Srinivasa Ramanujan: life and mathematical contributions

Ramanujan

The Improbable Life and Work of Ramanujan

The correlation between mathematics and spirituality may not seem immediately apparent. Indeed, to some, there is something quite distinctly disparate in the relationship between religion and any science. However, the life and accomplishments of Indian-born mathematician Srinivasa Ramanujan stand in contrast to this perception. Widely considered brilliant by those who knew him and yet mired in an ascetic life of poverty and illness, Ramanujan stands as a towering figure in the field of mathematics. Recognized for a categorical speed and dexterity in resolving equations, proving theorems and achieving technical representation of his theoretical insights almost effortlessly. Many of the theorems which he would propose would be proven and reinforced in the decades following his very premature death, and indeed, would live their own life in the revelations yielded to mathematicians and quantum physicists even to present day.

His mathematical skill and insight seems most improbable in light of the biographical details that are available to us. Quite to the point, one of the most immediately striking things about Ramanujan's story is the total absence of formal education, and even moreso, a life of outright struggle in the academic context. In spite of what can be perceived as a disadvantage, he far outshone all of his peer in his command of existing principles and the ability to imagine frequently accurate new principles. As denoted in a 1999 interview with a mathematician inspired by his work, Ramanujan "had just one year of education in a small college; he was basically self-taught. Working in isolation for most of his short life of 32 years, he had little contact with other mathematicians." (Berndt, 1)

This fact is hard to conceive considering the proclaimed relevance today of so many of his conceptual assumptions. Born in 1887 and dead by 1920 of what physicians retrospectively believe was a parasitic bacterial infection as a result of untreated dysentery, he untimely demise would be evidence of a life lived in squalor and self-neglect in a devastatingly poor and filthy India. (Wikipedia, 1) This made the uncommon talent commonly susceptible to the health and mortality, a reality for most living in India at the time. His mere survival to that point may be considered a matter of remarkable importance considering the infant deaths of one sibling prior and two after his birth as well as his unlikely success in a childhood bout with small pox. (Wikipedia, 1)

In spite of these conditions, and perhaps to the continuation of them, Ramanujan was known to work obsessively on his studies and his theorems, allowing little time and allotting little interest in the betterment of his situation. His brilliance and perspicacity would be recognized by those in the Indian and British mathematics community though. In spite of his poverty and shyness, his work would speak for itself to such important figures as Ramachandra Rao, who was a founding member of the Indian Mathematical Society. Rao described his first encounter with Ramanujan, telling that "a short uncouth figure, stout, unshaven, not over clean, with one conspicuous feature-shining eyes- walked in with a frayed notebook under his arm. He was miserably poor. ... He opened his book and began to explain some of his discoveries. I saw quite at once that there was something out of the way; but my knowledge did not permit me to judge whether he talked sense or nonsense. ... I asked him what he wanted. He said he wanted a pittance to live on so that he might pursue his researches" (O'Connor & Robertson, 1)

As history returns to Ramanujan's ideas and finds accuracy in most of them, Rao's response would demonstrate the degree to which the young man's internal insights had somehow transcended those of the best math minds amongst his predecessors and contemporaries. So would this be demonstrated in his trigonometric principles, such as that which is commonly referred to as the Ramanujan Conjecture. This is stated as "an assertion on the size of the tau function, which has as generating function the discriminant modular form ?(q), a typical cusp form in the theory of modular forms. It was finally proven in 1973, as a consequence of Pierre Deligne's proof of the Weil conjectures." (Wikipedia, 1) That it was proven so many years after his death is suggestive of the power of his ideas, which were formed into theories as a precursor to many complex ideas considered knowledge today.

From an educational perspective, there is value to Ramanujan's story for primary school, even if many of his mathematical principles are investigated more appropriately in the university and graduate school settings. This is because the narrative of his life is so compelling as a demonstration of that which can be accomplished against a host of insurmountable odds, not the least of which is the unfortunately short frame of time in which Ramanujan was able to make his mark. Though his arguments and ideas preceded the whole host or revelations yielded in 20th century science, it is nonetheless true that many of his ideas are held within the framework of such evolving discussions as that on string theory, a progressive argument concerning the dimensional structure of the universe. To the point, the importance of Ramanujan's accomplishments is overshadowed only by the fact that he did this without the educational formality or material comfort that might seem to us necessary for success.