About Srīnivāsa Ramanujan

Srīnivāsa Aiyangār Ramanujan FRS, better known as Srīnivāsa Aiyangār Ramanujan  pronunciation  (Tamil: சீனிவாச இராமானுஜன் or ஸ்ரீனிவாஸ ஐயங்கார் ராமானுஜன்) (22 December 1887 – 26 April 1920) was an Indian mathematician and autodidactwho, with almost no formal training in pure mathematics, made substantial contributions to mathematical analysis, number theory, series and continued fractions. Rumanian’s talent was said by the English mathematician G.H. Hardy to be in the same league as legendary mathematicians such as Euler, Gauss, Newton and Archimedes.

Born in Erode, Tamil Nadu, India, Ramanujan first encountered formal mathematics at age 10. He demonstrated a natural ability, and was given books on advanced trigonometry written by S. L. Looney. He mastered them by age 12, and even discovered theorems of his own. He demonstrated unusual mathematical skills at school, winning accolades and awards. By 17, Ramanujan conducted his own mathematical research on Bernoulli numbers and the Euler–Mascheroni constant. He received a scholarship to study at Government College in Kumbakonam, but lost it when he failed his non-mathematical coursework. He joined another college to pursue independent mathematical research, working as a clerk in the Accountant-General's office at the Madras Port Trust Office to support himself.^[3] In 1912–1913, he sent samples of his theorems to three academics at the University of Cambridge. Only Hardy recognized the brilliance of his work, subsequently inviting Ramanujan to visit and work with him at Cambridge. He became a Fellow of the Royal Society and a Fellow of Trinity College, Cambridge, dying of illness, malnutrition and possibly liver infection in 1920 at the age of 32.

During his short lifetime, Ramanujan independently compiled nearly 3900 results (mostly identities and equations).^[4] Although a small number of these results were actually false and some were already known, most of his claims have now been proven correct.^[5] He stated results that were both original and highly unconventional, such as the Ramanujan prime and the Ramanujan theta function, and these have inspired a vast amount of further research.^[6] However, the mathematical mainstream has been rather slow in absorbing some of his major discoveries. Recently, Ramanujan's formulae have found applications in crystallography and string theory.^{[citation needed]} The Ramanujan Journal, an international publication, was launched to publish work in all areas of mathematics influenced by his work

Early life

Ramanujan was born on 22 December 1887 in the city Erode, Tamil Nadu, India, at the residence of his maternal grandparents.^[8] His father, K. Srinivasa Iyengar worked as a clerk in a sari shop and hailed from the district of Thanjavur.^[9] His mother, Komalatammal or Komal Ammal was a housewife and also sang at a local temple.^[10] 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 named Sadagopan, who died less than three months later. In December 1889, Ramanujan had smallpox and recovered, unlike thousands in theThanjavur district who died from the disease that year. He moved with his mother to her parents' house in Kanchipuram, near Madras (now Chennai). In November 1891, and again in 1894, his mother gave birth, but both children died in infancy.

On 1 October 1892, Ramanujan was enrolled at the local school. In March 1894, he was moved to a Telugu medium school. After his maternal grandfather lost his job as a court official in Kanchipuram,^[13] Ramanujan and his mother moved back to Kumbakonam and he was enrolled in the Kangayan Primary School. After his paternal grandfather died, he was sent back to his maternal grandparents, who were now living in Madras. He did not like school in Madras, and he tried to avoid going to school. His family enlisted a local constable to make sure he attended school. Within six months, Ramanujan was back in Kumbakonam.

Since Ramanujan's father was at work most of the day, his mother took care of him as a child. He had a close relationship with her. From her, he learned about tradition and purines. He learned to sing religious songs, to attend pujas at the temple and particular eating habits – all of which are part of Brahmin culture. At the Kangayan Primary School, Ramanujan performed well. Just before the age of 10, in November 1897, he passed his primary examinations in English, Tamil, geography and arithmetic. With his scores, he finished first in the district. That year, Ramanujan entered Town Higher Secondary School where he encountered formal mathematics for the first time. 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 on advanced trigonometry written by S. L. Loney. He completely mastered this book by the age of 13 and discovered sophisticated theorems on his own. By 14, he was receiving merit certificates and academic awards which continued throughout his school career and also assisted the school in the logistics of assigning its 1200 students (each with their own needs) to its 35-odd teachers. He completed mathematical exams in half the allotted time, and showed a familiarity with infinite series. When he was 16, Ramanujan came across the book A Synopsis of Elementary Results in Pure and Applied Mathematics by George S. Carr. This book was a collection of 5000 theorems, and it introduced Ramanujan to the world of mathematics. The next year, 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 that they "rarely understood him" and "stood in respectful awe" of him.

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, Krishna swami Ayer. Ayer introduced Ramanujan as an outstanding student who deserved scores higher than the maximum possible marks.^[19] He received a scholarship to study at Government College in Kumbakonam, However, Ramanujan 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.^] In August 1905, he ran away from home, heading towards Visakhapatnam. He later enrolled at Pachaiyappa's College in Madras. He again excelled in mathematics but performed poorly in other subjects such as physiology. Ramanujan failed his Fine Arts degree exam in December 1906 and again a year later. Without a degree, he left college and continued to pursue independent research in mathematics. At this point in his life, he lived in extreme poverty and was often on the brink of starvation.