In 1913, a letter from a young, unknown shipping clerk in Madras, India, arrived at Cambridge University. Penned by Srinivasa Ramanujan, it contained pages of mathematical formulas so advanced and original that the recipient, the eminent G.H. Hardy initially suspected a fraud. Yet, these formulas were no hoax; they were the first glimpse into one of history’s most brilliant and intuitive mathematical minds. This is the story of a self-taught genius who, in a tragically short life, revolutionized number theory and left behind a legacy that continues to shape modern science.
A Mind Awakens in Kumbakonam
Srinivasa Ramanujan was born in 1887 into a poor but respected Brahmin family in southern India, a world steeped in spiritual devotion and modest living. As a child, he was quiet and introspective, often lost in his own thoughts. His true genius ignited upon his introduction to formal mathematics. By his early teens, he had not only mastered advanced trigonometry but was already deriving his own complex theorems, leaving his classmates and teachers far behind.
The most transformative event of his young life occurred when, at sixteen, he acquired a copy of G.S. Carr’s A Synopsis of Elementary Results in Pure and Applied Mathematics. This was no ordinary textbook. It was a stark, dense compendium of over 5,000 theorems, presented with almost no explanation or proof. For a mind like Ramanujan’s, this was the perfect catalyst. Each formula was a challenge, a divine statement whose hidden truth he had to uncover on his own. This book profoundly shaped his unique mathematical style: an unparalleled intuition for arriving at groundbreaking results, but with little training in the rigorous, step-by-step proofs prized by Western academia.
This singular obsession, however, became his academic downfall. After winning a scholarship to a local college, he found himself incapable of focusing on any subject besides mathematics. While others studied history or literature, Ramanujan filled notebooks with his own discoveries. Inevitably, he failed his exams, lost his scholarship, and was cast out of the formal education system, a genius deemed a failure.
The Letter That Crossed the Ocean
Adrift without prospects, Ramanujan spent years in poverty, his genius known only to a small circle of friends and patrons. His entire universe was contained within a series of frayed notebooks, filled cover-to-cover with thousands of original formulas he believed were revealed to him by his family deity, the goddess Namagiri. He famously said, “An equation for me has no meaning unless it expresses a thought of God.”
After securing a menial clerical job at the Madras Port Trust, he was finally encouraged to contact leading mathematicians in England. In 1913, he sent his work to G.H. Hardy at Cambridge. Hardy, a brilliant mathematician and a staunch believer in logical rigor, was initially baffled by the letter from the unknown Indian clerk. The pages contained bizarre and seemingly impossible claims alongside theorems of breathtaking beauty. Among them was his treatment of the sum of all natural numbers—traditionally undefined, but to which Ramanujan assigned a finite value.
The Path to a Startling Sum
Ramanujan’s work on this problem was part of his broader investigation into divergent series that do not approach a finite limit (that is, they have no defined value). His methods for assigning a finite value to such series, now known as Ramanujan summation, were highly original and not based on the rigorous techniques established in Europe at the time.
His notebooks, which he had been compiling for years in India, contain the explorations and calculations that led to these conclusions. The result can also be derived through a method related to the Riemann zeta function, ζ(s). The sum 1+2+3+… is the value of the zeta function at s=−1, which, through a process called analytic continuation, is assigned the value of −1/12.
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However, Ramanujan did not use the Riemann zeta function itself in his derivations. Instead, he developed his own summation method (often called Ramanujan summation) in his notebooks. He had his own way of assigning finite values to divergent series using transformations, the Euler–Maclaurin formula, and clever rearrangements.
This gave rise to the classic joke that the sum of all positive integers is a negative fraction.
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A Genius Revealed
It was this result, among others (around 120) in his letter, that initially stunned and intrigued G.H. Hardy. After initially suspecting the letter might be a hoax, Hardy realized that the formulas “must be true because, if they were not true, no one would have had the imagination to invent them.” This correspondence was the crucial step that led Hardy to invite Ramanujan to Cambridge, marking the beginning of their legendary collaboration.
While Ramanujan’s most prolific and formally published work was done in Cambridge with Hardy’s guidance, the foundational and highly intuitive discoveries, including the sum of all natural numbers, were a product of his isolated genius in India.
Triumph and Tragedy in a Foreign Land
Hardy knew he had to bring Ramanujan to Cambridge. But there was a formidable obstacle: Ramanujan’s Brahmin faith forbade him from crossing the ocean. Ramanujan respected and followed the rules of his faith devoutly, Moreover, his mother—deeply devoted to their faith—seemed to be his greatest obstacle. Only a divine intervention could change this, and so it did. One night, his mother had a powerful dream in which the goddess Namagiri appeared and commanded her not to stand in the way of her son’s destiny. With this divine sanction, the path was cleared. Ramanujan set sail for a new world.
The collaboration between the intuitive Ramanujan and the rigorous Hardy was a fusion of two vastly different worlds. At Cambridge, Ramanujan was finally in an environment that could cultivate his raw genius. Hardy mentored him tirelessly, teaching him the language of formal proof required to present his work to the West. The result was a period of stunning productivity.
Solving the Partition Problem
One of their most celebrated achievements was tackling the problem of partitions. A partition of an integer is a way of writing it as a sum of positive integers. For example, the number 5 has 7 partitions: 5, 4+1, 3+2, 3+1+1, 2+2+1, 2+1+1+1, and 1+1+1+1+1. While simple for small numbers, finding the number of partitions for a large number like 200 was a computational nightmare. Ramanujan and Hardy developed the “circle method,” a revolutionary analytical tool that produced an incredibly accurate formula for approximating the number of partitions of any integer, solving a problem that had stumped mathematicians for centuries.
Ramanujan gave the pattern for which the number of partitions of any number of the form 5n+4, 7n+5 and 11n+6 would be divisible by or a multiple of 5, 7 and 11 respectively. And for much larger numbers, Ramanujan and Hardy developed the Asymptotic Formula, which approximated the number of partitions with remarkable accuracy.
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Their circle method later became a foundation for attempts to tackle famous unsolved problems like Goldbach’s Conjecture. It was extremely effective on The Weak Goldbach’s Conjecture ( Every odd integer greater than 5 can be expressed as the sum of three prime numbers ). and laid the analytical foundation for The Strong Goldbach’s Conjecture ( Every even integer greater than 2 can be expressed as the sum of two prime numbers ) and posed the idea that it might be true with greater and greater confidence. Thus, pushing forward development on a solution for the conjecture that was posed in and had been unsolved since 1742.
Incredible Approximations of Pi
Ramanujan also produced a series of formulas for calculating the digits of Pi (π) that were astonishingly powerful and efficient. While previous methods required hundreds of terms to get a few decimal places, a single term of Ramanujan’s best formulas could yield many correct digits. These formulas were so advanced that their true power wasn’t fully unleashed until the advent of supercomputers decades later, where they became a cornerstone of modern computational mathematics.
A Monumental Achievement: Fellow of the Royal Society
These intellectual triumphs culminated in an achievement of immense historical and cultural significance. In 1918, Srinivasa Ramanujan was elected a Fellow of the Royal Society. This was not merely a high honor; it was a seismic event. At the zenith of the British Empire, a colonial subject from India, a man with no university degree, was being inducted into one of the most exclusive scientific bodies on Earth, an institution whose past fellows included Isaac Newton and Charles Darwin.
For an Indian to be granted this status, at a time when racial prejudice was systemic and overt, was an almost unimaginable validation of his genius. It was a testament to a mind so brilliant it could not be ignored, even by the highest echelons of a society that considered his people inferior.
Yet, these professional peaks were set against a backdrop of profound personal hardship. The damp English cold, malnutrition from a difficult vegetarian diet during wartime rationing, and intense loneliness plunged him into a deep depression, leading to a breakdown and a suicide attempt.
A Final, Brilliant Flare
By 1919, gravely ill, Ramanujan returned to India. He was a shell of the man who had left, emaciated and in constant, debilitating pain. But within his failing body, his mind burned as brightly as ever. In his final year, bedridden and cared for by his wife Janaki, he was utterly consumed by his one true passion.
Janaki would later recall the heartbreaking intensity of his final days.
“Day and night he worked on sums,” she said.
“He wouldn’t stop working even to eat. We had to make rice balls for him and place them in the palm of his hand.”
Even on the verge of death, he was forging new mathematics. In his last letter to Hardy, he described a new creation: the mysterious “mock theta functions.” It was his final gift, a last transmission from a universe only he could see. On April 26, 1920, at the age of 32, Srinivasa Ramanujan passed away, his notebooks filled with ideas still waiting to be born.
An Echo That Shapes the Future
Ramanujan’s death was not an end but a transfiguration. His true legacy, contained within his notebooks, was only just beginning to be understood. For over a century, these texts have been a source of endless inspiration and discovery for mathematicians.
The Lost Notebook and Black Holes
The “lost notebook,” a sheaf of 137 pages from his final year, was rediscovered in 1976 and set the mathematical world alight. It was filled with his final, deepest insights, including the mock theta functions. For decades, these were a complete enigma. Today, they are understood to be profoundly important, with shocking connections to other fields. In one of the most stunning applications of his work, these functions have been used to help calculate the entropy, or disorder, of black holes, linking the final thoughts of a dying genius in 1920 to one of the deepest mysteries of modern cosmology.
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From Pure Math to Modern Technology
The applications of his work have rippled through science and technology. His number theory has become a vital tool in cryptography, the science of secure communication that underpins the internet and digital security. His work on partitions and related functions is now used in statistical mechanics to model the behavior of materials and in quantum physics. The algorithms derived from his pi formulas are still used to test the processing power of modern computers. The patterns he discovered have been found in everything from the study of polymer chemistry to cancer research.
Ramanujan was a phenomenon, a man who saw the universe in a language of pure numbers. The “thoughts of God” he transcribed in his notebooks have become indispensable tools for humanity’s quest to understand everything from the quantum world to the vastness of space, securing his place as one of the most original and influential minds in history and all of this, just from his goddess Namagiri in his dreams. It makes us realize how much of the universe still lies beyond our understanding.
The Divine Mind and the Karmic Debt
The tragic story of Srinivasa Ramanujan a mind that communed with infinity, yet was trapped in a life of poverty, sickness, and an early death perfectly illustrates a spiritual truth explained by Sant Rampal Ji Maharaj. Many question how a man whose genius was a divine gift to the world could suffer so profoundly. This paradox is resolved by the immutable law of karma.
The true spiritual knowledge (Sat-Gyaan) reveals that our present life is an unfolding of our karmic accounts from innumerable past births. Ramanujan’s unparalleled mathematical insights were his labor in this lifetime, but his constant struggle and premature demise were the heavy price of a pre-existing karmic debt. He gave the world timeless formulas, but in return, he paid a debt he couldn’t see.
This is where the power of Satbhakti becomes clear. As outlined in the holy scriptures, the true worship of the Supreme God Kabir, when received from a Tatvadarshi Guru (True Spiritual Teacher), is the only method to eradicate all past karmic accounts. While God may grant a mind like Ramanujan’s a glimpse of divine patterns, only true worship can clear the soul’s ledger. This path doesn’t require a genius to suffer for their gifts. Instead, it evens the playing field, liberating the soul from the crushing weight of past deeds to achieve both worldly fulfillment and the ultimate goal of liberation (moksha).
Don’t cry because it’s over, smile because it happened
Srinivasa Ramanujan’s life was a paradox: a finite being bound by poverty and illness who left behind an infinite legacy. More than a century after his death, he is not a relic of history but an active collaborator in the science of the future. The divine thoughts he transcribed into his notebooks now probe the secrets of black holes and secure our digital world. While others discovered mathematics, Ramanujan seemed to invent it.
His was not the mathematics of mere calculation, but of pure revelation. His tragically short life stands in stark contrast to his infinite legacy, leaving behind work that remains a timeless echo of a mind that truly knew infinity. He was the humble clerk who conversed with gods, a mortal who gifted humanity a glimpse of eternity.
FAQs
1) What are the inventions of Ramanujan?
Ans:- As a pure mathematician, Ramanujan discovered groundbreaking formulas, not physical inventions. His key contributions include the Hardy-Ramanujan partition formula, his work on mock theta functions (now used in physics), and highly efficient infinite series for calculating pi (π).
2) Why is 1729 called the Ramanujan number?
Ans:- It’s named after a famous story. When mathematician G.H. Hardy visited a sick Ramanujan, he called his taxi number, 1729, “dull.” Ramanujan instantly replied that it was very interesting, as it’s the smallest number that is the sum of two cubes in two different ways: 13 + 123 and 93 + 103.
3) How did Ramanujan solve infinity?
Ans:- He created a method called Ramanujan summation to assign a useful value to infinite series that normally don’t have a sum. His most famous result using this method assigns the value -1/12 to the sum 1+2+3+…, though this is not a sum in the traditional sense.
4) How many theorems did Ramanujan discover?
Ans:- During his short life, Ramanujan compiled an astonishing number of results, mostly without proof, in his personal notebooks. It is estimated he discovered between 3,000 and 4,000 theorems and formulas.
5) When was Ramanujan born?
Ans:- Srinivasa Ramanujan was born on December 22, 1887.
6) When did Ramanujan die?
Ans:- Srinivasa Ramanujan died on April 26, 1920, at the age of 32.
