Srinivasa Ramanujan: School Projects

Math Project: Biography of Srinivasa Ramanujan

Early life:- Ramanujan was born on 22 december 1887 into a tamil brahmin family in erode, madras presidency (now tamil nadu), at the residence of his maternal grandparents. His father, k. Srinivasa iyengar, worked as a clerk in a sari shop and hailed from thanjavur district. His mother, komalatammal, was a housewife and also sang at a local temple. They lived in sarangapani street in a traditional home in the town of kumbakonam. The family home is now a museum. When ramanujan was a year and a half old, his mother gave birth to a son, sadagopan, who died less than three months later.

On 1 october 1892, Ramanujan was enrolled at the local school. After his maternal grandfather lost his job as a court official in kanchipuram, ramanujan and his mother moved back to kumbakonam and he was enrolled in the kangayan primary school. When his paternal grandfather died, he was sent back to his maternal grandparents, then living in madras. He did not like school in madras, and tried to avoid attending. His family enlisted a local constable to make sure the boy attended school. Within six months, ramanujan was back in kumbakonam.
16. Attentiontowardsmathematics:- ramanujan met deputy collector v. Ramaswamy aiyer, who had recently founded the indian mathematical society. Wishing for a job at the revenue department where ayer worked, ramanujan showed him his mathematics notebooks. As ayer later recalled: I was struck by the extraordinary mathematical results contained in it [the notebooks]. I had no mind to smother his genius by an appointment in the lowest rungs of the revenue department.

Aiyer sent Ramanujan, with letters of introduction, to his mathematician friends in madras. Some of them looked at his work and gave him letters of introduction to r. Ramachandra rao, the district collector for nellore and the secretary of the indian mathematical society. Rao was impressed by ramanujan’s research but doubted that it was his own work. Ramanujan mentioned a correspondence he had with professor saldhana, a notable bombay mathematician, in which saldhana expressed a lack of understanding of his work but concluded that he was not a phony.

Works:- Tamanujan wrote his first formal paper for the journal on the properties of bernoulli numbers. One property he discovered was that the denominators (sequence a027642 in oeis) of the fractions of bernoulli numbers were always divisible by six. He also devised a method of calculating bn based on previous bernoulli numbers. One of these methods follows: it will be observed that if n is even but not equal to zero,

(I) bn is a fraction and the numerator of bn n in its lowest terms is a prime number, (ii) the denominator of bn contains each of the factors 2 and 3 once and only once, (iii) 2n(2n – 1)bn n is an integer and 2(2n – 1)bn consequently is an odd integer. In his 17-page paper, “some properties of bernoulli’s numbers”, ramanujan gave three proofs, two corollaries and three conjectures. Ramanujan’s writing initially had many flaws.

Life in England:- Ramanujan departed from madras aboard the s.S. Nevasa on 17 march 1914. When he disembarked in london on 14 april, neville was waiting for him with a car. Four days later, neville took him to his house on chesterton road in cambridge. Ramanujan immediately began his work with littlewoods and hardy. After six weeks, ramanujan moved out of neville’s house and took up residence on whew ell’s court, a five-minute walk from hardy’s room. Hardy and littlewoods began to look at ramanujan’s notebooks.

Illness and death:- throughout his life, ramanujan was plagued by health problems. His health worsened in england. He was diagnosed with tuberculosis and a severe vitamin deficiency, and was confined to a sanatorium. In 1919 he returned to kumbakonam, madras presidency, and soon thereafter, in 1920, died at the age of 32. His widow, s. Janaki ammal, moved to bombay; in 1950 she returned to chennai (formerly madras), where she lived until her death in 1994 at age 95. A 1994 analysis of ramanujan’s medical records and symptoms by dr. D. A. B. Young concluded that it was much more likely he had hepatic amoebiasis, an illness then widespread in madras, rather than tb. He had two episodes of dysentery before he left india. When not properly treated, dysentery can lie dormant for years and lead to hepatic amoebiasis.Although difficult to diagnose, it is a readily curable disease.

The ramanujan conjecture:- although there are numerous statements that could have borne the name ramanujan conjecture, there is one that was very influential on later work. In particular, the connection of this conjecture with conjectures of andré weil in algebraic geometry opened up new areas of research. That ramanujan conjecture is an assertion on the size of the tau-function, which has as generating function the discriminant modular form δ(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. The reduction step involved is complicated. Deligne won a fields medal in 1978 for that work.

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