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Ramanujan

Ramanujan
SRINIVASA RAMANUJAM PART 1
CHILDHOOD
  • Ramanujan was born on 22 December 1887 into a Tamil Brahmin Iyengar family in Erode, Madras Presidency (now Tamil Nadu).
  • His father, K. Srinivasa Iyengar, originally from Thanjavur district, worked as a clerk in a sari shop.His mother, Komalatammal, was a housewife and also sang at a local temple.
  • They lived in a small traditional home on Sarangapani Sannidhi Street in the town of Kumbakonam. The family home is now a museum.
  • 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.
LIFE BEGINS
  • 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.
  • Since Ramanujan’s father was at work most of the day, his mother took care of the boy as a child. He had a close relationship with her. From her, he learned about tradition and puranas.
  • He learned to sing religious songs, to attend pujas at the temple, and to maintain particular eating habits – all of which are part of Brahmin culture.
  • Just before turning 10, in November 1897, he passed his primary examinations in English, Tamil, geography and arithmetic with the best scores in the district.That year, Ramanujan entered Town Higher Secondary School, where he encountered formal mathematics for the first time.
 MATHEMATICS
  • By 14, he was receiving merit certificates and academic awards that continued throughout his school career.He completed mathematical exams in half the allotted time, and showed a familiarity with geometry and infinite series.
  • In 1903, when he was 16, Ramanujan obtained from a friend a library copy of A Synopsis of Elementary Results in Pure and Applied Mathematics, G. S. Carr’s collection of 5,000 theorems.
  • Ramanujan reportedly studied the contents of the book in detail. The book is generally acknowledged as a key element in awakening his genius.
  • When he graduated from Town Higher Secondary School in 1904, Ramanujan was awarded the K. Ranganatha Rao prize for mathematics.
TROUBLE YEARS
  • It was in 1910, after a meeting between the 23-year-old Ramanujan and the founder of the Indian Mathematical Society , Ramaswamy Aiyer, also known as Professor Ramaswami, that Ramanujan started to get recognition within the mathematics circles of Madras.
  • On 14 July 1909, Ramanujan married Janaki a girl whom his mother had selected for him a year earlier.It was not unusual for marriages to be arranged with girls.Ramanujan’s father did not participate in the marriage ceremony.
  • After his successful surgery, Ramanujan searched for a job. He stayed at a friend’s house while he went from door to door around Madras looking for a clerical position. To make money, he tutored students at Presidency College.
CAREER
  • Ramanujan met deputy collector V. Ramaswamy Aiyer, who had founded the Indian Mathematical Society.Wishing for a job at the revenue department where Aiyer worked.
  • In early 1912, he got a temporary job in the Madras Accountant General’s office, with a salary of 20 rupees per month. He lasted only a few weeks. Toward the end of that assignment, he applied for a position under the Chief Accountant of the Madras Port Trust.
ENGLAND
  • In 1913, he began writing letters to British mathematicians. Out of these, G. H. Hardy was to be the one who would believe in Ramanujan’s skills.
  • Hardy asked a colleague, J. E. Littlewood, to take a look at the papers. Littlewood was amazed by Ramanujan’s genius. After discussing the papers with Littlewood, Hardy concluded that the letters were “certainly the most remarkable I have received” and said that Ramanujan was “a mathematician of the highest quality, a man of altogether exceptional originality and power”.
  • On 8 February 1913, Hardy wrote Ramanujan a letter expressing his interest in his work. Hardy contacted the Indian Office to plan for Ramanujan’s trip to Cambridge.
  • Hardy’s correspondence with Ramanujan soured after Ramanujan refused to come to England. Hardy enlisted a colleague lecturing in Madras, E. H. Neville, to mentor and bring Ramanujan to England.
  • Apparently, Ramanujan’s mother had a vivid dream in which the family goddess, the deity of Namagiri, commanded her “to stand no longer between her son and the fulfilment of his life’s purpose”.Ramanujan traveled to England by ship, leaving his wife to stay with his parents in India.
SRINIVASA RAMANUJAM PART 2
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 Littlewood and Hardy.
  • Hardy and Littlewood began to look at Ramanujan’s notebooks. Hardy had already received 120 theorems from Ramanujan in the first two letters, but there were many more results and theorems in the notebooks.
  • Hardy saw that some were wrong, others had already been discovered, and the rest were new breakthroughs.
  • Ramanujan left a deep impression on Hardy and Littlewood. Ramanujan spent nearly five years in Cambridge collaborating with Hardy and Littlewood, and published part of his findings there.
  • Their collaboration was a clash of different cultures, beliefs, and working styles.
  • Hardy was an atheist and an apostle of proof and mathematical rigour, whereas Ramanujan was a deeply religious man who relied very strongly on his intuition and insights.
  • While in England, Hardy tried his best to fill the gaps in Ramanujan’s education and to mentor him in the need for formal proofs to support his results, without hindering his inspiration – a conflict that neither found easy.
  • 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, the first part of which was published as a paper in the Proceedings of the London Mathematical Society.
  • On 6 December 1917, he was elected to the London Mathematical Society. In 1918 he was elected a Fellow of the Royal Society, the second Indian admitted to the Royal Society.
  • At age 31 Ramanujan was one of the youngest Fellows in the history of the Royal Society. On 13 October 1918, he was the first Indian to be elected a Fellow of Trinity College, Cambridge.
 ILLNESS AND DEATH
  • Throughout his life, Ramanujan was plagued by health problems. His health worsened in England; possibly he was also less resilient due to the difficulty of keeping to the strict dietary requirements of his religion in England and wartime rationing during 1914–1918.
  • He was diagnosed with tuberculosis and a severe vitamin deficiency at the time.In 1919 he returned to Kumbakonam, Madras Presidency, and soon thereafter, in 1920, died at the age of 32.
THE EXTERNAL SUPPORT
  • Ramanujan has been described as a person of a somewhat shy and quiet disposition, a dignified man with pleasant manners.He lived a simple life at Cambridge.
  • He credited his acumen to his family goddess, Mahalakshmi of Namakkal. He looked to her for inspiration in his work .Afterward he would receive visions of scrolls of complex mathematical content unfolding before his eyes.He often said, “An equation for me has no meaning unless it represents a thought of God.“
 MATHEMATICAL GENIUS
  • Ramanujam made substantial contributions to the analytical theory of numbers and worked on elliptic functions, continued fractions .He began to work on his own on mathematics summing geometric and arithmetic series.
  • He worked on divergent series. He sent 120 theorems on imply divisibility properties of the partition function.
  • Partition of whole numbers: Partition of whole numbers is another similar problem that captured ramanujan attention. Subsequently ramanujan developed a formula for the partition of any number, which can be made to yield the required result by a series of successive approximation
MATHEMATICAL GENIUS
  • Ramanujan studied the highly composite numbers also which are recognized as the opposite of prime numbers. He studies their structure, distribution and special forms.
  • Fermat Theorem: He also did considerable work on the unresolved Fermat theorem, which states that a prime number of the form 4m+1 is the sum of two squares.
  • Cubic Equations and Quadratic Equation:Ramanujam was shown how to solve cubic equations and he went on to find his own method to solve the quadratic.
  • Hypo geometric series: He worked hypo geometric series, and investigated relations between integrals and series
  • Ramanujan studied the highly composite numbers also which are recognized as the opposite of prime numbers. He studies their structure, distribution and special forms.
  • Fermat Theorem: He also did considerable work on the unresolved Fermat theorem, which states that a prime number of the form 4m+1 is the sum of two squares.
  • Cubic Equations and Quadratic Equation:Ramanujam was shown how to solve cubic equations and he went on to find his own method to solve the quadratic.
  • Hypo geometric series: He worked hypo geometric series, and investigated relations between integrals and series