positive integer, is way of writing n as a sum of positive integers. Take the integer 5 for example:
5
4+1
3+2
3+1+1
2+2+1
2+1+1+1
1+1+1+1+1
p(n) is the total number of partitions of n so p(5) = 7. The partition function increases very rapidly, as seen by the fact that while p(2)=2, p(200) =
3, 972, 999, 029, 388.
The actual equation we used in our theory was:
p(n) ? e c?n
          4n ?3
with the constant c being
? ?2/3) .

K: Astounding! It is no surprise at all that the Cambridge Philosophical Society and Royal Society of London are honoring you! I’m afraid we have run out of time for today. My best wishes to you for your recovery and in further mathematical endeavors.

R: Thank you. My best wishes to you as well.

Works Cited

Bell, ET. Men of Mathematics. Simon & Schuster: New York. 1965.

Judgement: It only mentions his name in passing. I’m not even sure why they bothered to list Ramanujan in the index. 1/2 Star.

Blatner, David. The Joy of Pi. Walker and Company: New York. 1997.

Judgement: When it comes to Ramanujan’s work in pi, it’s a superb resource. It gives a very brief overview of his life as well. It has three of his algorithms, although not explained, and notes his contributions to modern pi mathematicians. Two Stars.

History of Mathematics: An Introduction. Wm C Brown Publishers: Boston. 1995.

Judgement: It gives a moderate overview of his life. The most useful source by far when it came to understanding the work of Ramanujan with partitions. In fact, it was the ONLY source that tried to explain his work in very simple terms. Three Stars.

Grattan-Guinness, Ivor. The Rainbow of Mathematics. WW Norton & Company: New York. 1997.

Judgement: Not helpful at all. Once again, I’m unsure of why he was mentioned in the index. No Stars awarded.

O’ Connor, JJ and EF Robertson. Srinivasa Ramanujan. February 10, 2002. http://www-groups.dcs.st-and.ac.uk/~history/Mathematcians/Ramanujan.html

Judgement: The best resource I found by a huge margin. It gives his life in immaculate detail. No further explanation is necessary. Four Stars.

Rao, K Srinivasa. Srinivasa Ramanujan. The Institute of Mathematical Science, Madras. February 10, 2002. http://www.math.buffalo.edu/~aagarwal/RAMNUJAN/ramanujan.html

Judgement: This version of his life story focused more on what Ramanujan accomplished with Hardy than anything, but that’s not necessarily a bad thing. Three Stars.

February 10, 2002. http://www.top-biography.com/9094-S.Ramanujan

Judgement: I would advise people to use this site as an accessory so to speak. It provides humorous and remarkable anecdotes of Ramanujan’s life and a timeline that is aesthetically pleasing and not overwhelming. Three Stars.