The following Post was composed collaboratively by N.R.I.pathi & Shivoham

With the occasion of his Vardanthi last week, and the premiere of his new international movie this week, we inaugurate our comprehensive Series on Indic Personalities with self-taught genius, devout Shakti bhakta, and quite possibly India’s most brilliant mathematician, Srinivasa Ramanujan.

But the story of this great figure of Indic Civilization is one that is as touched by spirituality and tragedy as it is hard mathematics. In his brief lifetime, he would leave an imprint on Modern Maths that both the Academic and Cinematic worlds are only beginning to unravel.

Background

Born in Erode to a poor Tamil brahmin family, Srinivasa Ramanujan Iyengar spent his early years in what is now Tamil Nadu. His father was an accountant in Kumbakonam to a cloth merchant. Nevertheless, the family would face financial difficulties for long periods.

He studied in a “Pial” school, which was the traditional institution for boys of his background. The young lad was noted for being quiet, but frequently asking about the distances between stars [1] (much like ancient Indian mathematicians once did). Despite growing up in trying poverty, the precocious boy would develop an impressive mathematical faculty in relative isolation and with focused self-study. “He had a prodigious memory, and at school he would entertain his friends by reciting the various declensions of Sanskrit roots, and by repeating the value of the constant ‘pi’ to any number of decimal places.” [7]

But that was not all. Innate ability aside, it was an unmatched drive and focused concentration as an autodidact that would forge his name in the annals of history.

Srinivasa Ramanujan displayed advanced mathematical ability since age 11 after reading a book on advanced trigonometry written by S. L. Loney, lent by two college students, who were lodgers at his home, which he mastered by age 13 and discovered sophisticated mathematical theorems on his own. [5]

He used an introductory book to study Trigonometry and even basic Calculus even before his teen years. Once in his teens, he would master 18th and 19th century mathematics with another book. G.S. Carr’s work, “A Synopsis of Elementary Results in Pure and Applied Mathematics”, is credited with providing him with exposure to modern Mathematical methods, in tandem with his existing foundation. Ramanujan mastered it all on his own. If ever there were proof that our education does not end with school work, it is this.

A brilliant student, he received various awards and certificates from his early teens onward.  He would later go on to Government College in Kumbakonam but famously did not succeed in earning his B.A. in Maths. This was later repeated at another Chennai College. Though he scored hundred percent marks in Maths, he failed in his F.A., known as First Intermediate Examination in Arts.

He finished a three hour maths exam in thirty minutes, but due to his lack of interest in other subjects, was unable to perform on the others.[6] What gave him the strength to go on and endure?

He would later marry Kumari Janaki at the age of 22, and barely subsist by tutoring other students. To support his family, he obtained a job at the Madras Port Trust Office. A local mathematician named S.N. Aiyar encouraged him to correspond with Western Mathematicians; Ramanujan eventually clicked with one an entered into a friendship with G.H.Hardy of Cambridge. A letter with 120 Theorems was what secured the attention of this academic from Trinity College. Invited to study there, Ramanujan was initially reluctant, as his family resisted. It was here that the one of many spiritual experiences would intervene in the course of his magnificent life.

Eventually booking a ticket to England in 1914, Ramanujan would disembark from his ship only to find himself dogged by health problems, which would claim his life years later. Long thought to have been Tuberculosis, exacerbated by the dreary British climate, his health problems were a mystery then, though the present consensus is that a parasitic liver ailment was the actual cause. Unfortunately, this curable disease was not properly identified by doctors at that time, and hepatic amoebiasis would periodically assert itself when minor illnesses would give it cause. Ramanujan would heroically carry on his research both in collaboration with Hardy and on his own. In the process, he would earn an A.B. from Cambridge and be inducted in the Royal Society. Health (and dietary) problems, nevertheless, proved too much. He would return to India in 1917.

In a terrible loss to not only the Indic world but the mathematic as well, Sri Ramanujan passed away in 1920, only in his early thirties. One can only imagine how much more cosmic the contribution of this meteoric mathematician would have been had he lived a natural lifespan.

Spirituality

All sources, even mathematic academics, recognise that Srinivasa Ramanujan credited his remarkable work to the Goddess Namadevi, an incarnation of the Mahalakshmi aspect of Shakti. Particularly in an era where scholarship is intensely ego-driven, to the point of a new law being developed, Ramanujan’s lack of ahankar and respect for the divine is refreshing. Although critiqued by outsiders as “unrigorous” due to lack of “formal training”, Ramanujan is emblematic of a different sort of tradition that recognises not only the value of discipline and training, but realises that there is a significant space for ’embodied knowledge’ as well.

Ramanujan was deeply spiritual and credited his mathematical ability to his family goddess, Mahalakshmi of Namakkal. He apparently claimed to dream of blood drops that symbolised her male consort, Narasimha, after which he would receive visions of scrolls of complex mathematical content unfolding before his eyes. [5]

Achievements

• Auto-didact par excellence and Self-taught Mathematics genius who produced 3 notebooks of brilliant theorems and conceptual analyses.
• The 1st notebook has 351 pages, in 16 chapters.
  The 2nd notebook is a revised enlargement of the 1st with 256 pages, in 21 chapters.
  The 3rd notebook has only 33 pages. [2]
• Published more than 30 individual research papers in three years. Collaborated on several others with G.H.Hardy.
• The most notable collaboration was written on the partial function, which counts the number of ways a natural number can be reduced to smaller parts. This is now called the Circle Method.[7]
• Another collaboration resulted in the Normal Order Method. This paper gave birth to an entirely new branch of Mathematics called Probablistic Number Theory. [7]
• Wrote “a paper that would connect the computations of the digits of ‘pi’ to modular forms, a theory developed largely in the 20th century. “[3]
• Accordingly to Academics Murty & Murty, “the paper that really changed the course of 20th century mathematics was the one written by Ramanujan in 1916, modestly titled “On certain arithmetical functions.” In this paper, Ramanujan investigated the properties of Fourier coefficients of modular forms. At that time the theory of modular forms was not even developed. However, Ramanujan enunciated three fundamental conjectures that served as a guiding force for the development of the theory. “[7]
• A number of Theorists would go on to win Fields Medals (the “Math Nobel”) studying concepts that stemmed from Ramanujan’s work. Others would make a career out of teasing out numerous insights from his papers that would have implications for areas of study such as Physics.

According to an article at the Indian Mathematical Society:

So long as our planet continues to exist in the Universe, and so long as civilization exists on our planet, Ramanujan will be remembered because of the outstanding research contributions made by him to Number Theory and Analysis, because his work has kept first rate mathematicians busy till this date, because his work has had a tremendous influence on modern mathematics and has opened up new vistas for research, but also because he was able to do so without any formal training, without any means of support, and more so because he continued to produce work of the highest order even in the face of death.

Maths Anecdote

We see that many Indians supported SR in India. He did not go to England because he was “let down” etc, but possibly because his work could be shared with a wider audience and many could benefit. He knew he was doing a lot of new stuff. He also received support from Indians during his stay.

“Occasionally, his powers were put to good use. Some twelve hundred students attended the school and each had to be assigned to classrooms, and to the school’s three dozen or so teachers, while satisfying any special circumstances peculiar to particular students. At Town High, the senior math teacher, Ganapathi Subbier, was regularly shackled with the maddening job—and he would give it to Ramanujan.” [9]

The goal was to make sure that the students and teachers both show up in the right place and at right time. Headmaster, R. Viswanathan, gives the number of students in the school at about one thousand. N. Govindaraja Iyengar, quoted in P. K. Srinivasan, puts the figure at fifteen hundred. Ramanujan deserved higher than the maximum possible marks. [10]

Resources on Ramanujan’s Work

Legacy

https://www.youtube.com/watch?v=CCFck3laziI

In a tragedy worthy of Natya itself, there is something about the number of years Srinivasa Ramanujan spent on this Earth. There is something to this number 32. Not only did this bright luminary pass away at that young age, but so too did  Adi Sankaracharya himself.  The communion with the Divine by these giant figures of Indic Civilization is an oft-recognised, but quickly discounted, aspect in an age marked by materialism and atheism. But perhaps there is in fact something to that and them, after all.

Both were undoubtedly astonishing intellects, who attained great intellectual achievement, but rather than pontificate with bloated ego, they humbly credited their accomplishment to the grace of something greater than themselves. They wielded this humility to make the most of their brief lives. And in that, whether we are blessed with mathematical or analytical, linguistic or strategic, or the highest of them all, spiritual, intelligence, these two figures who lived to thirty two are an example to us all.

Cinema

With the release of much advertised and much acclaimed movie The Man who Knew Infinity, starring Dev Patel and Jeremy Irons (as G.H.Hardy), interest in Ramanujan is higher than ever before. Such artistic endeavours from abroad surely should receive appropriate support. At the same time, we must remember efforts that have already attempted to celebrate his life in the native idiom. There is of course the 2014 Tamil-English movie called Ramanujan, directed by Gnana Rajasekharan. Previous efforts to honour in celluloid the legacy of this legend can be found in such movies as the Matt Damon movie Good Will Hunting and countless documentaries. There is even an app that pays tribute to him!

Yet his legacy was not merely mathematical, cinematic, or spiritual, it was also cultural. At a time when India and Indic Civilization was at its lowest depth, when questions of not only competence but innate capability were popping up (or propped up…), Ramanujan inspired countless Indians at home and abroad, including no less than Nobel Prize-winner Subramanyan Chandrasekhar. [7] He proved a pivotal Personality at a time when India was just beginning to rediscover itself. His adopted son and family by this lineage carry his torch on today.

Conclusion

Ultimately, Ramanujan’s life and legacy remain as much an enigma as his notebooks. How could a man without “rigorous” and “classical training” manage to reach the Kailasan summits of the field of Mathematics? How could a man who lived so brief a life manage to make such an enormous impact that gifted academics continue to parse over his handwriting to this day? How can a tradition that mixes the sacred with the “secular”, and philosophical speculation with empirical fact, be credited with producing such a genius?

All these, and many more such questions best left to the pure theory professionals, will be answered in the days and years to come. But surely, there must be something worth learning about where the man came from and how he was taught, to determine why he accomplished what he did. Genius quite possibly is in the genes. But achievement, accomplishment, and academic legacy transcend even the genetic. Sometimes, there is something to not only the scholarly tradition, but to the sacred as well.

There is also a lesson for our suicide-prone, over-emotional and over-exam’ed students: even if you fail out of school, it is no reason to end your efforts or your life.

Long after the humiliation of failing is forgotten, your true potential may be revealed in a way that marks and entrance exams and placements never will. Perhaps, in a way, that is Ramanujan’s greatest legacy of all.

His work has had a fundamental role in the development of 20th century mathematics and his final writings are serving as an inspiration for the mathematics of this century [7]

References:

1. Hardy, G.H., P.V. Seshu Aiyar et al. Collected Papers of Srinivasa Ramanujan. Providence, R.I.: Chelsea Publ. 2000
2. “Srinivasa Ramanujan”.Indian Mathematical Society. University of Pune.http://www.indianmathsociety.org.in/sramanujan.htm
3. “Srinivasa Ramanujan: Life and Mathematics”. University of Vienna. http://www.mat.univie.ac.at/~kratt/vortrag/ramanuja.pdf
4. “An Overview of Ramanujan’s Workbooks”. University of Illinois. http://www.math.uiuc.edu/~berndt/articles/aachen.pdf
5. “Remembering Mathematical Genius Srinivasa Ramanujan”. Mid-Day. http://www.mid-day.com/articles/remembering-mathematical-genius-srinivasa-ramanujan/16792165
6. “Did Ramanujan Fail in Math?”. The Hindu. http://www.thehindu.com/opinion/op-ed/did-srinivasa-ramanujan-fail-in-math/article6254934.ece
7. “The Legacy of Srinivasa Ramanujan”. The Hindu. http://www.thehindu.com/sci-tech/science/the-legacy-of-srinivasa-ramanujan/article2746988.ece
8. Murty & Murty. The Mathematical Legacy of Srinivasa Ramanujan. New York: Springer. 2013
9. Kanigel, Robert. The Man Who Knew Infinity: A Life of the Genius Ramanujan. New York: Simon & Schuster. 1991
10. Srinivasan, P. K. An introduction to Creativity of Ramanujan. AMTS.1987.pg 121

*Special Acknowledgement to Shivoham for his time and intellectual contribution to this article,despite other obligations,and for making it a more "rigorous" endeavour than it otherwise would have been.