Dipak Kurmi
Every year on December 22, India observes National Mathematics Day to commemorate the birth of Srinivasa Ramanujan, a mathematician whose life and work continue to hover between legend and rigorous scholarship. Born in 1887, Ramanujan is often remembered as a prodigy who seemed to converse effortlessly with infinity, producing formulae of astonishing depth without recording the logical steps that led him there. This image, while captivating, carries the risk of reducing him to a mystical curiosity rather than a disciplined and deeply analytical thinker. National Mathematics Day therefore offers not merely an occasion for celebration, but also an opportunity to pause and examine how Ramanujan actually thought, worked, and trained his mind to see patterns that others missed.
Popular narratives frequently describe Ramanujan as an unknowable genius, someone whose insights arrived fully formed through divine inspiration. Indeed, there is a well-known anecdote from his years in England, when he was asked about the methods behind his discoveries and replied that the Hindu deity Namagiri revealed them to him in dreams. While this remark has been repeated endlessly, it has sometimes overshadowed the years of solitary study, intense practice, and intellectual struggle that shaped his mathematical vision. Mathematics is a discipline built on structure, proof, and method, and Ramanujan’s work, though unconventional in presentation, was deeply rooted in an internalized understanding of these principles. His notebooks reveal not chaos, but an alternative kind of order, one that came from relentless engagement with numbers.
Srinivasa Ramanujan was born into a Tamil Brahmin Iyenger family and spent much of his early life in the temple town of Kumbakonam in Tamil Nadu. From a young age, his extraordinary aptitude for mathematics was evident, yet his life was marked by financial hardship and a lack of formal academic support. Krishnaswami Alladi, an Indian-American professor of mathematics at the University of Florida, has written about the strong religious environment of Ramanujan’s upbringing, noting that his family venerated the goddess Namagiri, worshipped at the Namakkal temple. This spiritual backdrop formed part of Ramanujan’s worldview, but it coexisted with a fierce intellectual independence. For several years, he worked largely in isolation, teaching himself advanced mathematics from outdated textbooks and pursuing original ideas far beyond the syllabus of any institution.
The turning point in Ramanujan’s life came in 1913, when he wrote two letters to the renowned English mathematician G H Hardy. These letters contained a selection of theorems and formulae that immediately struck Hardy as extraordinary. Recognising a genius of the highest order, Hardy arranged for Ramanujan to travel to England. There, Ramanujan’s work finally received the exposure and recognition it deserved. He was elected as one of the youngest Fellows of the Royal Society and became the first Indian to be elected as a Fellow of Trinity College, Cambridge. Yet this period of professional success was also one of profound personal difficulty. The cold English climate, combined with his strict vegetarian diet and fragile health, led to frequent illnesses and repeated hospitalisations.
It was during one such hospital stay, at Putney, that one of the most famous anecdotes in the history of mathematics unfolded. Hardy visited Ramanujan, arriving in a taxicab whose number he described as dull and uninspiring: 1729. In a moment that has since become legendary, Ramanujan immediately disagreed. He remarked that 1729 was in fact a very interesting number, as it was the smallest number that could be expressed as the sum of two cubes in two different ways. He explained that 1 cubed plus 12 cubed equals 1729, and so does 9 cubed plus 10 cubed. What appeared to Hardy as an idle observation about a random number revealed, through Ramanujan’s response, a remarkable capacity to recognise rare numerical patterns instantaneously.
This number, now known as the Hardy–Ramanujan number, often leaves non-mathematicians wondering why it matters. After all, countless numbers possess curious properties, and the sum of two cubes may seem like a trivial curiosity. Yet the significance of this moment lies not in the arithmetic itself, but in what it reveals about Ramanujan’s mind. He did not stumble upon this pattern by chance, nor was it the result of a fleeting mystical insight. Rather, it reflected years of deep engagement with number theory, during which certain structures and relationships had become second nature to him. When Hardy mentioned 1729, Ramanujan’s mind instantly connected it to a web of mathematical ideas he had already explored extensively.
Later mathematicians and historians have emphasised this point to counter the myth of Ramanujan as merely an inspired savant. The 2016 book My Search for Ramanujan: How I Learned to Count, by Ken Ono and Amir D Aczel, revisits the Putney hospital incident and places it in a broader intellectual context. The authors note that Ramanujan was already aware of the special property of 1729 because of his earlier work on problems studied by the Swiss mathematician Leonhard Euler. Euler had investigated sums of powers, particularly cubes, and Ramanujan had engaged deeply with these ideas in his notebooks. The number 1729 also appears in Ramanujan’s work in connection with Fermat’s last theorem, suggesting that his interest went far beyond a single amusing numerical coincidence.
Fermat’s last theorem, proposed in 1637 by the French mathematician Pierre de Fermat, states that there are no whole numbers x, y, and z such that x to the power n plus y to the power n equals z to the power n for any integer n greater than 2. In simpler terms, no two cubes can add up exactly to another cube. While this theorem was only formally proven centuries later, mathematicians long explored its implications and boundaries. Ramanujan was fascinated by what might be called near misses, numbers that came tantalisingly close to violating this ancient claim without actually doing so. If 9 cubed plus 10 cubed had equalled 1728 instead of 1729, it would have contradicted Fermat’s assertion, since 1728 is 12 cubed. The fact that it fell short by just one captured Ramanujan’s imagination.
This fascination with near misses reveals a great deal about Ramanujan’s intellectual temperament. He was not content merely to accept established theorems; he probed their edges, looking for patterns, exceptions, and deeper structures. His ability to recall the property of 1729 so quickly was therefore not a miraculous stroke of luck, but the natural outcome of a mind trained to dwell obsessively on numerical relationships. He had internalised the logic of number theory to such an extent that certain results were instantly accessible, much like a musician who can hear a complex chord progression and immediately recognise its structure.
Ramanujan’s life was tragically short. He returned to India ill and died in 1920 at the age of just 32. Yet in those brief years, he produced work that continues to influence modern mathematics, from number theory to complex analysis. His notebooks, many of which were published only decades after his death, have inspired generations of mathematicians and led to new discoveries long after he was gone. They testify to a mind that was both intuitive and disciplined, capable of leaps of insight grounded in sustained and rigorous thought.
On his 138th birth anniversary, and on every National Mathematics Day, remembering Srinivasa Ramanujan should mean more than marveling at his genius. It should involve an effort to understand how that genius was formed: through solitude, persistence, deep curiosity, and an unwavering engagement with numbers. The Hardy–Ramanujan number stands as a symbol not just of a clever numerical trick, but of a way of thinking that blended imagination with structure. In recognising this, we move beyond the myth of the unknowable prodigy and closer to the real Ramanujan, a mathematician whose dreams were shaped by discipline, and whose discipline allowed his dreams to reshape mathematics itself.
(the writer can be reached at dipaknewslive@gmail.com)
