Srinivasa Ramanujan

                                         Srinivasa Ramanujan

 

Srinivasa Ramanujan was an Indian mathematician whose contributions to number theory included pioneering the discovery of partition function features.

 

When Ramanujan was 15 years old, he acquired a copy of George Shoobridge Carr's Synopsis of Elementary Results in Pure and Applied Mathematics, 2 vol. (1880-86), which contained thousands of theorems, many with only the briefest of proofs and with no material newer than 1860. Ramanujan verified the results in Carr's book, but went beyond it, developing his own theorems and ideas. In 1903 he obtained a scholarship to

 

Ramanujan kept working despite being unemployed and having the worst living conditions. He started looking for a job after getting married in 1909, and his search ended with an interview with Ramachandra Rao, a government employee. Rao, who was impressed by Ramanujan's aptitude for mathematics, initially helped to fund his research, but Ramanujan refused to live off donations and eventually found work as a secretary for the Madras Port Trust.

 

Early life

 

Ramanujan, who is known as the "younger brother of Rama" (a Hindu deity), was born on December 22, 1887, into a Tamil Brahmin Iyengar family in Erode, present-day Tamil Nadu. His father, Kuppuswamy Srinivasa Iyengar, was a clerk in a sari store and was a native of Thanjavur district. His mother, Komalatammal, was a homemaker who performed in a nearby temple. In the town of Kumbakonam, they resided in a modest traditional house on Sarangapani Sannidhi Street. Now a museum, the family house. Sadagopan, Ramanujan's mother's kid, was born when he was one year and a half old; he passed away less than three months later. Ramanujan got smallpox in December 1889, but he survived it, unlike the 4,000 other people in the Thanjavur district who perished during a poor year at this time. To his mother's parents' home in Kanchipuram, close to Madras (now Chennai), he moved along with her. In 1891 and 1894, his mother gave birth to two more children, both of whom passed away before turning one.

 

Ramanujan began attending the neighborhood school on October 1st, 1892. Ramanujan and his mother relocated to Kumbakonam, where he enrolled in Kangayan Primary School because his maternal grandfather's position as a court officer in Kanchipuram was lost. He was returned to his maternal grandparents, who were then residing in Madras, after the passing of his paternal grandfather. He made an effort to avoid going to Madras school because he disliked it. His parents hired a neighborhood constable to make sure he went to school. In less than a year, Ramanujan returned to Kumbakonam.

 

Since Ramanujan's father spent the majority of the day at work, the youngster was raised by his mother, with whom he had a close relationship. She taught him about tradition and the Puranas, how to sing religious songs, how to participate in temple pujas, and how to follow certain dietary customs—all aspects of Brahmin culture. Ramanujan did well in his classes at Kangayan Primary School. He achieved the highest marks in the district in his primary exams for English, Tamil, geography, and arithmetic in November 1897, just before turning 10 years old. Ramanujan enrolled in Town Higher Secondary School that year, where he first met formal mathematics.

By the time he was 11 years old, he had surpassed the mathematical acumen of two college students who were his housemates. Later, he was given a book on advanced trigonometry by S. L. Loney. By the time he was thirteen, he had mastered it while independently deducing complex theorems. At the age of 14, he began receiving academic medals and achievement certificates. He also helped the school organize the distribution of its 1,200 kids, each of whom had different needs, to its about 35 teachers. He demonstrated an understanding of geometry and infinite series while finishing math tests in half the time given. In 1902, Ramanujan was instructed on how to resolve cubic equations.

 

Ramanujan borrowed a copy of G. S. Carr's compilation of 5,000 theorems, A Synopsis of Elementary Results in Pure and Applied Mathematics, from a friend in 1903 when he was 16 years old. According to reports, Ramanujan carefully read the book's contents. Ramanujan independently created, studied, and calculated the Bernoulli numbers the following year, as well as the Euler-Mascheroni constant to 15 decimal places. They "rarely understood him" and "stood in respectful awe" of him, according to his peers at the time.

 

After meeting the 23-year-old V. Ramaswamy Aiyer, the founder of the Indian Mathematical Society, in 1910, Ramanujan started to gain respect in Madras' mathematical community, which led to the University of Madras including him as a researcher.

 

Adulthood in India

 

Ramanujan wed Janaki (Janakiammal; 21 March 1899 - 13 April 1994), a girl his mother had chosen for him a year earlier, on July 14, 1909, and who was ten years old at the time of their nuptials. The arrangement of young female weddings back then was commonplace. Rajendram, a village close to the Marudur (Karur district) Railway Station, was where Janaki was from. Ramanujan's father abstained from the wedding celebration. Janaki stayed in her mother's house for three years after her marriage, as was customary at the time, until she entered puberty. She and Ramanujan's mother moved to Madras with him in 1912.

 

Ramanujan's testis hydrocele began to develop after the marriage. His family could not afford the procedure, which would have released the obstructed fluid in the scrotal sac and corrected the ailment. A surgeon offered to do the procedure without charge in January 1910. 

 

Following a successful surgery, Ramanujan looked for employment. While searching for a job as a clerk, he spent the night at a friend's house and went door to door in Madras. He gave Fellow of Arts test prep lessons to Presidency College students as a means of supplementing his income.

 

Ramanujan was ill once more in late 1910. He worried about his health and instructed his friend R. Radhakrishnan Iyer to "hand [his 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." Ramanujan rode a train from Kumbakonam to Villupuram, a city governed by the French, after he recovered and obtained his notebooks from Iyer. Ramanujan relocated with his wife and mother to a home in George Town, Madras's Saiva Muthaiah Mudali Street in 1912, where they stayed for a few months. Ramanujan and his family relocated to Triplicane in May 1913 after he was offered a research job at Madras University.

 

Pursuit of a career in mathematics

 

Ramanujan and V. Ramaswamy Aiyer, the Indian Mathematical Society's founder, first met in 1910 as deputy collectors. Ramanujan displayed his maths notebooks to Aiyer and expressed his desire to work in the tax department where the latter was employed. Later, Aiyer recalled: 

The remarkable mathematical discoveries in [the notebooks] astounded me. I had no desire to stifle his brilliance by giving him a job in the revenue department's lowest positions.

 

Aiyer sent letters of introduction and Ramanujan to his Madras-based mathematics acquaintances. Some of them looked over his work and gave R. Ramachandra Rao, the district collector for Nellore and secretary of the Indian Mathematical Society, letters of introduction. Rao was fascinated by Ramanujan's research but he wasn't certain it was his own. In a letter they exchanged, Professor Saldhana, a well-known mathematician from Bombay, admitted to not fully comprehending Ramanujan's contributions but came to the conclusion that he was not a fraud. Ramanujan's buddy C. V. Rajagopalachari made an effort to soothe Rao's worries about Ramanujan's academic honesty. Ramanujan's explanations of elliptic integrals, hypergeometric series, and his theory of divergent series, which Rao claimed ultimately persuaded him of Ramanujan's brilliance, won Rao over. Rao decided to give Ramanujan another chance. Ramanujan said that he required employment and financial assistance when Rao inquired what he wanted. Rao sent him to Madras with his approval. With financial assistance from Rao, he continued his investigation. Ramanujan was able to publish his work in the Journal of the Indian Mathematical Society with the assistance of Aiyer.

 

Personality and spiritual life

 

Ramanujan has been described as a dignified man with excellent manners, with a shy and quiet demeanor. At Cambridge, he had a humble existence. Ramanujan's initial Indian biographers described him as a strict Hindu. Namagiri Thayar (Goddess Mahalakshmi) of Namakkal was his family goddess, he said. He drew inspiration from her in his paintings and claimed to have dreamed of blood droplets representing her consort, Narasimha. Later, he saw scrolls of complicated mathematical knowledge unroll in front of his eyes. He frequently stated, "An equation has no meaning for me unless it expresses a thought of God."

 

According to Hardy, Ramanujan stated that all religions seemed equally truthful to him. Hardy also said that Ramanujan's religious beliefs had been romanticized by Westerners and exaggerated by Indian biographers (about his belief, not practice). Simultaneously, he commented on Ramanujan's extreme vegetarianism. 

 

Similarly, Berndt stated in an interview with Frontline, "Many people falsely ascribe mystical powers to Ramanujan's mathematical thinking." It needs to be corrected. He painstakingly recorded every result in his three notebooks," assuming that Ramanujan worked out intermediate results on slate because he couldn't afford to record them more permanently on paper.