Background
Srinivasa Ramanujan was born into a poor Brahmin family at Erode, Madras Presidency (now Tamil Nadu), India on December 22, 1887. He was the son of K. Srinivasa Iyengar, a clerk in a sari shop, and Komalatammal, a housewife.
Ramanujan (centre) and his colleague G. H. Hardy (extreme right), with other scientists, outside the Senate House, Cambridge, c.1914–19.
Bust of Ramanujan in the garden of Birla Industrial & Technological Museum
(The influence of Ramanujan on number theory is without pa...)
The influence of Ramanujan on number theory is without parallel in mathematics. His papers, problems and letters have spawned a remarkable number of later results by many different mathematicians. Here, his 37 published papers, most of his first two and last letters to Hardy, the famous 58 problems submitted to the Journal of the Indian Mathematical Society, and the commentary of the original editors (Hardy, Seshu Aiyar and Wilson) are reprinted again, after having been unavailable for some time. In this, the third printing of Ramanujan's collected papers, Bruce Berndt provides an annotated guide to Ramanujan's work and to the mathematics it inspired over the last three-quarters of a century. The historical development of ideas is traced in the commentary and by citations to the copious references. The editor has done the mathematical world a tremendous service that few others would be qualified to do.
https://www.amazon.com/Collected-Srinivasa-Ramanujan-Chelsea-Publishing/dp/0821820761/ref=sr_1_3?s=books&ie=UTF8&qid=1530820367&sr=1-3&keywords=Srinivasa+Aiyangar&SubscriptionId=AKIAJRRWTH346WSPOAFQ&tag=prabook0b-20&linkCode=sp1&camp=2025&creative=165953
https://www.amazon.com/Studies-History-Language-Religion-Literature/dp/1330493338/ref=sr_1_1?s=books&ie=UTF8&qid=1530820367&sr=1-1&keywords=Srinivasa+Aiyangar&SubscriptionId=AKIAJRRWTH346WSPOAFQ&tag=prabook0b-20&linkCode=sp1&camp=2025&creative=165953
Srinivasa Ramanujan was born into a poor Brahmin family at Erode, Madras Presidency (now Tamil Nadu), India on December 22, 1887. He was the son of K. Srinivasa Iyengar, a clerk in a sari shop, and Komalatammal, a housewife.
Ramanujan attended the Kangayan Primary School in nearby Kumbakonam. At the Kangayan Primary School, Ramanujan performed well. In November 1897, he passed his primary examinations in English, Tamil, geography and arithmetic with the best scores in the district and entered Town Higher Secondary School, where he encountered formal mathematics for the first time. By the time he was 13, he could solve unaided every problem in Loney's Trigonometry, and at 14 he obtained the theorems for the sine and the cosine that had been anticipated by L. Euler.
In 1903 he came upon George Shoobridge Carr's Synopsis of Elementary Results in Pure and Applied Mathematics. The book, its coverage reaching 1860, opened a whole new world to him, and he set out to establish the 6,165 theorems in it for himself. Having no contact with good books, he had to do original research for each solution. Trying to devise his own methods, he made some astounding discoveries, among them several new algebraic series.
Ramanujan became so absorbed in mathematics that when he entered the Government Arts College, Kumbakonam in 1904 with a merit scholarship, he neglected his other subjects and lost the scholarship. He later enrolled at Pachaiyappa's College in Madras, but failed again, performing poorly in other subjects. Despite two attempts, he never qualified for the first degree in arts.
Later in life Ramanujan was awarded a Bachelor of Science degree by research (this degree was later renamed PhD) in March 1916 for his work on highly composite numbers.
It was in 1910, after a meeting between the 23-year-old Ramanujan and the founder of the Indian Mathematical Society, V. Ramaswamy Aiyer, that Ramanujan started to get recognition within the mathematics circles of Madras.
Ramanujan worked as clerk and made his mathematical investigations; in 1911 he started to publish some of his results. In January 1913 Ramanujan sent some of his work to G. H. Hardy, Cayley lecturer in mathematics at Cambridge. Hardy noticed that whereas Ramanujan had rediscovered, and gone far beyond, some of the latest conclusions of Western mathematicians, he was completely ignorant of some of the most fundamental areas. In May 1913 Ramanujan secured a research position at Madras University.
In 1914 Ramanujan went to Cambridge. He spent nearly five years in Cambridge collaborating with Hardy and Littlewood, and published part of his findings there. The university experience gave him considerable sophistication, but his mind, by this time somewhat hardened, generally continued to work according to the old pattern, in which intuition played a more important role than argument.
In 1917 Ramanujan had contracted tuberculosis, but his condition improved sufficiently for him to return to India. In 1919 he returned to Kumbakonam, Madras Presidency, and soon thereafter, in 1920, died at the age of 32. After his death, his brother Tirunarayanan chronicled Ramanujan's remaining handwritten notes consisting of formulae on singular moduli, hypergeometric series and continued fractions and compiled them.
(The influence of Ramanujan on number theory is without pa...)
Ramanujan was a deeply religious man who relied very strongly on his intuition and insights. He credited his acumen to his family goddess, Mahalakshmi of Namakkal. He looked to her for inspiration in his work.
Quotations:
"An equation means nothing to me unless it expresses a thought of God."
"No, it is a very interesting number, it is the smallest number expressible as a sum of two cubes in two different ways."
"While asleep, I had an unusual experience. There was a red screen formed by flowing blood, as it were. I was observing it. Suddenly a hand began to write on the screen. I became all attention. That hand wrote a number of elliptic integrals. They stuck to my mind. As soon as I woke up, I committed them to writing."
"To preserve my brains I want food and this is now my first consideration. Any sympathetic letter from you will be helpful to me here to get a scholarship."
On 6 December 1917, he was elected to the London Mathematical Society. In 1918 he was elected a Fellow of the Royal Society. He was elected "for his investigation in Elliptic functions and the Theory of Numbers." On 13 October 1918, he was elected a Fellow of Trinity College, Cambridge.
Although Ramanujan was almost completely unaware of modern developments in mathematics, his mastery of continued fractions was unequaled by any living mathematician. In hypergeometric series "he was unquestionably one of the great masters." His patience, memory, power of calculation, and intuition made him the greatest formalist of his day. But his passionate, prolific, and in some ways profound work in the theory of numbers and his work in analysis were seriously marred by misdevelopment. In Hardy's opinion, if Ramanujan's gift had been recognized early, he could have become one of the greatest mathematicians of all time.
Quotes from others about the person
“Michio Kaku: "Srinivasa Ramanujan was the strangest man in all of mathematics, probably in the entire history of science. He has been compared to a bursting supernova, illuminating the darkest, most profound corners of mathematics, before being tragically struck down by tuberculosis at the age of 33, like Riemann before him."
Robert Kanigel: "Ramanujan was an artist. And numbers — and the mathematical language expressing their relationships — were his medium. Ramanujan's notebooks formed a distinctly idiosyncratic record. In them even widely standardized terms sometimes acquired new meaning. Thus, an "example" — normally, as in everyday usage, an illustration of a general principle — was for Ramanujan often a wholly new theorem. A "corollary" — a theorem flowing naturally from another theorem and so requiring no separate proof — was for him sometimes a generalization, which did require its own proof. As for his mathematical notation, it sometimes bore scant resemblance to anyone else's."
George Frederick James Temple: "The great advances in mathematics have not been made by logic but by creative imagination. The title of mathematician can scarcely be denied to Ramanajan who hardly gave any proofs of the many theorems which he enumerated."”
Ramanujan married Janaki in 1909, when the girl was only 10 years old.