Srinivasa Ramanujan: Who Truly Knew the "Infinite"

22 December marks the birthday of the great Indian mathematician Srinivasa Ramanujan, who is counted among the greatest mathematicians of the world, and who commands the same reverence in mathematics that Albert Einstein does in science. Many of the formulas or theorems he authored remain unsolved to this day—or rather, their upapatti (mathematical proof) is still not available. Yet these formulas are being applied across diverse fields with immense success. Eminent scientists and mathematicians across the entire world continue to conduct rigorous research on the formulas penned by Ramanujan.

Srinivasa Ramanujan was born into an extremely modest family on 22 December 1887 in Erode, Tamil Nadu. From childhood, he was a boy of sharp intellect, endowed with extraordinary talent, reasoning ability, and creativity. In 1903, he passed his matriculation examination from the University of Madras, winning several prizes. Right after high school, he was awarded the highly prestigious “Subramanyam Scholarship”, which was then granted to exceptionally distinguished students of mathematics and English.

His mind was thoroughly engrossed in solving the most intricate mathematical problems; consequently, unable to pay adequate attention to other subjects, he failed the eleventh standard. In 1906, he once again enrolled in the eleventh standard at Pachaiyappa's College in Madras, and in 1907, he sat for the twelfth standard examination as a private candidate, but was unable to pass. His formal conventional education ended there, yet despite continually enduring diverse hardships and adversities in life, he persevered uninterruptedly with his research in mathematics.

Meanwhile, on 14 July 1909, Ramanujan married Janakiammal, daughter of Shri Rangaswamy, from a respected family in Rajendram village near Kumbakonam. Following this, he set out in search of employment, but despite strenuous efforts, met with no success. Later, on the recommendation of his former teacher Professor Aiyar, he met the then District Collector of Nellore, Shri R. Ramachandra Rao, who was also the President of the Indian Mathematical Society at the time.

Upon examining Srinivasa Ramanujan’s notebooks and recognizing his genius, R. Ramachandra Rao arranged a stipend of twenty-five rupees per month for him. Ramanujan continued to receive this stipend for about a year from the beginning of 1911. That same year, Ramanujan’s first research paper was published in the “Journal of the Indian Mathematical Society”, in which he presented an investigation into Bernoulli numbers.

After this one-year stipend concluded, on 1 March 1912, he took up a position as a Class III, Grade IV clerk at the Madras Port Trust on a modest monthly salary of thirty rupees to earn a livelihood; during this period, he carried out independent research across numerous branches of pure mathematics. The attitude of Ramanujan’s superiors at the Madras Port Trust was exceptionally cordial; they admired his mathematical prowess and wished for him to pursue his work in mathematics uninterrupted.

Ramachandra Rao also looked after Ramanujan with great care, and at his behest, Professor C. L. T. Griffith of the Madras Engineering College forwarded Ramanujan’s work to several renowned and knowledgeable mathematicians, chief among them being the eminent mathematician M. J. M. Hill of University College London. Prof. Hill offered Ramanujan valuable suggestions on multiple occasions regarding the refinement of his understanding and presentation, though he made no other substantive effort to help establish Ramanujan in the field of pure mathematical research.

Thereafter, Ramanujan began writing letters to prominent mathematicians at the University of Cambridge, enclosing specimens of his research so that they might evaluate his work prima facie. In the interim, another of Ramanujan’s former mentors, Prof. Seshu Aiyar, advised him to write to Prof. G. H. Hardy. On 16 January 1913, Ramanujan wrote to Prof. Hardy for the first time, appending the theorems he had discovered independently. Acknowledging Ramanujan’s genius, Prof. Hardy extended an invitation to him to come to England; however, due to personal reasons, Ramanujan was not willing to travel abroad at that time, though his correspondence with Prof. Hardy continued.

Later, in a letter written to Prof. Hardy on 22 January 1914, he agreed to travel to England, and on 17 March 1914, he departed for England by ship. From April onward, he met Prof. Hardy at Cambridge and commenced his research. There, in order to gain a firmer grasp of mathematical principles, he began attending lectures delivered by several accomplished professors. Gradually, Srinivasa Ramanujan began to impress everyone with his brilliance.

In March 1916, the University of Cambridge conferred upon him the degree of B.A. (by Research) on the strength of his 62-page research treatise published in English, titled “Highly Composite Numbers”. Between 1915 and 1918, he authored several research papers. On 6 December 1917, through the efforts of Prof. Hardy, Ramanujan was elected to the London Mathematical Society. Following this, in May 1918, Srinivasa Ramanujan was elected a Fellow of the Royal Society of London—a distinction of immense honor for any Indian in those times.

Even amidst failing health, his research continued unabated, and during his brief stay of four years, he attained extraordinary achievements. On 27 March 1919, Ramanujan returned to Bombay, yet his research did not cease. In his final days, he conducted groundbreaking research on mock theta functions and false theta functions, which is regarded as his most profound and distinctive contribution.

On 26 April 1920, having suffered from prolonged illness, Srinivasa Ramanujan lost consciousness in the early morning and, a few hours later, passed into eternal rest. To Srinivasa Ramanujan—the crest jewel and symbol of Indian genius, whose research and mathematical brilliance will continue to inspire us for eternity—a hundred salutations and humble homage.

– Vishal Agarwal (The author is an educationist and a profound scholar of Indian history and culture. His Rashtra Aradhak series on great Indian luminaries is well worth reading.)

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