India is the land that gave the world great mathematical concepts such as the decimal system, binary numbers, the concept of zero and so many more. It is also the land that gave birth to great mathematicians such as Aryabhata, Bhaskaracharya and Brahmagupta.
While most Indians know about these ancient mathematicians, it is truly surprising that very few Indians are familiar with one of the greatest mathematicians of the twentieth century, born in our own India- the incandescent genius Srinivasa Ramanujan.
The mathematical genius of Srinivasa Ramanujan continues to confound modern mathematicians even today, nearly a hundred years after his death. In death, Ramanujan left behind a legacy so profoundly enduring that every person associated with the field of mathematics is transfixed by it, almost hypnotically. A 2015 Hollywood movie by the name ‘The Man Who Knew Infinity’ paid tribute to the luminescent brilliance of Ramanujan.
Scientists of every ilk concede that the world has not seen a mathematician the likes of Ramanujan since. His natural genius is spoken of in the same breath as that of Euler, Gauss and Jacobi. His seminal work in mathematics is even more astounding owing to the fact that he had absolutely no formal training in the subject of pure mathematics ever.
Despite this, he has left behind a legacy of almost 4ooo theorems, all of which were proved to be correct by later mathematicians. His contribution to the numbers theory, infinite series, continued fractions, elliptic functions, mathematical analysis etc. is without parallel even today.
His original and highly unconventional results, such as the Ramanujan prime and the Ramanujan theta function, have inspired a vast amount of further research. The Ramanujan Journal, a peer-reviewed scientific journal, was established to publish work in all areas of mathematics influenced by Ramanujan.
Living on the edge of poverty his entire life and shuttling between Kanchipuram and Kumbakonam towns throughout his childhood owing to poverty ensured that his early schooling was erratic and unstructured. Yet, he passed his primary examinations at the age of ten in the subjects of Tamil, English, Arithmetic and Geography with the best scores in the entire district.
Around this time, his parents had two college students staying as lodgers in their home. By age 11, he had mastered the books on Mathematics they had as course material. Later on, by the age of 14-15, he had mastered several books such as S. L. Loney’s Advanced Trigonometry, G. S. Carr’s ‘A Synopsis of Elementary Results in Pure and Applied Mathematics’, while discovering sophisticated theorems on his own. The latter book is considered instrumental in awakening his inherent mathematical genius.
At age 16, Ramanujan independently developed and investigated the Bernoulli numbers and calculated the Euler-Mascheroni constant up to 15 decimal places. In subsequent years he filled two large notebooks with his theorems, conclusions and equations, all derived independently, in isolation.
He published a 17-page paper on Bernoulli numbers in the Journal of the Indian Mathematical Society in 1911.
Gradually, his work and maths genius started to get noticed in Indian mathematical circles. Ramanujan showed his notebooks, filled with his theorems, to several maths proponents in India, who in turn were awed by the extent and brilliance of his work.
Finally, in 1913, the twenty-five-year-old Ramanujan, with no formal education or degree to his name, wrote a letter to G.H. Hardy, the celebrated British mathematician. The letter contained about a hundred of Ramanujan’s maths discoveries and begged Hardy’s opinion regarding these. Hardy realized that the letter was a work of genius. The letter contained several theorems that were already in prevalence, but it also contained derivations that were new and unparalleled in the maths world.
In Hardy’s own words, “Ramanujan was a mathematician of the highest quality, a man of altogether exceptional originality and power”.
Hardy arranged Ramanujan’s journey to England, and his stay at Trinity College, Cambridge. Thus began one of the most productive and extraordinary scientific collaborations in history. During the five years he spent at Cambridge, and with Hardy’s help and guidance, Ramanujan published more than twenty papers of his findings in hypergeometric series, highly composite numbers, divergent series and many more.
In 1918, Ramanujan was elected as a fellow of the Cambridge Philosophical Society and then as a fellow of the Royal Society of London. His name had been proposed and seconded by an impressive list of mathematicians. At 30 years of age, he was one of the youngest Fellows of the Society ever.
After a phenomenal stint in England, Ramanujan returned to India in 1919. He died of Tuberculosis in 1920, leaving behind a vast legacy of his seminal work in the form of three notebooks and a sheaf of papers, found much later, known as the ‘lost notebook’.
Many of his theorems are so complicated that the full scope of Ramanujan’s legacy has yet not been understood fully. Till today, his work remains the focus of much mathematical research. Cambridge University Press published his collected papers in 1927.
Ramanujan’s birth anniversary, December 22, is celebrated as National Mathematics Day in India every year.