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## Inspiring Indians - Srinivasa Ramanujan

Srinivasa Ramanujan was a pioneering mathematician who gave the world new theories and formulas that revolutionized this field of study. He is considered as one of the world's greatest-ever mathematicians, proving over 3,000 theorems.

### Early Life

Srinivasa Aiyangar Ramanujan was a child prodigy and a largely self-taught mathematician. Born on 22 December 1887, in Erode, Tamil Nadu, by the age of twelve he had mastered trigonometry so thoroughly, that he was inventing sophisticated theorems that astonished his teachers. By 14, his genius was beginning to show, not only did he achieve merit certificates and academic awards throughout his school years, he was assisting the school in the logistics of assigning its 1200 students (each with their own needs) to its 35-odd teachers, completing exams in half the allotted time and was already showing his familiarity with infinite series.

### Adulthood in India

He got a job as a clerk in the Chennai Accountant General's Office. He was advised by an Englishman to contact researchers in Cambridge. Ramanujan desired the luxury to completely focus on mathematics without having to hold a job. He doggedly solicited support from influential Indian individuals and published several papers in Indian mathematical journals, but was unsuccessful in his attempts to foster sponsorship.

In 1913, Ramanujan enclosed a long list of complex theorems in a letter to three Cambridge academics: H. F. Baker, E. W. Hobson, and G. H. Hardy. Only Hardy, a Fellow of Trinity College, noticed the genius in Ramanujan's theorems.

Upon reading the initial unsolicited missive by an unknown and untrained Indian mathematician, Hardy and his colleague J.E. Littlewood commented that, "not one theorem could have been set in the most advanced mathematical examination in the world." Although Hardy was one of the pre-eminent mathematicians of the day and an expert in several of the fields, he added that many of them "defeated me completely. I had never seen anything in the least like them before". After some initial skepticism, Hardy replied and invited Ramanujan to England.

### Life in England

Hardy began to make plans to bring Ramanujan to England. As an orthodox Brahmin, Ramanujan consulted the astrological data for his journey because of religious concerns that he would lose his caste by travelling to foreign shores. Ramanujan's mother had a dream, in which the family Goddess told her not to stand in the way of her son's travel, and so he made plans accordingly. He took pains to keep a proper Brahmin lifestyle as far as he could. Ramanujan credited his understanding to his family Goddess, Namagiri, and looked to her for inspiration in his work. He often said, "An equation for me has no meaning, unless it represents a thought of God."

A fruitful collaboration fostered and Hardy, a prominent mathematician in his own right, stated in an interview that his greatest contribution to mathematics was the discovery of Ramanujan and compared Ramanujan to the mathematical giants Leonard Euler and Carl Gustav Jacob Jacobi in terms of genius.

Plagued by health problems all his life, Ramanujan's condition worsened in England, perhaps exacerbated the scarcity of vegetarian food during the First World War. He was also diagnosed with tuberculosis and a severe vitamin deficiency. He returned to India in 1919 and died soon after in Kumbakonam on 26 April 1920. His final gift to the world was the discovery of 'mock Theta functions'.

Ramanujan mainly worked in analytical number theory and is famous for many summation formulas involving constants such as ?, prime numbers and the partition function. Often, his formulae were stated without proof and were only later proven to be true.

### His notebooks

While in India, Ramanujan recorded much of the results of his work in the form of three notebooks of loose-leaf paper. Only the results of his work were recorded in the notebooks. This was likely influenced by a number of factors. Since paper was very expensive, Ramanujan would do most of his work and perhaps his proofs on slate and then transfer only the results to paper. Using only a slate was common for students in India at that time. The three original Ramanujan notebooks are with the Library of the University of Madras, some of the correspondence, papers, letters on or about Ramanujan are with the National Archives at New Delhi and the Tamil Nadu Archives, and a large number of his letters and connected papers/correspondence and notes by Hardy, Watson, Wilson are with the Wren Library of Trinity College, Cambridge.

### Tribute to the great Mind

• | The Ramanujan Institute for Advanced Study in Mathematics of the University of Madras is situated at a short distance from the famed Marina Beach |

• | A prize for young mathematicians from developing countries has been created in the name of Srinivasa Ramanujan by the International Centre for Theoretical Physics (ICTP) |

• | The Ramanujan Rolling Shield is the award given to the team which wins the Mathematics Quiz event at the Colloquium, the annual national-level inter-collegiate mathematics symposium held at the College of Engineering, Guindy, Chennai |

• | In 1997, the Ramanujan Journal was launched to publish work "in areas of mathematics influenced by Ramanujan" |