Hall of Fame: Srinivasa Ramanujan-The Man Who Knew Infinity

Srinivasa Ramanujan was born on 22 December 1887 into a Tamil family in Erode, Madras Presidency (now Tamil Nadu, India) at his maternal grandparent’s home. His father was K. Srinivasa Iyengar, an accounting clerk for a clothing merchant, and his mother was Komalatammal, a homemaker. His parents moved around a lot, and so he attended a variety of different elementary schools. In November 1897, after passing his primary examinations he entered Town High Secondary School in the same year and encountered formal mathematics for the first time.

Discovery as a Genius Mathematician At the age of 11, he had outrun the mathematics knowledge of two college students who were lodgers at his home. Later, he was lent a book written by S. L. Loney on advanced trigonometry. By the age of 13, he had mastered it and discovered theorems on his own. He used to complete a mathematics exam in half the allotted time and showed familiarity with geometry and infinite series.

In 1902, he showed how to solve cubic equations. He also developed his own methods and thus showed exceptional skills in mathematics. At the age of 15, he obtained a copy of George Shoobridge Carr’s Synopsis of Elementary Results in Pure and Applied Mathematics. It consisted of thousands of theorems. He studied the contents of the book in detail and went beyond and developed his own theorems and ideas. It is said that he independently developed and investigated the Bernoulli numbers and calculated the Euler-Mascheroni constant up to 15 decimal places. He secured a scholarship in 1903 at the University of Madras but lost it in the following years due to the negligence of all other subjects in pursuit of mathematics.

Career in Mathematics He tutored students at Presidency College in Madras who were preparing for their Fellow of Arts exam. He met with the founder of the Indian Mathematical Society, V Ramaswamy Aiyer in 1910 and began to gain recognition in Madras mathematical circles which lead to his inclusion as a researcher at the University of Madras. With the help of Aiyer, his work got published in the Journal of the Indian Mathematical Society.

In 1912 he got the job as an accounting clerk with the Madras Port Trust and his financial condition improved. His intelligence and genius slowly gained recognition and he began a correspondence in 1913 with the British mathematician Godfrey H. Hardy that led to a special scholarship from the University of Madras and a grant from Trinity College, Cambridge.

Life in England He travelled to England in 1914, where Hardy tutored him. Ramanujan brought his notebooks from India which were filled with thousands of identities, equations, and theorems that he discovered for himself in the years 1903 to 1914. Some were discovered by earlier mathematicians; some through inexperience, were mistaken, and many were entirely new. Even though he had very little formal training in mathematics he spent around 5 years in Cambridge collaborating with Hardy and J.E. Littlewood and published part of his findings there.

Illness and Death He contracted tuberculosis in 1917. His condition improved so that he could return to India in 1919. He died the following year. He left behind three notebooks and some pages, also known as the “lost notebook” that contained various unpublished results. Mathematicians continued to verify these results after his death.

Major Works and Legacy He worked in several areas including the Riemann series, the elliptic integrals, hypergeometric series, and his own theory of divergent series, using a technique he invented ,that came to be known as Ramanujan summation. His papers were published in English and European Journals.

He was elected to the Royal Society of London in 1918 and became the second Indian admitted, after Ardaseer Cursetjee in 1841. In October 1918, he was the first Indian to be elected a Fellow of Trinity College, Cambridge. “1729” is famous as Hardy-Ramanujan number and generalization of this idea have generated the notion of “Taxicab numbers”.  A biographical drama film titled The Man Who Knew Infinity, was released in 2015. It was based on the 1991 book of the same name by Robert Kanigel.

Vishakha

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