Srinivasa Ramanujan
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"Ramanujan" redirects here. For other uses, see Ramanujan (disambiguation).
| Srinivasa Ramanujan FRS | |
|---|---|
 | |
| Born | 22 December 1887 Erode, Madras Presidency, British Raj (now Tamil Nadu, India) |
| Died | 26 April 1920 (aged 32) Kumbakonam, Madras Presidency, British Raj (now Tamil Nadu, India) |
| Residence | Kumbakonam, Madras Presidency Madras, Madras Presidency London, United Kingdom |
| Nationality | Indian |
| Fields | Mathematics |
| Institutions | Trinity College, Cambridge |
| Alma mater | Government Arts College (no degree) Pachaiyappa's College (no degree) Trinity College, Cambridge (BSc, 1916) |
| Thesis | Highly Composite Numbers (1916) |
| Academic advisors | G. H. Hardy J. E. Littlewood |
| Known for | Landau–Ramanujan constant Mock theta functions Ramanujan conjecture Ramanujan prime Ramanujan–Soldner constant Ramanujan theta function Ramanujan's sum Rogers–Ramanujan identities Ramanujan's master theorem |
| Influences | G. S. Carr |
| Influenced | G. H. Hardy |
| Notable awards | Fellow of the Royal Society |
Signature | |
In this Indian name, the name Srinivasa is a patronymic, not a family name, and the person should be referred to by the given name, Ramanujan.
Srinivasa Iyengar Ramanujan FRS (pronunciation: 
i/ˈʃriːniˌvɑːsə ˈrɑːmɑːˌnʊdʒən/; 22 December 1887 – 26 April 1920) was an Indian mathematician and autodidact who lived during the British Raj. Though he had almost no formal training in pure mathematics, he made substantial contributions to mathematical analysis, number theory, infinite series, and continued fractions. Ramanujan initially developed his own mathematical research in isolation; it was quickly recognized by Indian mathematicians. When his skills became obvious and known to the wider mathematical community, centred in Europe at the time, he began a partnership with the English mathematician G. H. Hardy. The Cambridge professor realized that Srinivasa Ramanujan had produced new theorems in addition to rediscovering previously known ones.
i/ˈʃriːniˌvɑːsə ˈrɑːmɑːˌnʊdʒən/; 22 December 1887 – 26 April 1920) was an Indian mathematician and autodidact who lived during the British Raj. Though he had almost no formal training in pure mathematics, he made substantial contributions to mathematical analysis, number theory, infinite series, and continued fractions. Ramanujan initially developed his own mathematical research in isolation; it was quickly recognized by Indian mathematicians. When his skills became obvious and known to the wider mathematical community, centred in Europe at the time, he began a partnership with the English mathematician G. H. Hardy. The Cambridge professor realized that Srinivasa Ramanujan had produced new theorems in addition to rediscovering previously known ones.
During his short life, Ramanujan independently compiled nearly 3,900 results (mostly identities and equations).[1] Nearly all his claims have now been proven correct.[2] His original and highly unconventional results, such as the Ramanujan prime and the Ramanujan theta function, have inspired a vast amount of further research.[3] The Ramanujan Journal, a peer-reviewed scientific journal, was established to publish work in all areas of mathematics influenced by Ramanujan.[4]
Deeply religious,[5] Ramanujan credited his substantial mathematical capacities to divinity: '"An equation for me has no meaning," he once said, "unless it expresses a thought of God."'[6]
Contents
[hide]- 1Name
- 2Early life
- 3Adulthood in India
- 4Life in England
- 5Mathematical achievements
- 6Hardy–Ramanujan number 1729
- 7Other mathematicians' views of Ramanujan
- 8Posthumous recognition
- 9In media
- 10Selected publications on works of Ramanujan
- 11See also
- 12Notes
- 13Selected publications about Ramanujan and his work
- 14External links
Name[edit]
The name Ramanujan means "younger brother of the god Rama."[7] The name Srinivasa is a combination of Sri and Nivasa; Sri refers to the female energy of God while Nivasa means a living place, so the word Srinivasa literally means the place where the female energy of the God lives."[8] Iyengar is a caste of Hindu Brahmins of Tamil origin whose members follow the Visishtadvaita philosophy propounded by Ramanuja; there are several opinions concerning its etymology.
Early life[edit]
Ramanujan was born on 22 December 1887 into a Tamil Brahmin Iyengar family in Erode, Madras Presidency (now Tamil Nadu), at the residence of his maternal grandparents.[9] His father, K. Srinivasa Iyengar, worked as a clerk in a sari shop and hailed from Thanjavur district.[10] His mother, Komalatammal, was a housewife and also sang at a local temple.[11] They lived in a small traditional home on Sarangapani Sannidhi Street in the town of Kumbakonam.[12] 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. In December 1889, Ramanujan contracted smallpox, but unlike the thousands in the Thanjavur district who died of the disease that year, he recovered.[13] He moved with his mother to her parents' house in Kanchipuram, near Madras (now Chennai). His mother gave birth to two more children, in 1891 and 1894, but both died in infancy.
On 1 October 1892, Ramanujan was enrolled at the local school.[14] After his maternal grandfather lost his job as a court official in Kanchipuram,[15] Ramanujan and his mother moved back to Kumbakonam and he was enrolled in the Kangayan Primary School.[16] 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]
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.[17] At the Kangayan Primary School, Ramanujan performed well. 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.[18] That year, Ramanujan entered Town Higher Secondary School, where he encountered formal mathematics for the first time.[18]
By age 11, he had exhausted the mathematical knowledge of two college students who were lodgers at his home. He was later lent a book by S. L. Loney on advanced trigonometry.[19][20] He mastered this by the age of 13 while discovering sophisticated theorems on his own. By 14, he was receiving merit certificates and academic awards that continued throughout his school career, and he assisted the school in the logistics of assigning its 1200 students (each with differing needs) to its 35-odd teachers.[21] He completed mathematical exams in half the allotted time, and showed a familiarity with geometry and infinite series. Ramanujan was shown how to solve cubic equations in 1902; he developed his own method to solve the quartic. The following year, not knowing that the quintic could not be solved by radicals, he tried to do so.
In 1903, when he was 16, Ramanujan obtained from a friend a library copy of a A Synopsis of Elementary Results in Pure and Applied Mathematics, G. S. Carr's collection of 5,000 theorems.[22][23]Ramanujan reportedly studied the contents of the book in detail.[24] The book is generally acknowledged as a key element in awakening his genius.[24] The next year, Ramanujan independently developed and investigated the Bernoulli numbers and calculated the Euler–Mascheroni constant up to 15 decimal places.[25] His peers at the time commented that they "rarely understood him" and "stood in respectful awe" of him.[21]
When he graduated from Town Higher Secondary School in 1904, Ramanujan was awarded the K. Ranganatha Rao prize for mathematics by the school's headmaster, Krishnaswami Iyer. Iyer introduced Ramanujan as an outstanding student who deserved scores higher than the maximum.[21] He received a scholarship to study at Government Arts College, Kumbakonam,[26][27] but was so intent on mathematics that he could not focus on any other subjects and failed most of them, losing his scholarship in the process.[28] In August 1905, Ramanujan ran away from home, heading towards Visakhapatnam, and stayed in Rajahmundry[29] for about a month.[30] He later enrolled at Pachaiyappa's College in Madras. There he passed in mathematics, choosing only to attempt questions that appealed to him and leaving the rest unanswered, but performed poorly in other subjects, such as English, physiology and Sanskrit.[31] Ramanujan failed his Fellow of Arts exam in December 1906 and again a year later. Without a FA degree, he left college and continued to pursue independent research in mathematics, living in extreme poverty and often on the brink of starvation.[32]
It was in 1910, after a meeting between the 23-year-old Ramanujan and the founder of the Indian Mathematical Society, V. Ramaswamy Aiyer, also known as Professor Ramaswami, that Ramanujan started to get recognition within the mathematics circles of Madras, subsequently leading to his inclusion as a researcher at the University of Madras.[33]
Adulthood in India[edit]
On 14 July 1909, Ramanujan married Janaki (Janakiammal) (21 March 1899 – 13 April 1994), then a ten-year-old girl whom his mother had selected for him a year earlier.[34][35] It was not unusual for marriages to be arranged with young girls. Some sources claim Janaki was ten years old when they married.[36] She came from Rajendram, a village close to Marudur (Karur district) Railway Station. Ramanujan's father did not participate in the marriage ceremony.[37] As was common at that time, Janakiammal continued to stay at her maternal home for three years after marriage till she attained puberty. In 1912, when Janaki was twelve years old, she and Ramanujan's mother joined Ramanujan in Madras.[38]
After the marriage, Ramanujan developed a hydrocele testis.[39] The condition could be treated with a routine surgical operation that would release the blocked fluid in the scrotal sac, but his family did not have the money for the operation. In January 1910, a doctor volunteered to do the surgery for free.[40]
After his successful surgery, Ramanujan searched for a job. He stayed at a friends' house while he went from door to door around Madras looking for a clerical position. To make money, he tutored students at Presidency College who were preparing for their F.A. exam.[41]
In late 1910, Ramanujan was sick again. He feared for his health, and told his friend R. Radakrishna Iyer to "hand these [Ramanujan's mathematical notebooks] over to Professor Singaravelu Mudaliar [the mathematics professor at Pachaiyappa's College] or to the British professor Edward B. Ross, of the Madras Christian College."[42] After Ramanujan recovered and retrieved his notebooks from Iyer, he took a train from Kumbakonam to Villupuram, a coastal city under French control.[43][44] In 1912, Ramanujan moved to a house in Saiva Muthaiah Mudali street, George Town, Madras with his wife and mother where they lived for a few months.[45] In May 1913, upon securing a resear
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