Karmayog- Dr. Srinivasa Ramanujan

Ramanujan has been described as a person with a somewhat shy and quiet disposition, a dignified man with pleasant manners.He lived a rather spartan life while at Cambridge. Ramanujan’s first Indian biographers describe him as rigorously orthodox. Ramanujan credited his acumen to his family goddess, Mahalakshmi of Namakkal. He looked to her for inspiration in his work,and claimed to dream of blood drops that symbolised her male consort, Narasimha, after which 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.”

Hardy cites Ramanujan as remarking that all religions seemed equally true to him. Hardy further argued that Ramanujan’s religiousness had been romanticized by Westerners and overstated—in reference to his belief, not practice—by Indian biographers. At the same time, he remarked on Ramanujan’s strict observance of vegetarianism.

Srinivasa Ramanujan Iyengar  (22 December 1887 – 26 April 1920) was an Indian mathematician and autodidact. Though he had almost no formal training in pure mathematics, he made extraordinary 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.

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 geometry and infinite series. Ramanujan was shown how to solve cubic equations in 1902 and he went on to find his own method to solve the quartic. The following year, not knowing that the quintic could not be solved by radicals, he tried to solve the quintic.

In 1903 when he was 16, Ramanujan obtained from a friend a library-loaned copy of a book by G. S. Carr.The book was titled A Synopsis of Elementary Results in Pure and Applied Mathematics and was a collection of 5000 theorems. Ramanujan reportedly studied the contents of the book in detail.The book is generally acknowledged as a key element in awakening the genius of Ramanujan.The next year, he had independently developed and investigated the Bernoulli numbers and had calculated the Euler–Mascheroni constant up to 15 decimal places.His peers at 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, Krishnaswami Iyer. Iyer introduced Ramanujan as an outstanding student who deserved scores higher than the maximum possible marks.He received a scholarship to study at Government Arts College, 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 and stayed in Rajahmundryfor about a month.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 Fellow of Arts 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.

On 14 July 1909, Ramanujan was married to a ten-year-old bride, Srimathia Janki (Janakiammal) (21 March 1899 – 13 April 1994).She came from Rajendram, a village close to Marudur (Karur district) Railway Station. Ramanujan’s father did not participate in the marriage ceremony.

After the marriage, Ramanujan developed a hydrocele testis, an abnormal swelling of the tunica vaginalis, an internal membrane in the testicle.The condition could be treated with a routine surgical operation that would release the blocked fluid in the scrotal sac. His family did not have the money for the operation, but in January 1910, a doctor volunteered to do the surgery for free.

After his successful surgery, Ramanujan searched for a job. He stayed at friends’ houses while he went door to door around the city of Madras (now Chennai) looking for a clerical position. To make some money, he tutored some students at Presidency College who were preparing for their F.A. exam.

In late 1910, Ramanujan was sick again, possibly as a result of the surgery earlier in the year. He feared for his health, and even 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.” After Ramanujan recovered and retrieved his notebooks from Iyer, he took a northbound train from Kumbakonam to Villupuram, a coastal city under French control.

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 for only a few weeks.Toward the end of that assignment he applied for a position under the Chief Accountant of the Madras Port Trust. In a letter dated 9 February 1912, Ramanujan wrote:

Sir,
I understand there is a clerkship vacant in your office, and I beg to apply for the same. I have passed the Matriculation Examination and studied up to the F.A. but was prevented from pursuing my studies further owing to several untoward circumstances. I have, however, been devoting all my time to Mathematics and developing the subject. I can say I am quite confident I can do justice to my work if I am appointed to the post. I therefore beg to request that you will be good enough to confer the appointment on me.

The number 1729 is known as the Hardy–Ramanujan number after a famous anecdote of the British mathematician G. H. Hardy regarding a visit to the hospital to see Ramanujan. In Hardy’s words:

I remember once going to see him when he was ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen. ‘No’, he replied, ‘it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways.’

The two different ways are

1729 = 13 + 123 = 93 + 103.

Generalizations of this idea have created the notion of “taxicab numbers”. Coincidentally, 1729 is also a Carmichael number.

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