Ramanujan

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Srinivasa Ramanujan(December 22, 1887 – April 26, 1920) was an Indian mathematician widely regarded as one of the greatest mathematical minds in recent history. With almost no formal training in mathematics, he made profound contributions in the areas of analysis and number theory. A child prodigy, Ramanujan was largely self-taught and compiled nearly 3,884 theorems during his short lifetime. Although a small number of these theorems were actually false, most of his statements have now been proven to be correct. His deep intuition and uncanny algebraic manipulative ability enabled him to state highly original and unconventional results that have inspired a vast amount of research; however,some of his discoveries have been slow to enter the mathematical mainstream. Recently his formulae have begun to be applied in the field of crystallography and physics. The Ramanujan Journal was launched specifically to publish work "in areas of mathematics influenced by Ramanujan".

Ramanujan was born in 1887 in Erode, Tamil Nadu, India, at the place of residence of his maternal grandparents. His father worked as an accountant and hailed from the fertile Thanjavur district in Tamil Nadu. His mother was a housewife. They lived in Saarangapani Street in a south-Indian-style house (now a museum) in the town of Kumbakonam. In 1898, at the age of 10, Ramanujan entered the town high school, THSS [3], where he encountered formal mathematics for the first time. By the age of 11 he had devoured the mathematical knowledge of two lodgers at his home who were students at the Government College. He was lent advanced trigonometry written by S.L. Loney (ISBN 1-4181-8509-4) and he completely mastered this book by the age of 13 and was discovering sophisticated theorems of his own. His biographer reports that by 14 his true genius was evident. He achieved merit certificates and academic awards throughout his school career and was also assisting the school in the logistics of assigning its 1200 students (each with their own needs) to its 35-odd teachers, completing mathematical exams in half the allotted time, and showing familiarity with infinite series. By the age of 17, he had independently developed and investigated the Bernoulli numbers and had calculated Euler's constant up to 15 decimal places. His peers of the time commented later, "We, including teachers, rarely understood him" and "stood in respectful awe" of him.

Ramanujan received a scholarship to study at Government College in Kumbakonam but was so intent on studying mathematics that he could not focus on any other subjects and failed most of them, losing his scholarship in the process. He failed again in the next college he joined but continued to pursue independent research in mathematics. At this point in his life, he was financially poor and was quite often near the point of starvation.

After his marriage (in 1909), to a nine-year old bride, Janaki Ammal, as per the customs of India at that time he began searching for work. With his collection of mathematical discoveries, he travelled door to door around the city of Madras (now Chennai) looking for a clerical position. He finally managed to find a job at the Accountant General's Office. Ramanujan desired to focus completely on mathematics and was advised by his supervisor, who was also interested in mathematics, to contact scholars in Cambridge. He doggedly solicited support from influential Indians and published several papers in Indian mathematical journals, but was unsuccessful in his attempts to foster sponsorship. (It might be the case that he was supported by Ramachandra Rao, then the collector of the Nellore district and a distinguished civil servant. Rao, an amateur mathematician himself, was the uncle of the well-known mathematician, K. Ananda Rao, who went on to become the Principal of the Presidency College.)In late 1912 and early 1913, Ramanujan sent letters and samples of his theorems to three Cambridge academics: H. F. Baker, E. W. Hobson, and G. H. Hardy. Only Hardy, to whom Ramanujan wrote in January 1913, recognized the genius demonstrated by the theorems. Upon reading the initial unsolicited missive by an unknown and untrained Indian mathematician, Hardy and his colleague J.E. Littlewood commented that, “not one [theorem] could have been set in the most advanced mathematical examination in the world.” Although Hardy was one of the most eminent mathematicians of his day and an expert in a number of fields that Ramanujan was writing about, he commented that, "many of them defeated me completely; I had never seen anything in the least like them before."

After some initial skepticism (Kanigel 1991 pp161–3), Hardy replied with comments, requesting proofs for some of the discoveries, and began to make plans to bring Ramanujan to Cambridge. Ramanujan was at first reluctant to travel overseas due to religious reasons but eventually agreed to come to England. He spent about five years in Cambridge collaborating with Hardy and Littlewood and published some of his findings there. In 1918, Ramanujan was elected as a Fellow of Trinity and as a Fellow of the Royal Society.

Plagued by health problems all through his life, living in a country far away from home, and obsessively involved with his mathematics, Ramanujan's health worsened in England, perhaps exacerbated by stress, and by the scarcity of vegetarian food during the First World War. He was diagnosed with tuberculosis (Henderson, 1996) and a severe vitamin deficiency and was confined to a sanitorium. Ramanujan returned to Kumbakonam, India in 1919 and died soon thereafter at the age of 32. His wife, S. Janaki Ammal, lived outside Chennai (formerly Madras) until her death in 1994.

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, a parasitic infection of the liver. This is supported by the fact that Ramanujan had spent time in Madras, where the disease was widespread. He had had two cases of dysentery before he left India. When not properly treated, dysentery can lie dormant for years and lead to hepatic amoebiasis.[1] It was a difficult disease to diagnose, but once diagnosed would have been readily curable (Berndt, 1998).

Ramanujan believed in Hindu gods all his life and lived as an observant Tamil Brahmin. The "Iyengar" in his name refers to a class of brahmins in southern India who are followers of the god Vishnu, the preserver of the universe. His first Indian biographers described him as rigorously orthodox. Ramanujan credited his acumen to his family goddess, Namagiri, and looked to her for inspiration in his work. He often said, "An equation for me has no meaning, unless it represents a thought of God."