The Scene
January 16, 1913. Madras. A 25-year-old clerk at the Madras Port Trust sits at his wooden desk, surrounded by shipping manifests and customs ledgers. His name is Srinivasa Ramanujan. His salary is 25 rupees a month. His formal mathematical education ended when he failed every subject except mathematics at college, twice.
In front of him is a letter he’s been writing and rewriting for weeks. It’s addressed to Professor G.H. Hardy at Trinity College, Cambridge, one of the most respected mathematicians in the world. Ramanujan has never left South India. He has no degree. He has no recommendations. He has no credentials that the Western academic world recognizes.
What he has is a stack of notebooks filled with over 3,000 mathematical formulas, theorems, identities, infinite series, continued fractions, that he’s been writing since he was a teenager. He’s derived them alone, mostly at night, sitting on the floor of his family home in Kumbakonam with a slate and chalk (paper was too expensive). He would work out a result on the slate, verify it, transfer the final formula to his notebook, then wipe the slate clean and start the next one. The working, the proofs, the intermediate steps, was erased. Only the results survived.
This method of working would later confound mathematicians for a century. Ramanujan’s notebooks are full of results without proofs, not because he couldn’t prove them, but because the slate was too small and chalk was too precious to preserve the reasoning. It’s as if Shakespeare had written his plays on a whiteboard and only preserved the final lines.
He’s already written to two Cambridge professors. H.F. Baker didn’t reply. E.W. Hobson didn’t reply. Both likely looked at the letter from an unknown Indian clerk, saw no university credentials, and set it aside. This letter to Hardy is his last attempt. He includes nine pages of his work, formulas for infinite series, properties of highly composite numbers, results that overlap with what European mathematicians spent decades deriving. Some of his results have no known proof. Some have no known precedent. Some will take 80 years to verify.
He folds the letter, addresses the envelope, and posts it from the General Post Office on Beach Road. The letter will take two weeks to reach Cambridge. It will take centuries to fully understand what it contains.
The Backstory
Ramanujan was born on December 22, 1887, in Erode, Tamil Nadu, and grew up in Kumbakonam, a temple town on the banks of the Kaveri River known as the “Cambridge of South India” for its traditional Sanskrit learning centres. His father, K. Srinivasa Iyengar, was a clerk in a sari shop earning barely enough to keep the family fed. His mother, Komalatammal, sang devotional songs at the local Sarangapani Temple.
The family was Brahmin but poor, a combination that gave Ramanujan access to a certain intellectual tradition (he learned Sanskrit and Hindu philosophical texts early) but none of the material comforts that would have made his path easier. The house in Kumbakonam where he grew up, now a museum, is a modest structure with a narrow veranda where Ramanujan would sit cross-legged, slate on his knees, working through the night while his family slept.
He showed mathematical ability from a very young age. By 11, he had exhausted the knowledge of two college students who boarded at his home. By 13, he was working through advanced trigonometry from S.L. Loney’s textbook, which he borrowed from a neighbour. He mastered it in a year and began deriving results that went beyond the book.
At 15, a pivotal event: he obtained a copy of G.S. Carr’s “Synopsis of Elementary Results in Pure and Applied Mathematics”, a dry, formula-heavy reference book published in 1886 that listed 5,000 mathematical results with minimal proofs. Most students would find it unreadable. Ramanujan treated it like a puzzle book. He began independently deriving every result in it, then going beyond, creating mathematics that had never existed.
Carr’s book shaped Ramanujan’s mathematical style permanently. Because Carr presented results without detailed proofs, Ramanujan learned to think the same way, leaping from insight to result, trusting his mathematical intuition to bridge gaps that formal training would have filled with step-by-step reasoning. This made his work simultaneously brilliant and frustrating: he could see truths that trained mathematicians couldn’t, but he often couldn’t (or didn’t bother to) explain how he got there.
He won a scholarship to Government Arts College in Kumbakonam but lost it because he couldn’t pass English, history, or science. He tried again at Pachaiyappa’s College in Madras. Failed again. By the standards of the Indian education system, Srinivasa Ramanujan was a dropout and a failure.
By the standards of mathematics, he was producing work that rivaled Euler, Gauss, and Jacobi, alone, without training, without access to a library, without anyone to talk to who could understand what he was doing.
The years between 1905 and 1912 were the hardest. Ramanujan lived in near-poverty, dependent on the kindness of friends and family, moving between Kumbakonam and Madras, trying to find anyone who would take his mathematics seriously. He showed his notebooks to R. Ramachandra Rao, a civil servant and mathematics enthusiast, who was astonished by the work but couldn’t fully appreciate it. Rao supported Ramanujan financially for a time and helped him get the Port Trust clerkship that put bread on the table, barely.
During this period, Ramanujan published his first paper in the Journal of the Indian Mathematical Society in 1911, a modest beginning, but it brought him to the attention of a small circle of Indian mathematicians who realised something extraordinary was happening in their midst. They encouraged him to write to England. To Cambridge. To the people who might actually understand.
The Turning Point
When Hardy opened Ramanujan’s letter in Cambridge on February 8, 1913, his first reaction was scepticism. The letter looked like the work of a crank, extraordinary claims from an unknown Indian clerk with no qualifications. Hardy received dozens of such letters. Most went straight into the dustbin.
But something about this one was different. The formulas weren’t the usual pseudo-mathematical nonsense. They were dense, specific, and, Hardy noticed, some of them looked like they might actually be true.
He sat down after dinner with his colleague J.E. Littlewood, one of the few mathematicians in the world who could evaluate the work, and they went through the formulas one by one. The session lasted hours. Some results were already known, which proved Ramanujan wasn’t a fraud (he had independently rediscovered what Europe’s best minds had taken decades to establish). Some were new and provable, which proved he was genuine. And some were so strange, so unexpected, so unlike anything in the European mathematical tradition, that Hardy later wrote: “They must be true, because if they were not true, no one would have had the imagination to invent them.”
Hardy later called that letter “certainly the most remarkable I have received” and rated the experience of reading it as the single most romantic incident of his career. He told a friend: “I had never seen anything in the least like them before. A single look at them is enough to show that they could only be written by a mathematician of the highest class.”
Hardy arranged for Ramanujan to come to Cambridge. It wasn’t easy. Ramanujan was a devout Brahmin. Crossing the ocean, the “kala pani” (black water), meant ritual pollution and loss of caste. His mother initially refused. The family consulted astrologers. Legend says Komalatammal relented after the family goddess, Namagiri of Namakkal, appeared in her dream and told her to let her son go. Whether the dream was real or a convenient resolution to an impossible family argument, it worked.
Ramanujan arrived at Cambridge in April 1914, weeks before the outbreak of World War I. He was vegetarian in a country that didn’t understand vegetarianism. He was Hindu in a Christian institution. He was dark-skinned in an empire built on racial hierarchy. He was a college dropout among PhDs. He cooked his own food because no one in Cambridge knew how to prepare South Indian meals without animal products. He suffered from the cold, Kumbakonam’s average temperature is 30°C; Cambridge’s is 10°C.
And yet, in those adverse conditions, he produced some of the most extraordinary mathematics the world has ever seen.
The Hardy-Ramanujan collaboration was one of the most productive partnerships in the history of mathematics. Hardy provided the rigour and the formal training; Ramanujan provided the intuition and the results. Hardy once rated mathematicians on a scale of 1 to 100. He gave himself 25, Littlewood 30, the great David Hilbert 80, and Ramanujan 100. It wasn’t modesty on Hardy’s part, it was honest assessment.
The Work That Changed Mathematics
In his five years at Cambridge (1914-1919), Ramanujan published 21 papers and filled hundreds of pages of notebooks. His contributions span number theory, analysis, infinite series, and continued fractions. Some of his most significant work includes:
The Partition Function
A partition of a number is the number of ways it can be expressed as a sum of positive integers. The number 4, for example, has 5 partitions: 4, 3+1, 2+2, 2+1+1, 1+1+1+1. Simple for small numbers. For large numbers, the partition function grows astronomically, the number 200 has over 3.9 trillion partitions.
Hardy and Ramanujan developed the “circle method”, a technique for calculating the partition function that produced results of astonishing accuracy. Their formula, published in 1918, was one of the landmarks of 20th-century mathematics. The circle method is now used across number theory, combinatorics, and theoretical physics.
Highly Composite Numbers
Ramanujan’s study of highly composite numbers, numbers with more divisors than any smaller positive integer, was his first major paper at Cambridge and remains a foundational work in number theory. The results have applications in computer science, particularly in optimization algorithms and database design.
Mock Theta Functions
In January 1920, three months before his death, Ramanujan wrote his last letter to Hardy from India. In it, he described a new class of functions he called “mock theta functions.” He provided 17 examples but no proofs, no formal definitions, just results that seemed to come from nowhere.
For decades, nobody understood what mock theta functions were. Then, in 2002, Dutch mathematician Sander Zwegers showed that they were part of a much larger theory, harmonic Maass forms, that connected to some of the deepest structures in mathematics. Mock theta functions are now used in string theory, black hole physics, and quantum gravity. A dying man in Madras had seen, in his final months, mathematical objects that the rest of the world would need 80 years to comprehend.
Ramanujan’s Tau Function and Conjecture
The Ramanujan conjecture, proposed in 1916, concerned the size of certain coefficients of modular forms. It was finally proved by Pierre Deligne in 1973 as part of his work on the Weil conjectures, work that won Deligne the Fields Medal (mathematics’ equivalent of the Nobel Prize). Ramanujan’s intuition had pointed toward one of the deepest results in algebraic geometry, 57 years before it was proven.
The Taxicab Number
The most famous Ramanujan anecdote involves the number 1729. When Hardy visited Ramanujan in hospital and mentioned that his taxi had the rather dull number 1729, Ramanujan immediately replied: “No, it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways.” (1729 = 1³ + 12³ = 9³ + 10³.) The story illustrates what made Ramanujan unique: numbers were not abstractions to him. They were personalities. He knew them the way most people know faces.
The Ripple Effect
Ramanujan was elected Fellow of the Royal Society in 1918, one of the youngest in history, the first Indian mathematician to receive the honour. He was elected Fellow of Trinity College, the first Indian to hold that distinction. These honours came from a society that in almost every other respect treated Indians as colonial subjects.
But Cambridge’s climate destroyed him. The cold, the loneliness, the food he couldn’t eat, the wartime rationing that made even basic provisions scarce, and the racism he endured daily took a devastating toll. He contracted tuberculosis, though recent research by Dr. D.A.B. Young suggests hepatic amoebiasis (a parasitic liver condition common in India) was the more likely diagnosis. He attempted suicide at least once, throwing himself onto the London Underground tracks, and was saved only because a guard saw him and pulled the emergency brake.
He returned to India in March 1919, desperately ill. He spent his final year in Madras, continuing to work, the mock theta functions were produced during this period. His wife Janaki later described him working with his slate and chalk even in the final weeks, stopping only when he was too weak to hold the chalk.
He died on April 26, 1920. He was 32 years old.
In those 32 years, Ramanujan left behind results that mathematicians are still proving and applying a century later. His three notebooks and the “lost notebook” (found in a library trunk at Trinity College in 1976, 56 years after his death) contain an estimated 3,900 results. Many have been verified. Some remain unproven. A few have been shown to be incorrect, remarkably few, given that he worked without formal training or peer review.
The influence of his work extends far beyond pure mathematics:
- String theory and black hole physics, Mock theta functions are used in calculating the entropy of black holes. The mathematical foundations India contributed to the world continue to shape our understanding of the universe.
- Computer science, Partition theory is used in compiler design, data compression, and algorithm optimisation. Every time you stream a video or compress a file, Ramanujan’s mathematics is somewhere in the background.
- Cryptography, Results in number theory that Ramanujan pioneered underpin modern encryption systems.
- Cancer modelling, Researchers at the University of Wisconsin have used Ramanujan’s work on Rogers-Ramanujan identities to model the spread of cancerous cells.
- Artificial intelligence, Pattern recognition algorithms draw on mathematical structures that Ramanujan first described.
What Ramanujan Says About India
India celebrates December 22, Ramanujan’s birthday, as National Mathematics Day. Streets, institutes, and awards bear his name. The Ramanujan Prize, awarded by the International Centre for Theoretical Physics, recognizes young mathematicians from developing countries. Indian universities invoke his name as proof that Indian genius can compete with the world.
But the real lesson of Ramanujan isn’t about celebration. It’s about failure, the failure of a system to recognise its own genius.
Ramanujan was failed by the Indian education system, which couldn’t accommodate a mind that excelled in one area and was indifferent to others. He was failed by the colonial system, which valued credentials over ability. He was failed by the academic establishment, which almost missed him entirely, two out of three professors he wrote to didn’t bother to reply.
The question Ramanujan forces India to answer is this: how many Ramanujans are sitting in Kumbakonams right now, filling notebooks that nobody will ever read? How many are failing exams in subjects that don’t matter while their real abilities go unseen? How many brilliant minds are working as clerks, as drivers, as day labourers, not because they lack talent, but because the system that is supposed to find and nurture talent doesn’t work?
India’s chess revolution shows what happens when access is democratised and talent can emerge regardless of background. Ramanujan’s story shows what happens when it can’t, when the most extraordinary mind of a generation has to write three letters to three strangers in a foreign country, hoping one of them will notice.
Hardy noticed. That was luck. India cannot afford to run on luck. It needs systems that find its Ramanujans before they’re lost.
“An equation for me has no meaning unless it expresses a thought of God.”, Srinivasa Ramanujan
This article is part of unite4india’s “Builders of Modern India” series, cinematic stories of the people who shaped the nation.