Srinivasa Ramanujan: the genius who discovered infinity in numbers

Few names in mathematics carry the mystique of Srinivasa Ramanujan, an Indian clerk from Madras whose notebooks upended long-held assumptions about numbers. Born in 1887 in Kumbakonam, he left school without a degree, taught himself from a discarded copy of Carr's "Synopsis of Elementary Results," and produced theorems still being extended a century later.

His story reads like a meditation on intuition. Unlike many self-taught thinkers, his outputs slotted into the centrepieces of number theory, forcing professionals to revise programmes they had believed complete.

For Australian audiences, the appeal runs deeper than biography. The University of Melbourne and the Australian National University in Canberra run number theory seminars that still cite his identities, and the Australian Mathematical Society has hosted special sessions on his contributions. Australian high-school competitions frequently include partition problems drawn from his notebooks.

The article traces Ramanujan's path from a Madras port office to Trinity College, Cambridge, and asks why a man who attributed his insights to his family goddess Namagiri remains a touchstone for those who believe discovery can come from anywhere.

A childhood surrounded by numbers in Kumbakonam

Ramanujan was born into a Tamil Brahmin family on 22 December 1887. His mother sang devotional songs at the temple, his father worked as a saree shop clerk, and the household had little money for academic fees. By eleven he had exhausted the mathematical knowledge of his lodgers.

What distinguished him was a stubborn refusal to accept results on authority alone. He failed examinations because he refused to score well in English, choosing instead to spend the hours on his own proofs. Scholarships dissolved, tutoring came and went, and he drifted through unemployed stretches carrying a thick ledger later called his first notebook.

Within those pages he assembled identities that would not be proved for decades, rediscovering results of Bernoulli and Euler. Family accounts describe how he would wake at night with new equations running through his mind and commit them to paper before dawn.

The letter that crossed the oceans

By 1911, Ramanujan had published his first paper in the Journal of the Indian Mathematical Society. In January 1913 he wrote to G. H. Hardy at Trinity College, including nine pages of theorems with little proof, a missive Hardy later called the most remarkable he had ever received.

Hardy initially suspected a fraud. He showed the letter to J. E. Littlewood, and the two spent an evening trying to dismiss the results. They failed. Hardy arranged a scholarship, and Ramanujan sailed from Madras in March 1914, arriving in London with little more than his notebooks.

The five years that followed were turbulent. World War I had begun, and food rationing made the vegetarian Ramanujan chronically ill. Hardy brought him into the circle of British analysts, and the two developed the Hardy-Ramanujan asymptotic partition formula, central to analytic number theory.

Cambridge, illness, and return to India

Ramanujan was elected a Fellow of the Royal Society in 1918, the second Indian to receive the honour, and named a Fellow of Trinity College. His health had deteriorated badly. He was diagnosed with tuberculosis, complicated by vitamin deficiencies and wartime rationing. In 1919 he returned to Kumbakonam with Janaki and died the following April at thirty-two.

Even in his final months he was writing. Two years after his death, G. N. Watson began publishing his analysis of Ramanujan's mock theta functions. Watson, based at Birmingham, lectured in Australian venues during the 1930s and helped keep these ideas alive in the Southern Hemisphere.

Researchers in Perth and Adelaide now use the digitised Ramanujan archives to work on identities in q-series and integer partitions, fields featured prominently at the Australian Mathematical Society's annual gatherings.

The mathematics that outlived him

Ramanujan's contributions cluster around a handful of themes. The Hardy-Ramanujan asymptotic formula counts the number of ways an integer can be written as a sum of smaller integers, a sequence that begins 1, 2, 3, 5, 7, 11 and grows almost exponentially. His work on highly composite numbers influenced subsequent studies in analytic number theory.

He also produced the celebrated taxicab number 1729, the smallest integer expressible as the sum of two cubes in two different ways. The anecdote in which Hardy arrived in a taxi numbered 1729 and called it dull, only to be corrected by Ramanujan on the spot, has become a teaching staple from Chennai to Canberra.

His notebooks contain over three thousand entries, many still unproved. Among the most striking are congruences for partition functions, theta function identities, and prime number conjectures that anticipated later theorems. He also foreshadowed results central to string theory.

Why Ramanujan still speaks to a sceptical age

In a century saturated with data and algorithmic shortcuts, Ramanujan's insistence on guided intuition offers a counterpoint. He tested every claim against numerical evidence, treating the mind as an antenna tuned to deep structure. Critics of pseudoscience often invoke him to argue that intuition without verification is dangerous, yet his work shows the opposite.

For Australian readers concerned about science in public life, his biography is a useful case study. It illustrates how a brilliant mind from a non-elite background can flourish when merit is rewarded over pedigree. Australian schools that struggle to engage Indigenous and rural students sometimes cite Ramanujan's story as proof that talent is everywhere.

The practical value lies in careful reading. Hardy himself warned against deifying Ramanujan, insisting that the equations, not the man, were the legacy, a distinction that publications such as scientificindia.net/news cover in their reporting on superstition and pseudoscience in Indian public life.

A side-by-side look at Ramanujan's major contributions

Contribution Year Collaborator Modern application
Hardy-Ramanujan asymptotic formula 1918 G. H. Hardy Cryptography and statistical mechanics
Partition congruences 1919 Solo Combinatorics and q-series
Taxicab number 1729 1919 G. H. Hardy Teaching tool in number theory
Mock theta functions 1920 Posthumous (Watson) String theory and modular forms
Highly composite numbers 1915 Solo Signal processing algorithms

Ways to engage with Ramanujan's work today

A useful next step is to download Ramanujan's first notebook from the University of Madras digital archive and spend an hour tracing his divisor function identity line by line.