Srinivasa Iyengar Ramanujan – 1729 Taxicab Numbers

Srinivasa Iyengar Ramanujan  22 December 1887 – 26 April 1920) was an Indian mathematician and autodidact. He is recognized as one of the greatest mathematicians of his time, but Srinivasa Ramanujan had almost no formal training in math.Many of his mathematical discoveries were based on pure intuition – but most of them were later proved to be true. He displayed a natural ability in mathematics at an early age.

Ramanujan was born on 22 December 1887 into a Tamil Brahmin Iyengar family in Erode in the southern Indian State of Tamil Nadu. His father, K. Srinivasa Iyengar, worked as a clerk in a sari shop. Ramanujan was married to Janaki Ammal in 1909, who was 9-year-old at that time. He passed his primary examinations in English, Tamil, geography and arithmetic with the best scores in the district. Ramanujan in his homeland of India is revered as a genius much as Albert Einstein is so recognized in Europe and America. Each in their early lives worked as a clerk, and at first, each developed their prodigious insights without inspiration from scientific journals or academic colleagues.

At the age of about fifteen, he borrowed a copy of G. S. Carr’s Synopsis of Pure and Applied Mathematics, which was the most influential book in Ramanujan’s development. Carr was a tutor and compiled this compendium of approximately 4000–5000 results (with very few proofs) to facilitate his tutoring at Cambridge and London. One or two years later, Ramanujan entered the Government College of Kumbakonam, often called “the Cambridge of South India,” because of its high academic standards.

It was in 1913 that that a letter from 25-year-old Ramanujan containing mathematical formulae was scrutinized by renowned Cambridge mathematicians G.H. Hardy and J.E. Littlewood, which led to Ramanujan’s award of a research studentship at Trinity College in April 1914. Within four months of his arrival in England, the outbreak of the World War affected not only the contact with continental mathematicians, but significantly also created food shortages.

Ramanujan (centre) with other scientists at Trinity College

Ramanujan departed from Madras aboard the S.S. Nevasa on 17 March 1914. Ramanujan spent nearly five years in Cambridge collaborating with Hardy and Littlewood, and published part of his findings there. In 1918 he was elected a Fellow of the Royal Society, the second Indian admitted to the Royal Society, following Ardaseer Cursetjee in 1841.

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 SocietyHe compiled 3,900 results (mostly identities and equations), before he lost his life at the age of 32. His infinite series for pi was one of his most celebrated findings.

Hardy–Ramanujan number 1729

The number 1729 is known as the Hardy–Ramanujan number after a famous visit by Hardy to see Ramanujan at a hospital. 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”.

Throughout his life, Ramanujan was plagued by health problems. His health worsened in England. He was diagnosed with tuberculosis and a severe vitamin deficiency, and was confined to a sanatorium. In 1919 he returned to Kumbakonam, Madras Presidency, and soon thereafter, in 1920, died at the age of 32. After his death, his brother Tirunarayanan chronicled Ramanujan’s remaining handwritten notes consisting of formulae on singular moduli, hypergeometric series and continued fractions and compiled them. Ramanujan’s widow, Smt. Janaki Ammal, moved to Bombay; in 1950 she returned to Madras, where she lived in Triplicane until her death in 1994 at the age 95.

In 2011, on the 125th anniversary of his birth, the Indian Government declared that 22 December will be celebrated every year as National Mathematics Day. Then Indian Prime Minister Manmohan Singh also declared that the year 2012 would be celebrated as the National Mathematics Year.

There is also a museum dedicated to telling Ramanujan’s life story. It is located in Chennai and has many photographs of his home and family, along with letters to and from friends, relatives, etc.

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